Guided sparse decomposition with anisotropic fusion for medical image enhancement

Introduction

Background and motivation

Medical imaging has revolutionized the field of healthcare (1). Techniques such as X-rays, magnetic resonance imaging (MRI), and computed tomography (CT) scans are essential tools for visualizing anatomical structures and identifying pathological changes. By analyzing high-quality medical images, emerging deep learning algorithms have demonstrated significant potential in disease diagnosis, and have even been shown to have comparable diagnostic performance to that of human clinicians (2). Nonetheless, variations in light transmission and clinical imaging conditions can lead to uneven illumination or blurry texture details in medical images (3-5). Various studies (6-8) have demonstrated that these issues may significantly hinder disease screening, examination, and diagnosis. Consequently, reliable medical image enhancement techniques are considered essential as a preliminary step in clinical applications. These techniques are vital for producing high-quality images with detailed and clear contrast. Enhancing the clarity of low-quality medical images can significantly improve clinical observation and diagnosis, thereby reducing the need for re-examinations. However, the inherent complexity of these images presents substantial challenges in improving their clarity and detail while preserving critical structural information.

In recent decades, a variety of methods have been proposed for medical image enhancement. These methods can be mainly divided into three categories: histogram- decomposition-, and deep learning-based methods. Histogram-based methods are based on histogram equalization (9-11). Most of these methods are efficient, but they fail to consider spatial information, and thus may be affected by discontinuities between neighboring regions. Conversely, deep learning-based methods (3,12-14) address image enhancement as regression problems and employ neural networks to solve them. These methods work well when there is a large amount of labeled data. However, due to the ill-defined nature of the image enhancement task, there is a lack of widely accepted datasets to train models. Decomposition-based methods rely on edge-preserving filters, such as the bilateral filter (15), weighted symmetric filter (16), and weighted least square filter (17). These methods provide a general framework for both tone and detail manipulation. However, these filters may exhibit various artifacts.

In this study, we aimed to develop a decomposition-based method for medical image enhancement. To this end, the guided image filter (GIF) (18) is a practical and popular choice, as it is free of gradient reversal artifacts and highly efficient. Despite its advantages, the GIF is not without limitations. Specifically, it is known to produce luminance halo and detail halo artifacts. Luminance halo artifacts manifest as unnatural light rings around edges (see Figure 1A,1B), which can mislead clinicians as to the true characteristics of the tissues being imaged. These artifacts arise from the L2 regularization term in the linear ridge regression model. Conversely, detail halo artifacts (see Figure 1C,1D) can obscure important details, reducing the overall interpretability of medical images. These artifacts originate from the large linear coefficients around salient edges. To address these issues, we proposed a novel decomposition method, named guided sparse decomposition with anisotropic fusion (GSDAF). The major technical contributions of this study are as follows:

• It used a weighted sparse regression model to address and reduce the luminance halos observed in the ridge regression model of the guided filter;
• It employed an anisotropic coefficient fusion strategy to reduce the detail halo artifacts associated with the average-fusion method of the guided filter;
• It conducted experiments that showed the superiority of the proposed method in enhancing detail and tone in X-ray and retinal fundus images.

Figure 1 Medical image enhancement based on guided image filtering often results in luminance and detail halos. (A) An input retinal fundus image; (B) the enhanced retinal fundus image displaying luminance halos (see the room-in patches); (C) an input chest X-ray image; (D) the enhanced X-ray image displaying detail halos (see the room-in patches).

The remainder of this article is structured as follows. A brief literature review is conducted in “Literature review” section. An in-depth description of the proposed method is provided in “Methods” section. The experimental results on detail and tone enhancement in medical images are provided in “Results” section. A comprehensive discussion is presented in “Discussion” section. Finally, the article is concluded in “Conclusions” section.

Literature review

Decomposition-based medical image enhancement methods are essentially based on edge-preserving filters. The bilateral filter (19) was one of the earliest edge-preserving filters developed using explicitly defined filter kernels. It computes the weighted average of the pixel intensities in a local neighborhood, where the weights are determined based on the spatial and intensity similarities. The bilateral filter effectively smooths out image details while preserving edges. However, it produces severe luminance halo and gradient reversal artifacts, and has a high computational cost.

