Computed tomography ring artifact correction method with super-pixel segmentation and adaptive relative total variation

Introduction

Computed tomography (CT), a revolutionary technology in medical diagnostics, has profoundly transformed the landscape of medical imaging since its inception. Offering an unparalleled view of the human body’s internal architecture, CT plays a pivotal role in both diagnostic and therapeutic strategies, contributing significantly to areas ranging from oncology to neurology (1). The evolution of CT technologies, marked by enhanced imaging capabilities and improved patient safety, underscores its indispensable value in modern medicine. However, the advent of photon counting CT (PCCT) has introduced a new dimension of challenges, most notably the emergence of ring artifacts. These artifacts, appearing as concentric rings on CT images, are a result of various factors including detector malfunctions and calibration errors. They can substantially degrade image quality, potentially leading to misinterpretations in clinical diagnoses. This degradation affects the reliability of CT scans in critical medical decision-making, thus jeopardizing patient diagnosis and treatment efficacy (2-10). The ongoing research in addressing these artifacts, such as the development of advanced calibration algorithms and deep learning techniques, highlights the complexity and significance of this issue in the field of medical imaging.

Recent advancements in PCCT have significantly enhanced imaging resolution while concurrently reducing radiation exposure, marking substantial progress in medical imaging. Despite these strides, an unintended consequence has been the increased occurrence of ring artifacts, a challenge highlighted in studies by Li et al. (11). This issue has attracted considerable attention in the medical community due to its impact on imaging quality. Hein et al. detailed the detrimental effects of ring artifacts in PCCT, particularly their potential to obscure vital anatomical details, a concern of paramount importance in precision-critical fields like tumor identification and neuroimaging (3). Patil et al. pinpointed detector non-uniformity as a key contributor to these artifacts, affecting both the visual quality and interpretative accuracy of CT images (12). In a comparative study, Lee et al. highlighted the negative implications of both metal and ring artifacts on essential procedures, such as tumor detection and treatment planning (13). Furthermore, Konishi et al. emphasized the importance of artifact reduction strategies, noting that minimizing ring artifacts can significantly improve the quantitative accuracy of single photon emission computed tomography (SPECT)/CT imaging, thereby influencing patient management approaches (14). These findings collectively underscore the necessity of effectively reducing ring artifacts in PCCT to enhance image quality and ensure diagnostic precision. This improvement is not only vital for accurate physician diagnosis but also carries significant implications for patient treatment and overall management strategies.

PCCT, as a next-generation CT technology, offers significant advantages, including high spatial resolution (0.25 mm), multi-energy imaging capabilities, and low-dose imaging. However, due to the non-uniformity of detector elements and the discrete nature of photon counting, PCCT is more sensitive to detector gain variations and calibration errors, resulting in more severe ring artifacts than conventional CT. These artifacts not only exhibit higher intensity but also demonstrate more complex patterns, especially under high flux conditions. This unique characteristic makes ring artifacts a critical issue in PCCT, directly impacting image quality and the accuracy of clinical diagnoses.

Various approaches have been developed to address ring artifacts. Pre-processing methods in projection or sinogram domain, such as detector calibration and filtering techniques, have shown effectiveness but require access to raw data (9,15,16). Post-processing methods operating in image domain provide more flexibility but face challenges in preserving image details while removing artifacts (6,17). Recent deep learning approaches demonstrate promise but often require extensive training data (7). Despite these advances, the correction of severe ring artifacts remains challenging, particularly in PCCT imaging.

Our research proposes a novel, integrative methodology that combines Super-pixel segmentation with relative total variance (RTV) techniques. This approach is specifically designed to address the persistent issue of severe ring artifact correction, a notable challenge inadequately met by previous methods. Super-pixel segmentation is recognized for its precise capability in clustering pixels with analogous characteristics, making it exceptionally suited for identifying and isolating ring artifacts. Coupled with RTV, which is esteemed for its role in preserving image smoothness, our proposed method promises a more robust and comprehensive solution for artifact correction in CT imaging. Furthermore, we acknowledge the imperative necessity for adaptability and flexibility in medical imaging solutions. Addressing this, our study introduces a pioneering technique employing mesh adaptive direct search (MADS) for the automatic optimization of hyperparameters, as detailed in Audet and Mohamed’s work (18-21). This approach not only simplifies the artifact correction process but also significantly enhances the adaptability and applicability of our methodology across diverse imaging settings and CT systems. This innovation marks a substantial stride in overcoming the prevalent limitations of existing ring artifact reduction methods, offering a more versatile and effective solution in clinical imaging scenarios.