In response to some of the limitations of the bilateral filter, the GIF (18) has emerged as an efficient alternative for local image filtering. It operates under the principle that local linear models can effectively capture the desired relationships between pixels in the presence of edges. One significant advantage of the GIF is its ability to avoid gradient reversal artifacts. However, it produces luminance and detail halos. Several studies (20-23) sought to address the luminance halo issue by incorporating edge-aware weights into the model design. These methods aim to enhance the performance of the filter by increasing its sensitivity to edges. However, a significant limitation affects these models—L2 regularization cannot effectively enforce sparsity in the solution space. One study (24) examined the origins of detail halos and proposed strategies to reduce their effect on image quality. However, this approach is not effective for thin structures, which are common in medical images and other high-detail applications. Other popular local image filters, such as the domain transform filter (25) and the side window filter (SWF) (26), generally offer efficient processing capabilities, but their smoothing quality is often inferior to that achieved by state-of-the-art filters.

In terms of optimization-based filters, most consist of a fidelity term and a regularization term. The fidelity terms of these models are almost the same (i.e., the summed square distance between the input and output). The weighted least square filter (27) incorporates a regularization term that considers the weighted least squares of the output gradients. In the ensuing years, research has integrated sparse regularization terms into the filtering process. Notable examples include L0 (28) or L1 (29). These advancements aim to improve the ability of filters to preserve structural features and edges in images.

Extending the concepts of gradient regularization, recent studies (30,31) have focused on gradient reconstruction techniques. By reconstructing gradients rather than merely regularizing them, these studies have shown a marked improvement in smoothing quality. Additionally, cutting-edge research has begun to exploit non-convex penalty functions for regularization purposes. Functions such as the Welsch (32), generalized Charbonnier (33), truncated Huber (34), and bilateral (35) methods are increasingly being used. These non-convex approaches provide greater flexibility and adaptability in handling various types of noise and artifacts. In contrast to conventional global methods that primarily rely on partial differential equations, a novel soft clustering-based optimization model was explored in (36). While global methods are widely appreciated for their exceptional smoothing quality, it is important to note that they often impose significant demands on computational resources.

In recent years, rapid advancements in deep learning techniques have led to the emergence of various learning-based filters. Most of these filters are designed and trained in a supervised manner, using datasets that are generated through traditional filtering methods (37,38), curated through manual labeling efforts (39), or synthesized from a combination of structural and textural images (40). The fundamental goal of these methods is to replicate the behavior of traditional filters or to imitate synthetic smoothing effects. Conversely, methods discussed in (41,42) are based on unsupervised learning, which allows them to operate without the need for ground truth labels. These unsupervised approaches employ gradient descent techniques to solve optimization models informed by predefined network architecture. Due to the highly optimized deep learning frameworks currently available, learning-based filters can achieve notable efficiency. However, despite these advancements, the potential of deep learning in the context of image smoothing has not yet been fully realized. This shortfall is largely due to the scarcity of well-established and comprehensive datasets to train these models. As a result, the smoothing quality achieved by these learning-based filters is often limited, which prevents them from harnessing the full power and capabilities of deep learning methodologies.

Methods

Weighted sparse regression

We followed the original guided filter and assumed linear relations between local patches of the guidance and output images. However, unlike the original guided filter, we regularized the linear coefficients with weighted sparse constraints (43) to ensure sparse solutions, thus alleviating the luminance halos. Specifically, our model expressed as:

minak,bk∑i∈Ωk12(akGi+bk−Ii)2+ϵτk|ak|[1]

where, I and G are the input and guidance images, respectively; (Note that in practice, I and G can refer to the same image); Ω_k is the k-th window; i is the i-th pixel; a_kand b_kare the linear coefficients of the linear regression model; ϵ is the balancing parameter; ϵ|ak|/τk is the term to enforce sparsity; and τ_k is the edge-aware weight, which is defined as:

τk=1n∑j=1nσk2+ισj2+ι[2]

where, σk2 is the variance of the pixels in the k-th 3×3 window of the guidance image; ι=10⁻⁶ is a small constant that avoids division by zero error; and n is the total number of pixels. Note that all τ_k can be evaluated in linear time, as given an image G, ∑j=1n1/(σj2+ι) is a constant that is independent of k. Large values of τ_k indicates salient edges, while small values of τ_k indicate fine details.

The least absolute shrinkage and selection operator (LASSO) regularization and edge-aware weight τ_kimprove the edge-preserving capacities of the model and reduce the luminance halo artifacts. The former enforces the sparsity of the output, thus enabling sharp transitions between neighboring regions. While the latter assigns different weights to salient edges and fine details, enabling different regularization strengths to be imposed on them (i.e., salient edges are assigned smaller values of ϵ/τk, thus milder penalties are imposed in a_k and the edges are protected, while fine details are associated with larger values of ϵ/τk, such that the details are enhanced, while the edges are kept). Figure 2 provides an example of tone mapping on an input image, where Figure 2A is the input image, and Figure 2B is the illumination map. By comparing Figure 2D,2E, we see that the weighted approach produces a better result than the non-weighted approach. Note that for tone mapping, the decomposition is performed on the illumination map T (Eq. [13]); that is, the maximum intensity among the three channels of that pixel plus a small constant (Eq. [12]). Consequently, the weight map τ_kis also calculated from T. As a result, τ_k inherently follows the structures of T rather than the input.

Figure 2 Efficacy of the edge-aware weight τ_k. (A) An input image; (B) illumination map; (C) the edge-aware weights (enhanced for better visualization); (E) the tone-enhanced result derived with the weights is better than (D) that of the one without.

According to (43), the weighted sparse LASSO regression shown in Eq. [1] can be efficiently solved as:

ak={(ρkτk−ϵ)/(ζk2τk+ν),0,(ρkτk+ϵ)/(ζk2τk+ν),if ρk>ϵ/τkif −ϵ/τk≤ρk≤ϵ/τkif ρk<−ϵ/τk[3]

bk=I¯k−akG¯k[4]

where, ρ_k is the covariance calculated from the patches Ω_k in the guidance and input images, while ζk2 is the variance of the patch Ω_k in the guidance image. The parameter ν=10⁻⁶ enables computational stability. Note that ζk2 is different from σk2, even though both are variances. σk2 is used to calculate the edge-aware weight τ_k. To enable it to accurately locate and assign large weights to the thin edges, we use a small 3×3 window. Conversely, ζk2 is the variance in the neighborhood Ω_k, which determines the smoothing extent of the filter. Ω_k can be a window that has a size other than 3×3.

To demonstrate our point, consider a case in which G=I. In this scenario, we have ρk=ζk2. Regions with salient edges exhibit larger variances ζk2, which results in larger values of a_k, thus they would be protected. Conversely, when the variance ζk2 falls below a threshold ϵ/τk (regions with fine details), then a_k is set as 0, thus the details would be smoothed.

Anisotropic fusion strategy

In the previous subsection, we showed how to solve the weighted sparse regression model. However, the linear coefficients a_k and b_k are calculated for each window k rather than each pixel. Note that each pixel is included in multiple overlapping windows. A naive solution to calculate the coefficients for a specific pixel is to average the coefficients over the windows that contain this pixel. This is the strategy employed in the original GIF. However, the isotropic averaging strategy could cause large values of a_k near salient edges (as shown in Figure 1C), thus resulting in detail halos around the edges, as the details in these areas are not adequately smoothed. In this study, following (24), we propose an anisotropic fusion strategy as follows:

ai†=∑k∈Ωiδkak∑k∈Ωiδk[5]

bi†=∑k∈Ωiδkbk∑k∈Ωiδk[6]

where, the anisotropic weight δ_kis defined as:

δk=ω(ζk2β+ω)[7]

where, β is a non-negative parameter that controls the sensitivity in deriving δ_k, and we always have β≥0. Further, throughout this study, we uniformly set ω=1. Finally, the structural image is computed as follows:

Si=ai†Gi+bi†[8]

The detail layer can then be derived as:

D=I−S[9]

The anisotropic weight δ_kis pixelwise (i.e., it does not vary with the central pixel), thus it can be efficiently calculated with elementwise operations. It can be drawn from Eq. [7] that pixels in a high-variance areas would have smaller weights, and would thus make fewer contributions to the averaged linear coefficients of nearby pixels. This ensures that the regions near the edges would not have large values of a_k, thereby reducing the detail halo artifacts. Figure 3 shows the effect of the anisotropic weight, where Figure 3A is the input, and Figure 3B shows the anisotropic weight. By comparing Figure 3C,3D, we see that the anisotropic weight δ_k improves a_k.

Figure 3 Efficacy of the anisotropic weight δ_k. (A) An input image; (B) the anisotropic weight δ_k; (D) the anisotropic fusion shrinks the a_k values better than (C) the average-fusion method.