The contributions of this study are as follows:

• We introduce a novel approach that combines super-pixel segmentation with RTV techniques for the effective correction of severe ring artifacts in CT images. This hybrid methodology addresses a core issue in previous methods and promises a more robust and general solution to ring artifact correction.
• Unlike pre-processing techniques that rely on raw projection data, the proposed method operates in the image domain, making it independent of the availability of raw data. This feature enhances the applicability of the method in clinical settings where access to raw projection data may be limited.
• We introduce an innovative approach that employs MADS for the automatic learning of hyper-parameters. This not only streamlines the artifact correction process but also enhances the adaptability of the method across different imaging settings and CT systems. The automatic learning of hyper-parameters ensures the method’s robustness and transferability in diverse imaging conditions. The code is publicly available for reproducibility. Github: https://github.com/XiaoNa-gdmu/Ring

Methods

Super-pixel segmentation for high-intensity ring artifact correction

This study employs the Simple Linear Iterative Clustering (SLIC) algorithm for super-pixel segmentation (22). By initializing cluster centers uniformly and performing clustering within local neighborhoods, SLIC enhances segmentation speed, making it well-suited for high-resolution CT images and meeting the demands of clinical real-time processing. The algorithm effectively preserves edge information, ensuring accurate detection and correction of ring artifacts while maintaining structural details. SLIC consistently generates uniform super-pixels across various CT images, enhancing robustness, and allows parameter tuning to optimize both segmentation accuracy and efficiency.

Figure 1 illustrates the super-pixel segmentation workflow, a technique developed to correct high-intensity ring artifacts in CT images. Our approach begins by processing the raw, uncorrected CT images, referred to as Iu. These images are divided into n super-pixels, each encompassing a cluster of pixels that are similar in grayscale values and closely situated in space. For each super-pixel, we determine an initial center, designated as gi, xi, yi. Here, gi signifies the average grayscale value of the pixels within the super-pixel, while xi and yi indicate the spatial coordinates of this central point.

Figure 1 Workflow of the super-pixel segmentation for high-intensity ring artifact correction. Iu: uncorrected CT; Is: super-pixel segmentation; It: texture image; Pt1: polar image of texture; Pr1: polar image of ring; Ir1: ring image in the first stage; Ic1: corrected image in the first stage. CT, computed tomography.

The key to our segmentation process is the minimization of a specifically defined energy function:

E=∑i=1n∑(x,y)∈Si{[g(x,y)−gi]2+(x−xi)2+(y−yi)2}[1]

In this formula, E denotes the total energy of the segmentation, with n representing the total number of super-pixels. Si defines the area of the th super-pixel. The term g(x,y) corresponds to the grayscale value at a specific point (x,y) within the image. The centroid values of super pixel Si are calculated using the following formula: gi=1|Si|∑(x,y)∈SiI(x,y), xi=1|Si|∑(x,y)∈Six, yi=1|Si|∑(x,y)∈Siy. Where |Si| is the number of pixels in the super pixel. This energy function’s objective is to reduce the variance in grayscale values and the spatial distances between each individual pixel in a super-pixel and its central values of gi, xi, yi. Minimizing this function ensures that the pixels within each super-pixel align more uniformly in terms of both grayscale value and spatial positioning, thereby enhancing the effectiveness of our image segmentation approach. The first term of the energy equation [g(x,y)−gi]2, measures the variance of grayscale values within a super-pixel. The subsequent terms, (x−xi)2 and (y−yi)2, account for the differences in spatial coordinates, serving as an indicator of how closely the points within the image align to their respective super-pixel centers.

We calculate the average grayscale value of each super-pixel region, denoted as Gi, using the formula:

Gi=1|Si|∑(x,y)∈SiIu(x,y)[2]

Here, Si signifies the pixel count in the ith super pixel region, and Iu(x,y) represents the grayscale value at coordinates (x,y) in Iu. Following this, each pixel in Iu is reassigned to the average grayscale value of its respective super-pixel region:

Is(x,y)=GSi,forall(x,y)∈Si[3]

In this equation, Is(x,y) indicates the grayscale value at coordinates (x,y) in the processed image Is, and GSi is the average grayscale value of the super-pixel region Si containing the pixel at (x,y). This technique effectively simplifies the image structure while retaining essential features of pixel groups, proving particularly beneficial in segregating ring artifacts and distinct structures in severe cases.

By subtracting the super-pixel segmented image Is from the original Iu, we obtain the texture image It. We then convert It, in Cartesian coordinates, to a polar coordinate representation Pt1. Consider a two-dimension grayscale image It with dimensions 512×512 pixels, centered at (cx,cy)=(256,256). Our goal is to transform each pixel in the Cartesian coordinate image It into a polar coordinate image Pt1. This process involves a series of steps. First, we shift the center of the image to the origin of the coordinate system. This translation adjusts each pixel’s coordinates from (x,y) to (x′,y′) where x′=x−cx and y′=y−cy. Next, we convert these translated coordinates into polar coordinates. The radial distance r is calculated as r=x′2+y′2, and the angle θ is determined using the arctan2 function, θ=arctan2(y′,x′). This function is essential for accurately determining the angle, taking into account the signs of x′ and y′. Finally, using these polar coordinates (r,θ), we construct the polar coordinate image Pt1.

To enhance the extraction of bar artifacts, present in Pt1, we refine our approach by computing the average pixel intensity for each row within the image matrix. This process is mathematically delineated as the calculation of mean pixel intensities across the horizontal axis for each individual row. Following this, we construct a one-dimensional average vector that mirrors these averages. This vector is then replicated and expanded to align with the column count of the original image, culminating in the formation of a bar artifact image Pr1. In this image, each row is characterized by an average intensity value that corresponds to its counterpart in Pt1.

The subsequent phase involves converting these values into Cartesian coordinates, thereby generating a ring artifact image, denoted as Ir1. The final step in our process is the derivation of the corrected image Ic1, which notably possesses enhanced ring artifacts. This is achieved by subtracting the ring artifact image Ir1 from the original image Iu, effectively isolating and emphasizing the desired features.