Decomposition algorithm

Based on the above discussion, we sketch the proposed GSDAF method as Algorithm 1. Note that μG,μI,ϱG,ϱGI are the box-filtered images of G,I,G⊗G,G⊗I, respectively, where ⊗ stands for the elementwise product. The box-filtered images include the mean values in each window, which are then leveraged to calculate the variance ζ and the covariance ρ. Therefore, our algorithm only involves a number of box filtering and elementwise operations. Given that box filtering can be efficiently implemented using the integral image technique in linear time, the time complexity of the proposed algorithm is O(n) (where n is the total number of pixels), which is highly efficient. Figure 4 shows a flow chart of the proposed algorithm. The proposed decomposition method is used to enhance the detail and tone of medical images, obtained are from publicly available datasets, including the coronavirus disease of 2019 (COVID-19) chest X-ray dataset (44), and the Child Heart and Health Study in England—Database 1 (CHASE-DB1) dataset (45). The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments.

Figure 4 Flow chart of the proposed algorithm.

Algorithm 1 Guided sparse decomposition with anisotropic fusion

Results

To evaluate the proposed image decomposition method, we used it to experiment on detail and tone enhancement in medical images. Two image modalities were leveraged (i.e., X-ray and retinal fundus images). For the X-ray images, we used the COVID-19 chest X-ray dataset (44), which includes 317 images. For the retinal fundus images, we used the CHASE-DB1 dataset (45), which comprises 28 images from 14 children. The method was rigorously tested on the respective test sets from these datasets.

We compared the proposed method with a range of state-of-the-art image decomposition techniques (see Table 1). For the traditional filters, we fine-tuned the parameters according to the recommended settings. For the deep learning-based methods, we used the official pre-trained models, which have no tunable parameters.

The proposed method was evaluated using both quantitative and qualitative results. In relation to the quantitative results, we leveraged spatial-spectral entropy-based quality (SSEQ) (48) and the convolutional neural network image quality assessment (CNNIQA) (49) to evaluate image quality. Note that for both the SSEQ and CNNIQA, a smaller value indicates a higher quality. We did not explore the peak-signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM), as the task of medical image enhancement does not involve widely acknowledged ground truth labels, and there was no way to derive the PSNR or SSIM without the ground truth labels. Thus, only blind image quality metrics, such as SSEQ and CNNIQA, were used to evaluate the proposed method. Further, we recorded and compared the running time of the proposed method to the running times of state-of-the-art methods. In relation to the qualitative results, we detailed and described the visual results. All the measures were recorded on a Desktop with an Intel i5-12400F central processing unit (CPU) and an NVIDIA RTX 3070 graphics processing unit (GPU), along with 16 GB main memory.

Detail enhancement

The proposed method can enhance the detail of medical images. Specifically, decomposing the input image I with our method, results in:

[Sd,Dd]=F(I)[10]

where, S_dis the structural image; D_dis the detail layer; and F(⋅) is the proposed image decomposition method. Detail enhancement can then be accomplished by magnifying D_dand composing it back to S_d; that is:

Rd=ηDd+Sd[11]

where, R_dis the detail-enhanced image; and η is the magnification factor.

Table 2 sets out the quantitative results for detail enhancement in the X-ray image dataset (44). Notably, the proposed method largely outperformed the state-of-the-art methods. Indeed, our proposed method consistently ranked 1st and 2nd on all the metrics across multiple subsets. The advantage of the proposed method was also validated by the qualitative results shown in Figure 5. Notably, all the methods improved the input image (Figure 5A). However, as the blue squares show, the SWF (Figure 5B) and GSF (Figure 5C) produced detail halo artifacts (i.e., the details around the edges are not significantly enhanced). While, as the red squares show, the iterative least square (ILS) (Figure 5D) and SDF (Figure 5E) methods produced luminance halos. Conversely, our method enhanced the details without generating halo artifacts.

Figure 5 Qualitative results for detail enhancement on an (A) input X-ray image. As the blue squares show, the details around the edges in the (B) SWF and (C) GSF results were not significantly enhanced (i.e., they exhibit detail halos). As the red squares show, the (D) ILS and (E) SDF results exhibit luminance halos. Conversely, (F) our result provides adequate details and is free of halos. GSDAF, guided sparse decomposition with anisotropic fusion; GSF, generalized smoothing framework; ILS, iterative least square; SDF, static dynamic filter; SWF, side window filter.