Adaptive edge-preserving filtering for low-intensity ring artifact correction

Figure 2 illustrates the application of an adaptive edge-preserving filtering technique for rectifying low-intensity ring artifacts. This method begins by processing the initial image, denoted as Ic1, using adaptive RTV, resulting in the Irtv image. Both Ic1 and Irtv are then converted into polar coordinates, forming Pc1 and Prtv respectively. The disparity between these two images is used to generate the texture image Pt2. By applying a one-dimensional Gaussian low-pass filter (with a window size of 15 pixels) to each row of Pt2, the stripe artifacts are extracted, resulting in Pr2. Pr2 is then transformed back to Cartesian coordinates to produce the ring artifact image Ir2. Subtracting Ir2 yields the corrected image Ic2. This process effectively separates the artifacts while preserving image details. Subsequently, Pr2 is transformed back into Cartesian coordinates, yielding the ring artifact image Ir2. The final corrected image, Ic2, is achieved by subtracting Ir2 from Ic1.

Figure 2 Workflow of the adaptive edge-preserving filtering for low-intensity ring artifact correction. Ic1: corrected image in the first stage; Irtv: adaptive RTV; Pc2: polar image of texture in the second stage; Prtv: polar image of adaptive RTV; Pr2: polar image of ring in the second stage; Ir2: ring image in the second stage; Ic2: final corrected image. RTV, relative total variation.

RTV

The RTV technique is a notable advancement in image processing, especially in distinguishing structures within images with mixed or textured elements. One of the main challenges in this field is the varied nature of textures, ranging from regular to irregular patterns, which complicates the distinction between textural elements and main image structures. RTV addresses this by integrating advanced local variation metrics within a robust optimization framework, aiming to effectively differentiate between content and textural edges, enhancing the clarity and separation of primary structures.

RTV uses two key metrics to quantify variation within a local neighborhood of a pixel, for both the horizontal x and vertical y directions. These metrics are given by:

Dx(p)=∑q∈R(p)wp,q⋅|(∂xIrtv)q|Dy(p)=∑q∈R(p)wp,q⋅|(∂yIrtv)q|[4]

Where Dx(p) and Dy(p) denote the local variation measures in the x and y directions at pixel p, R(p) respectively; represents the local neighborhood centered at pixel p; wp,q is the Gaussian spatial weighting function; (∂xIrtv)q and (∂yIrtv)q represent the partial derivatives of the Irtv image at point q in the x and y directions, respectively.

The RTV technique’s core concept is the ratio of windowed TV to windowed inherent variation, crucial in differentiating between texture and structure in an image. The primary RTV formula is:

Irtv=∑p(Irtv,p−Ic1,p)2+λ[Dx(p)Lx(p)+ϵ+Dy(p)Ly(p)+ϵ][5]

In this equation, Irtv refers to the image processed by the RTV method; Ic1,p represents the pixel value of the original image at point p; λ is a balancing factor used to adjust the trade-off between structure preservation and texture removal; ϵ is a small constant to prevent division by zero; Dx(p) and Dy(p) denote the local variation measures in the x and y directions, respectively; Lx(p) and Ly(p) represent the local gradient measures in the x and y directions, respectively.

The application of RTV involves starting with the original image Is as the initial approximation for the structural image Irtv, followed by an iterative optimization process. This includes calculating gradient-based weights and solving a linear system iteratively through weighted least squares, usually over 3-5 iterations until convergence. The final output, Ir, emerges with minimized textures, emphasizing the primary structures.

MADS for Auto RTV

In Eq. [5], the parameter λ plays a pivotal role in the effectiveness of ring artifact correction. A disproportionately large value of λ can induce excessive smoothing, leading to a significant loss of structural detail. In contrast, a value for λ that is set too low may prove insufficient for the effective removal of ring artifacts. Thus, determining an optimal value for λ is of critical importance. The super-pixel-segmented image Is effectively preserves structural information while remaining devoid of ring artifacts, qualifying it as an exemplary template image. In light of this, our study introduces an adaptive approach to selecting the value of λ:

λ*→=argmin‖Irtv(λ)−Is‖0 s.t. 0.004<λ<0.01[6]

The primary aim of our approach is to refine the objective function so it effectively minimizes the discrepancy between the modified image Irtv(λ) and the super-pixel-segmented counterpart Is. A crucial aspect of this process is the precise selection of the λ value, which is key in reducing this difference to the minimum. To achieve this, we utilize the MADS algorithm, an optimization tool notably adept at handling non-linear, discontinuous, and potentially non-smooth objective functions, such as the one we are dealing with.

In our application of the MADS algorithm, we commence by assigning a λ value, ensuring it falls within the prescribed range of 0.004<λ<0.01. Following this, we establish an initial ‘mesh size’, a parameter that sets the starting search interval for λ. The MADS algorithm then embarks on a search around the chosen λ value, pinpointing points that lead to a reduction in the objective function’s value. Should the algorithm identify a more optimal λ value within the current mesh size, it persists in its search around this new point, simultaneously reducing the mesh size for a more detailed and precise search. Conversely, if no superior points are discovered, the algorithm expands the mesh size to encompass a wider array of potential values. This iterative process continues until a specific stopping criterion is satisfied, such as reaching a pre-set number of iterations or the observed improvements dipping below a certain predefined threshold.

An important aspect of this procedure is maintaining a balance between exploration, which involves searching for λ values across a broad spectrum, and exploitation, which focuses on refining the search within regions known to yield good results. The MADS algorithm adeptly maintains this equilibrium by dynamically adjusting the mesh size. This strategic approach ultimately leads to the identification of an optimal λ value. The result is the effective removal of ring artifacts in the image, while simultaneously preserving its structural integrity and fine details.

Super-pixel segmentation effectively reduces the impact of photon noise by dividing the image into pixel groups with similar grayscale values and spatial locations. The RTV technique, through adaptive edge-preserving filtering, addresses variations between detection elements, ensuring structural details are preserved while smoothing the image.

Implementation detail

The proposed ring artifact correction algorithm was implemented using MATLAB R2023b, chosen for its robust numerical computing and advanced image processing capabilities. The MATLAB environment offers a comprehensive library and intuitive interface, enhancing the efficiency of our method. Our experiments utilized a high-performance computing setup designed for intensive image processing. The system comprises an Intel Core i5 13600KF processor, known for its high-speed and efficient data processing, complemented by 64GB RAM to manage large datasets and complex computations effectively. We opted for Windows 11 due to its stability, broad software compatibility, and efficient resource management.

The CT images analyzed were uniformly 512×512 pixels per slice, ensuring consistent dataset processing. The filtered back projection (FBP) method we employed uses the Ram-Lak filter, which provides good response at high frequencies and is suitable for enhancing edge details in images. The initial stage of our method involved super-pixel segmentation, with the segment count n set at 250. This number balances computational load and the granularity needed for effective artifact correction. The segmentation partitions the image into clusters of pixels based on similar characteristics, facilitating precise identification and isolation of high-intensity ring artifacts.

In the second stage, we employed adaptive edge-preserving filtering, initializing the λ parameter in the MADS optimization at 0.006. This value was determined through preliminary tests to optimally balance artifact removal and detail preservation in the images.

Results

Case study on digital simulation patient

In this digital simulation case study, our goal was to replicate the formation of ring artifacts in CT imaging. We started by acquiring CT images and converting them into projection domain images. The focus was on addressing ring artifacts, commonly arising from pixel gain variations in flat panel detectors. To mimic these artifacts, we intentionally altered random detector elements, creating parallel, noise-free stripes in the sinogram domain. Using this altered sinogram, we were able to reconstruct CT images showcasing the ring artifacts. For comparison purposes, we also produced artifact-free authentic images using the Filtered Back Projection algorithm.

Our visual analysis is systematically presented in Figure 3. The first column, marked with red lines in Sample 1, pinpoints the locations of the artifacts. The second column reveals the ring artifacts isolated with our proposed method, illustrating patterns that do not correspond to the original image data. Upon artifact generation, we applied our correction method to the CT images, as evident in the third column. This section clearly demonstrates our technique’s effectiveness, with the corrected images being noticeably sharper and clearer than the uncorrected versions. The fourth column acts as a benchmark, displaying genuine images reconstructed without these simulated artifacts for reference. Furthermore, to further assess the structural fidelity of the corrected images, we calculated the peak signal-to-noise ratio (PSNR) of the corrected images relative to the original artifact-free images. The results show that the PSNR values of the corrected images obtained using our method were significantly higher than those of the comparison methods (increased from approximately 30.5 to 34.5 dB), indicating that our approach effectively eliminates ring artifacts while preserving structural information in the images.

Figure 3 Comparison of CT image artifacts correction using the proposed method across three different samples. Row-wise from top to bottom, each row presents a distinct sample case. Column 1: original CT images with ring artifacts indicated by the red line in Sample 1. Column 2: super-pixel segmentation image. Column 3: extracted ring artifacts using the proposed method. Column 4: corrected CT images after applying the proposed artifact correction technique. Column 5: ground truth images for reference. Column 6: one-dimensional profile analysis of the CT values along the red line in the first column, depicting the intensity values with and without correction in comparison to the ground truth. The effectiveness of the artifact correction can be observed by the improved alignment of the ‘with correction’ profile to the ‘ground truth’ profile, particularly evident in the diminished fluctuations characteristic of ring artifacts. 1D, one-dimensional; CT, computed tomography; HU, Hounsfield unit.

The fifth column introduces a one-dimensional profile analysis, offering a quantifiable measure of our method’s success. This analysis compares CT values along a specified line in the original image, both before and after correction, against true values. The profiles post-correction shows a significant reduction in fluctuation, aligning closely with the profiles of the true values, confirming our artifact correction technique’s efficacy. A notable finding is the reduction in average CT value discrepancy in the corrected images, from a range of 60 Hounsfield units (HU) down to within 5 HU, marking a substantial enhancement in image fidelity. This comparative analysis conclusively demonstrates that our method effectively minimizes ring artifacts, resulting in a more accurate representation of the scanned tissue. The minor shift phenomenon primarily stems from regions with stronger ring artifacts. This shift can be verified through the one-dimensional profile analysis, where the discrepancies between the corrected image and the gold standard are mainly concentrated in areas with stronger ring artifacts. To further evaluate the performance of our method, we analyzed other three image quality metrics. First, we calculated the energy-weighted CT numbers (EWCN). The EWCN of corrected image (6.201×10⁵) is closer to the ground truth (6.268×10⁵) compared to the image with artifacts (6.306×10⁵), indicating improved accuracy after correction. Second, as shown in Figure 4A, the noise power spectrum (NPS) analysis reveals that our method effectively reduces noise in both high and low frequency regions. The corrected image (blue line) shows lower NPS compared to the image with artifacts (red line). Third, we assessed CT number consistency across energy bins. As demonstrated in Figure 4B, the standard deviation of CT numbers in the corrected image (blue line) is significantly lower than that in the uncorrected image (red line) across all energy bins, confirming improved consistency after correction.