Tone enhancement

The proposed method can be also leveraged for tone enhancement to improve the visibility of medical images based on the framework proposed in (50). Given an input image I, we first estimate the coarse illumination map T as:

Ti=maxc∈{r,g,b}Iic+θ[12]

In this formula, the illumination at pixel i is initialized as the maximum intensity among the three channels of that pixel plus a small constant θ=0.2. The initial illumination map T is then decomposed with our method that is expressed as follows:

[St,Dt]=F(T)[13]

where S_tand D_trepresent structure and detail, respectively. The reflectance E can then be calculated as:

E=I⊘(Stγ)[14]

Eventually, the tone-enhanced image can be derived as:

Rt=(1−Stγ)⊗Φ(E)+StγE[15]

where, γ is the parameter for gamma correction; and ⊘ is the elementwise division operation. Note that tone enhancement could introduce severe noise, thus a denoising step Φ(⋅) is needed to improve quality.

Table 3 shows the quantitative results for the task of tone enhancement. Notably, our method ranked 1st and 3rd on the SSEQ and CNNIQA metrics, respectively. The superiority of the proposed method for tone enhancement was also validated by the qualitative results shown in Figure 6. Notably, all the methods improved the input image (Figure 6A). However, by comparing Figure 6B-6F, we found that our method produced a better result.

Figure 6 Qualitative results for detail enhancement in (A) an input retinal fundus image. The (B) SWF and (C) GSF results are short of contrasts. The dark areas are not brightened in the (D) ILS and (E) SDF results. Conversely, (F) our result is of high contrast and visibility did not have the above problems. GSDAF, guided sparse decomposition with anisotropic fusion; GSF, generalized smoothing framework; ILS, iterative least square; SDF, static dynamic filter; SWF, side window filter.

Efficiency

For a thorough evaluation of the proposed method, we compared its running time with those of state-of-the-art methods (see Table 4). Notably, we recorded the CPU (Intel i5-12400F) and GPU (NVIDIA RTX 3070) times for the traditional and deep learning-based methods, respectively. We reported both the CPU and GPU times for our method. Our method outperformed most of the traditional and deep learning-based methods in terms of its efficiency. It was slightly slower than the GIF, but it produced much better results. Thus, our method was highly efficient, and it was able to process 720P color images at more than 30 frames per second.

Discussion

This study proposed a novel image decomposition method GSDAF for medical image enhancement. The goal was to overcome the two principal artifacts (i.e., luminance halos and detail halos), which are commonly associated with the traditional GIF. In line with the study objectives, our method integrates a weighted sparse regression model and an anisotropic coefficient fusion strategy to preserve critical image details and improve tonal clarity in medical images. Experimental evaluations across both retinal fundus and X-ray datasets confirmed the effectiveness of GSDAF in enhancing image details and tones while reducing undesired artifacts. Further, the proposed method had high computational efficiency and enabled the real-time processing of 720P color images on modern GPUs.

Despite these promising outcomes, several limitations of the study warrant careful consideration. First, the evaluation primarily relied on blind image quality metrics, due to the absence of standard ground truth labels for enhanced medical images. Although these metrics provide useful insights, they do not fully capture diagnostic relevance of the enhanced images, and clinical evaluation by radiologists or ophthalmologists remains absent. Second, the experimental datasets only included COVID-19 X-ray images and CHASE-DB1 fundus images, and thus represent a narrow subset of medical imaging modalities. The generalization of GSDAF to other image types such as CT, MRI, or ultrasound remains to be validated. Third, while the method addresses luminance and detail halos effectively, other potential artifacts (e.g., noise amplification during tone enhancement) could occur under different imaging conditions or anatomical contexts. Finally, the choice of hyperparameters may require dataset-specific tuning, which limits out-of-the-box deployment.

Conclusions

To address the limitations of the GIF, we proposed a novel method named GSDAF. Specifically, we proposed a weighted sparse regression model to reduce the luminance halos artifacts produced by the ridge regression model. Further, we proposed an anisotropic coefficient fusion strategy to reduce the detail halo artifacts. We experimented with the proposed method on the tasks of detail and tone enhancement in medical images. Both the quantitative and qualitative results showed the advantages of the proposed method. Further, our method was shown to be highly efficient and capable of processing 720P color images in real time on modern GPUs.

Acknowledgments

None.

Footnote

Funding: This paper was funded by the Medical Research Project of Jiangsu Provincial Health Commission (No. ZQ2024028), National Science Foundation of China (No. 61402205), and Startup Foundation for Advanced Talents of Jiangsu University (No. 13JDG085).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-675/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. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments.

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/.

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