Figure 4 Image quality assessment of the proposed ring artifact correction method. (A) Noise power spectrum analysis comparing corrected artifact (blue line) and original image with artifact (red line). (B) CT number standard deviation across energy bins for corrected artifact (blue line with circles) and original image with artifact (orange line with squares). CT, computed tomography.

Analysis of low-intensity rings in phantom and patient study

In this study, we assessed the effectiveness of our algorithm using genuine Catphan©504 phantoms and patient cone-beam CT (CBCT) images. The scanner setting and reconstruction parameters are shown in Table 1. We detail the CBCT acquisition parameters in the accompanying table, highlighting the differences between phantom and patient studies. These differences are particularly notable in aspects such as X-ray energy, pulse width, and the use of a bowtie filter in patient studies.

We’ve included showcase results from the Catphan©504 phantom and axial patient head images (Figure 5). The first row of images depicts the original, uncorrected versions. In contrast, the second-row features images after applying our proposed correction method. The third row is dedicated to showing the impact of our correction technique on ring artifacts, displaying them more clearly. We set the imaging parameters to a range of [−700, 300] HU to effectively compare the corrected and uncorrected image states. The third row, however, is adjusted to a range of [−1,200, −700] HU, specifically to accentuate the visibility of the ring artifacts. Observing the images in columns (A-C), which represent the phantom, and columns (D-F), which depict patient heads, it’s clear that our method markedly reduces the presence of low-intensity ring artifacts. This result not only proves our algorithm’s capability in artifact reduction but also implies an improvement in the diagnostic quality of CBCT imaging.

Figure 5 Results of the Catphan©504 and axial images of a patient’s head are presented. Row 1 displays images in their original state, without any correction processing. In contrast, the images in row 2 have undergone correction processing as proposed in this study. Additionally, row 3 specifically showcases the ring artifact effects extracted using this correction method. Regarding the image display parameter settings, rows 1 and 2 have their display windows set at [−700, 300] HU, while row 3 is set at [−1,200, -700] HU, to more clearly exhibit the distinct image characteristics. Columns (A-C) represent the axial images of different layers of the phantom, while columns (D-F) depict axial images of different layers of the patient’s head. HU, Hounsfield unit.

Analysis of high-intensity rings in PCCT

In this study, ring artifacts with a CT value error greater than 60 HU are defined as high-intensity artifacts, while those with a CT value error below 60 HU are classified as low-intensity artifacts. We utilized PCCT to evaluate the effectiveness of our proposed algorithm in eliminating high-intensity ring artifacts. These artifacts are a significant challenge in PCCT, arising from the discrete nature of photon counting and inconsistencies in detector elements. Such non-uniformities can be amplified by factors like variable photon flux, calibration errors in detectors, and electronic noise. These artifacts typically appear as concentric rings, obscuring structural details and potentially hindering accurate diagnosis.

In this experiment, three baseline methods were selected to compare with the proposed algorithm: Method 1 (6) represents image-domain-based approaches, Method 2 (7) represents deep learning-based approaches, and Method 3 (16) represents projection-domain-based deep learning-based approaches.

Figure 6 provides a comparative analysis of various circular artifact correction methods. The initial uncorrected image, showing pronounced circular artifacts, serves as a baseline for evaluating the correction techniques. Following this, four images demonstrate the results of artifact reduction using Method 1, Method 2, and Method 3, and our proposed method. Below each corrected image, ‘difference’ images illustrate the removed artifacts, with the intensity of any remaining rings indicating the persistence of artifacts.

Figure 6 Comparison of different ring artifact correction methods. The uncorrected image displays the initial circular artifacts visible in the CT scan. The four corrected images respectively show the results of artifact removal using Method 1 (6), Method 2 (7), Method 3 (16), and the proposed method. The ‘difference’ images below each corrected image reveal the artifacts that were removed, with the intensity of the rings correlating to the extent of the artifact presence. CT, computed tomography.

Our analysis reveals that Method 1 significantly reduces ring artifacts but fails to eliminate them entirely, leaving residual effects. Method 2, while removing some artifacts, adversely affects the structural integrity and grayscale balance of the image, leading to potential loss of crucial details for interpretation. Method 3 is more effective in artifact removal, but the ‘difference’ image shows that it also removes important structural details, compromising spatial resolution and introducing significant errors in CT number values.

In contrast, our proposed method shows superior performance. The minimal structural details in its ‘difference’ image indicate that spatial resolution is largely maintained. Additionally, errors in CT values are noticeably lower compared to the other methods. This indicates that our method achieves a better balance between artifact removal and image quality preservation, which could lead to more accurate diagnoses without sacrificing the critical details essential for clinical assessment. To quantitatively evaluate the performance of our proposed method, we compared its results with those of the baseline methods in terms of Structural Similarity Index (SSIM) and CT value error. Our method achieved an SSIM of 0.95, outperforming Method 1 (0.89), Method 2 (0.87), and Method 3 (0.90). Regarding CT value accuracy, our method kept the error within 5 HU, whereas the errors of the other methods ranged from 15 to 30 HU. These quantitative results indicate that our method achieves a better balance between artifact removal and preservation of image details.

Figure 7 illustrates the image correction effects from various CT devices. As seen in the correction results from the second and fourth rows, our proposed method is applicable and effective across diverse samples.

Figure 7 Ring artifact correction results for image samples from different CT devices. The first and third rows display uncorrected images with ring artifacts, while the second and fourth rows show the results after applying our proposed correction method (23,24). CT, computed tomography.

Discussion

Our proposed method not only delivers visually superior results but also exhibits significant advantages in quantitative metrics. Compared to existing methods, our approach achieved the best performance in two key metrics: SSIM and CT value accuracy. Additionally, our method’s computational efficiency (2.5 seconds per image) is comparable to the fastest baseline method (Method 1, 2.3 seconds per image) and outperforms the others. The ring artifact correction method presented in this article focuses specifically on effectively correcting ring artifacts of both high and low intensities. This approach significantly preserves image quality and detail through a meticulously designed two-stage processing procedure. The first stage involves applying super-pixel segmentation techniques to correct high-intensity ring artifacts. This is followed by using adaptive RTV techniques for low-intensity ring artifacts. Our findings, based on both digital simulations and real-world case studies, show that this method effectively reduces ring artifacts while preserving the structural details and grayscale balance of the images. Compared to traditional ring artifact correction techniques, our method stands out for its efficient handling of both high and low-intensity ring artifacts, as well as its adaptability in maintaining high image quality. However, further research is required to enhance the generalizability of this method, particularly in its application across various imaging equipment and in diverse clinical scenarios. We chose the super-pixel segmentation parameter n=250 and the RTV parameter λ based on the analysis of different parameters’ impact on image quality (SSIM and CT value error) shown in Figure 8. The experiments demonstrated that n=250 achieves an optimal balance between segmentation detail and computational efficiency, while λ=0.006, optimized through the MADS algorithm, ensures the best result in terms of artifact removal and detail preservation. Therefore, these parameters effectively enhance the correction performance and ensure the reliability of the results.

Figure 8 Visual depiction of the correlation between super-pixel parameter n and image quality metrics in a digital simulation patient case study. The horizontal axis displays the super-pixel parameter, while the vertical axes represent two key metrics: the SSIM shown by the green line, and the CT value error indicated by the red line. This graph illustrates the inverse relationship between SSIM and CT value error as the super-pixel parameter escalates, pinpointing an optimal image quality at a super-pixel parameter setting of 250. CT, computed tomography; SSIM, Structural Similarity Index Measure.

In our study, we aim to enhance the correction of ring artifacts in CT images by conducting a detailed analysis of super-pixel segmentation, a crucial pre-processing step in artifact correction. Central to this process is the super-pixel parameter, denoted as n, which greatly influences the segmentation’s granularity and, consequently, the effectiveness of artifact correction. Choosing the optimal n value requires a fine balance. If n is too high, the resulting overly fine segmentation can ironically impair the correction process by producing numerous small segments, each ineffective for meaningful artifact reduction. On the other hand, a low n value results in excessively large super pixels, masking critical structural details and contours of the image. Our research highlights the limitations of a universal approach to selecting n. Given the variability in CT images, influenced by patient-specific factors and diverse imaging equipment, an adaptive strategy for super-pixel segmentation is essential. We propose developing an automated system or algorithm that intelligently determines the ideal n for each CT image. This system would assess various image characteristics, such as intensity, artifact type and distribution, and the necessity to maintain image integrity. This relationship is illustrated in Figure 8, which clearly shows the correlation between the super-pixel parameter n and two key image quality metrics: the SSIM and the CT Value Error. As n changes, these metrics exhibit a striking inverse relationship. Our analysis identifies a critical point at n=250, where SSIM peaks and CT value error is minimized, indicating an optimal balance for artifact correction. This balance represents a sweet spot in our adaptive method for selecting super-pixel segmentation, enhancing the correction of ring artifacts in CT imaging by preserving structural integrity.

Our proposed ring artifact correction method for CT imaging has proven effective, but it faces practical limitations that need addressing. One major challenge is its performance with CT images displaying highly irregular or complex artifact patterns. This difficulty stems from the method’s reliance on accurately identifying and isolating artifacts, a task that becomes more complex in these scenarios. Moreover, our method’s computational efficiency is a concern, particularly with large datasets or high-resolution images. The process, which involves super-pixel segmentation followed by adaptive RTV, is computationally demanding. This can lead to extended processing times, potentially unsuitable for time-sensitive clinical settings. To improve this method, several enhancements are worth considering. First, integrating deep learning techniques for segmentation could refine the selection of the super-pixel hyperparameter n. Deep learning models, especially those trained on diverse CT images with various artifact patterns, could offer a more nuanced and context-aware approach to super-pixel segmentation. This adaptation could result in more accurate artifact isolation, especially in complex cases, and adjust the number of superpixels based on each image’s specific features. Another improvement avenue is boosting the algorithm’s computational efficiency. Optimizing the code for parallel processing would allow for more effective handling of large datasets or high-resolution images. Furthermore, using advanced hardware like Graphics Processing Units could significantly decrease processing times (25). Combining hardware acceleration with algorithmic enhancements would make the method more suitable for real-time or near-real-time clinical applications, enhancing its practicality and appeal.

Given the potential of PCCT to significantly enhance image resolution, the method proposed in this paper is particularly valuable for future clinical use (26-30). PCCT, as a sophisticated imaging technology, improves the detail in images but also tends to introduce additional ring artifacts. The ring artifact correction technique we present can be effectively applied to PCCT to not only optimize image quality but also to increase the utility of PCCT in precision medicine. This is especially relevant in fields like tumor diagnosis and interventional radiology, where our method could enhance the accuracy of image-guided diagnostics and treatments. Such advancements promise to deliver more precise and personalized medical services to patients.

Since our algorithm operates in the image domain, it is highly adaptable and can be applied to multi-energy PCCT data. Super-pixel segmentation and RTV techniques can effectively identify and correct ring artifacts without the need for specialized adjustments for different energy spectra.

Despite challenges in handling intricate artifact patterns and a need for enhanced computational efficiency, these issues do not preclude its use in clinical settings. The algorithm could, for instance, be employed as a preprocessing tool to improve image quality in non-critical scenarios or to boost diagnostic precision in specific research settings. Besides, our method has certain limitations when handling ring artifacts, particularly when the center of the artifact is displaced from the image center or when the artifact shape is irregular. The current approach assumes that the ring artifact’s center is located at the center of the image and that it exhibits a relatively standard circular shape, which is common in high-resolution charge coupled device (CCD) devices. However, in practical applications, factors such as uneven electric field distribution can cause the center of the ring artifact to shift or the shape to deform, leading to suboptimal segmentation and correction results. To address this issue, future research will focus on developing more flexible artifact detection and correction algorithms that can accommodate different types and shapes of ring artifacts, thereby improving the generalization ability of the method. Looking ahead, as hardware and algorithms evolve, this technique has the potential to integrate into real-time or near real-time clinical applications. This advancement would significantly increase the accuracy of lesion detection and the effectiveness of treatment planning.

Conclusions

This study introduces an innovative approach to correct ring artifacts in CT images, with particular relevance to the emerging field of PCCT. Our method uniquely combines super-pixel segmentation with adaptive RTV. This addresses the challenge of both high and low-intensity ring artifacts while preserving essential image details. Enhanced by the MADS algorithm for optimal parameter tuning, our approach represents a significant advancement in artifact correction technology. It not only improves image quality but also has substantial clinical implications, especially in precision medicine. It enhances the accuracy of diagnostic imaging and the effectiveness of image-guided treatments. The successful application of our method in various case studies, including digital simulations, phantom, and patient studies, highlights its potential as a versatile and robust solution for artifact correction in contemporary medical imaging. By overcoming the limitations of current CT imaging and improving diagnostic clarity, our approach fosters more accurate, reliable, and patient-centered medical imaging solutions. This significantly contributes to the progress of medical diagnostics and patient care.

Acknowledgments

None.

Footnote

Funding: This work was partly supported by grants from the Funds for PHD researchers of Guangdong Medical University in 2023 (GDMUB2023009).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-24-1102/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

References

1. Kalender WA. X-ray computed tomography. Phys Med Biol 2006;51:R29-43. [Crossref] [PubMed]
2. Liu X, Xie Y, Diao S, Tan S, Liang X, Unsupervised CT. Metal Artifact Reduction by Plugging Diffusion Priors in Dual Domains. IEEE Trans Med Imaging 2024;43:3533-45. [Crossref] [PubMed]
3. Hein D, Liappis K, Eguizabal A, Persson M, editors. Deep learning ring artifact correction in photon-counting spectral CT with perceptual loss. 7th International Conference on Image Formation in X-Ray Computed Tomography; 2022: SPIE.
4. Lv X, Ren X, He P, Zhou M, Long Z, Guo X, Fan C, Wei B, Feng P. Image denoising and ring artifacts removal for spectral CT via deep neural network. IEEE Access 2020;8:225594-601.
5. Murata K, Ogawa K. Ring-artifact correction with total-variation regularization for material images in photon-counting CT. IEEE Transactions on Radiation and Plasma Medical Sciences 2020;5:568-77.
6. Liang X, Zhang Z, Niu T, Yu S, Wu S, Li Z, Zhang H, Xie Y. Iterative image-domain ring artifact removal in cone-beam CT. Phys Med Biol 2017;62:5276-92. [Crossref] [PubMed]
7. Wang T, Liu X, Zhang C, He Y, Chan Y, Xie Y, Liang X. Ring artifacts correction for computed tomography image using unsupervised contrastive learning. Phys Med Biol 2023;
8. Guo X, Wu W, Duan X, Yu H, Chang D, He P, Wang J, Zhou R, Du Y, An K. Nonlinear deviation correction for ring-artifact removal with cone-beam computed tomography. IEEE Transactions on Instrumentation and Measurement 2022;71:1-10.
9. Kowalski G. Suppression of ring artefacts in CT fan-beam scanners. IEEE Transactions on Nuclear science 1978;25:1111-6.
10. Liang X, Jiang Y, Zhao W, Zhang Z, Luo C, Xiong J, Yu S, Yang X, Sun J, Zhou Q, Niu T, Xie Y. Scatter correction for a clinical cone-beam CT system using an optimized stationary beam blocker in a single scan. Med Phys 2019;46:3165-79. [Crossref] [PubMed]
11. Li Y, Zhao Y, Ji D, Han S, Zheng M, Lv W, Xin X, Li F, Zhao X, Liu D, Hu C. 3D ring artifacts removal algorithm combined low-rank tensor decomposition with spatial-sequential total variation regularization and its application in phase-contrast microtomography. Med Phys 2022;49:393-410. [Crossref] [PubMed]
12. Patil BD, Singhal V, Agrawal U, Langoju R, Hsieh J, Lakshminarasimhan S, Das B. Deep learning based correction of low performing pixel in computed tomography. Biomed Phys Eng Express 2022;
13. Lee CL, Park J, Nam S, Choi J, Choi Y, Lee S, Lee KY, Cho M. Metal artifact reduction and tumor detection using photon-counting multi-energy computed tomography. PLoS One 2021;16:e0247355. [Crossref] [PubMed]
14. Konishi T, Shibutani T, Okuda K, Yoneyama H, Moribe R, Onoguchi M, Nakajima K, Kinuya S. Metal artifact reduction for improving quantitative SPECT/CT imaging. Ann Nucl Med 2021;35:291-8. [Crossref] [PubMed]
15. Rashid S, Lee SY, Hasan MK. An improved method for the removal of ring artifacts in high resolution CT imaging. EURASIP Journal on Advances in Signal Processing 2012;2012:93.
16. Eldib ME, Hegazy M, Mun YJ, Cho MH, Cho MH, Lee SY. A Ring Artifact Correction Method: Validation by Micro-CT Imaging with Flat-Panel Detectors and a 2D Photon-Counting Detector. Sensors (Basel) 2017.
17. Ji D, Qu G, Hu C, Zhao Y, Chen X. Combine TV-L1 model with guided image filtering for wide and faint ring artifacts correction of in-line x-ray phase contrast computed tomography. J Xray Sci Technol 2018;26:51-70. [Crossref] [PubMed]
18. Audet C, Dennis JE Jr. Mesh adaptive direct search algorithms for constrained optimization. SIAM Journal on Optimization 2006;17:188-217.
19. Audet C, Dennis JE Jr, Le Digabel S. Globalization strategies for mesh adaptive direct search. Computational Optimization and Applications 2010;46:193-215.
20. Mohamed FA, Koivo HN. System modelling and online optimal management of microgrid using mesh adaptive direct search. International Journal of Electrical Power & Energy Systems 2010;32:398-407.
21. Audet C, Dennis JE Jr. Pattern search algorithms for mixed variable programming. SIAM Journal on Optimization 2001;11:573-94.
22. Achanta R, Shaji A, Smith K, Lucchi A, Fua P, Süsstrunk S. SLIC superpixels compared to state-of-the-art superpixel methods. IEEE Trans Pattern Anal Mach Intell 2012;34:2274-82. [Crossref] [PubMed]
23. Chao Z, Kim HJ. Removal of computed tomography ring artifacts via radial basis function artificial neural networks. Phys Med Biol 2019;64:235015. [Crossref] [PubMed]
24. Yan L, Wu T, Zhong S, Zhang Q. A variation-based ring artifact correction method with sparse constraint for flat-detector CT. Phys Med Biol 2016;61:1278-92. [Crossref] [PubMed]
25. Shi L, Chen H, Sun J, Li K. vCUDA: GPU-accelerated high-performance computing in virtual machines. IEEE Transactions on Computers 2011;61:804-16.
26. Willemink MJ, Persson M, Pourmorteza A, Pelc NJ, Fleischmann D. Photon-counting CT: Technical Principles and Clinical Prospects. Radiology 2018;289:293-312. [Crossref] [PubMed]
27. Hsieh SS, Leng S, Rajendran K, Tao S, McCollough CH. Photon Counting CT: Clinical Applications and Future Developments. IEEE Trans Radiat Plasma Med Sci 2021;5:441-52. [Crossref] [PubMed]
28. Si-Mohamed SA, Boccalini S, Lacombe H, Diaw A, Varasteh M, Rodesch PA, et al. Coronary CT Angiography with Photon-counting CT: First-In-Human Results. Radiology 2022;303:303-13. [Crossref] [PubMed]
29. Wang AS, Pelc NJ. Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment. IEEE Trans Radiat Plasma Med Sci 2021;5:453-64. [Crossref] [PubMed]
30. Ballabriga R, Alozy J, Bandi F, Campbell M, Egidos N, Fernandez-Tenllado J, Heijne E, Kremastiotis I, Llopart X, Madsen B. Photon counting detectors for X-ray imaging with emphasis on CT. IEEE Transactions on Radiation and Plasma Medical Sciences 2020;5:422-40.