A novel approach for contrast enhancement in medical images based on quantum-inspired enhancement algorithm

Introduction

Medical imaging plays a crucial role in the diagnosis and treatment planning of various diseases, particularly in oncology. The quality of medical images directly affects diagnostic accuracy and the effectiveness of subsequent treatments. Among various imaging modalities, magnetic resonance imaging (MRI) and computed tomography (CT) are the most widely used in clinical practice due to their high resolution and non-invasive nature (1). However, due to the complex structure of human tissues and limitations of imaging systems, CT and magnetic resonance (MR) images can be prone to poor contrast and blurred anatomical details, which can compromise clinical decision-making (2-4).

To facilitate better visualization and analysis of anatomical structures and pathological lesions, numerous image enhancement preprocessing methods for CT and MR images have been proposed (5). For instance, Zhang et al. developed a local histogram equalization (HE)-based contrast enhancement algorithm for low-dose lung CT images (6). Magudeeswaran et al. introduced a brightness-preserving bi-level fuzzy HE (FHE) method for enhancing brain MRI images (7). Li et al. proposed a fusion algorithm combining wavelet and spatial domains to enhance CT image quality (8). Although traditional enhancement methods, such as HE and filtering techniques, have been extensively applied, some of them fail to fully exploit the underlying complex structures present in medical images, leading to limited enhancement performance.

In recent years, quantum computing and its potential usage in the oncology field have gained increasing attention (9,10). For image enhancement applications, Eldar et al. introduced the quantum signal processing (QSP) framework, which incorporates quantum mechanical principles—such as measurement, coherence, and quantization—into signal processing algorithms for tasks such as detection, estimation, sampling, and multi-user communication (11). Quantum-inspired approaches have demonstrated superior capabilities in handling complex nonlinear information processing tasks (12). Due to its excellent performance, the QSP framework has been applied in various areas of image processing, contributing to noise reduction, contrast enhancement, and overall image quality improvement (13). For example, Zhang et al. proposed an enhanced quantum representation for digital images that encodes grayscale values using the basis states of qubit sequences, enabling high compression ratios and accurate reconstruction of classical images (14). Notably, Rubio et al. (15) employed a QSP framework for microcalcification detection in mammograms, demonstrating its potential in medical imaging. Building upon these advancements, this study aimed to extend the QSP framework specifically for contrast enhancement in CT and MR images, addressing a gap in the current literature.

This study addresses this gap by introducing a novel quantum-inspired enhancement (QIE) algorithm for CT and MR images. The proposed algorithm aims to improve diagnostic accuracy by enhancing image contrast and structural clarity. Its performance is systematically evaluated and compared against the widely used HE method (16,17), offering new insights into the potential of quantum-inspired techniques in medical image processing.

Methods

QIE algorithms

The physical goal of the QIE method is to enhance edge contrast by using a three-pixel quantum system. The core idea of the operator is inspired by the principles of QSP, in which edge information is encoded in the probability amplitudes of quantum states. The key insight is that not all quantum basis states are equally informative—we selectively accumulate the probabilities of edge-sensitive basis states while ignoring the others, thereby reducing noise and redundant computation (15).

Based on the QSP framework, as illustrated in Figure 1, the QIE algorithm for medical image processing consists of three main steps.

Figure 1 QSP framework. QSP, quantum signal processing.

Normalization of pixel grayscale values

To map image data from grayscale space to quantum space, the grayscale values are first normalized using the following transformation:

f(m,n)=g(m,n)−GminGmax−Gmin[1]

where f(m,n)∈[0,1] represents the normalized grayscale value at pixel location (m,n), g(m,n) is the original grayscale value at that location, and Gmin and Gmax denote the minimum and maximum grayscale values in the original grayscale image, respectively.

Mapping a pixel to a quantum state

Each pixel f(m,n) in a grayscale image can be represented by a quantum state |q(m,n)⟩, which is a superposition of the ground states |0⟩ and |1⟩ of a single qubit:

|q(m,n)⟩=c0|0⟩+c1|1⟩[2]

where |0⟩ denotes the non-edge state, |1⟩ presents the edge state, and c0 and c1 are complex probability amplitudes defined as:

c0=1−f(m,n),c1=f(m,n)[3]

The squared magnitudes |c0|2 and |c1|2 represent the probabilities of measuring the quantum state as |0⟩ and |1⟩, respectively. These coefficients must satisfy the normalization condition: |c0|2+|c1|2=1.

Quantum measurement

In a grayscale image, a 3 × 3 sliding window centered at pixel (m, n) is illustrated in Figure 2, where fi(i=1,…,9) represents the grayscale values of the central pixel and its eight neighboring pixels.

Figure 2 Associated location of a 3×3 window.

In a three-qubit correlation system, taking the horizontal direction as an example, the quantum correlation superposition state of the neighboring pixels Pm,n−1,Pm,n,Pm,n+1 can be represented as:

|Pm,n−1, Pm,n, Pm,n+1⟩=|Pm,n−1⟩⊗|Pm,n⟩⊗|Pm,n+1⟩= c0m,n−1c0m,nc0m,n+1|000⟩+c0m,n−1c0m,nc1m,n+1|001⟩+ c0m,n−1c1m,nc0m,n+1|010⟩+c0m,n−1c1m,nc1m,n+1|011⟩+ c1m,n−1c0m,nc0m,n+1|100⟩+c1m,n−1c0m,nc1m,n+1|101⟩+ c1m,n−1c1m,nc0m,n+1|110⟩+c1m,n−1c1m,nc1m,n+1|111⟩=(1−f8)(1−f1)(1−f4)|000⟩+…+f8f1f4|111⟩= ∑i=08wi|i⟩[4]

where wi is the probability amplitude of each ground state in the three qubits correlation system; wi2 is the corresponding probability satisfying the normalization condition ∑i=08|wi|2=1.

To enhance the edges, we retain only those terms that contain the edge state |1⟩ (i.e., |001⟩, |011⟩, |100⟩, |101⟩, |110⟩, |111⟩) and discard the no-edge terms such as |000⟩ and |010⟩. Consequently, the final enhancement operator becomes:

OPERθ(m,n)=sum{|wi|2|i=1,3,4,5,6,7}=(c0m,n−1c0m,nc1m,n+1)2+(c0m,n−1c1m,nc1m,n+1)2+(c1m,n−1c0m,nc0m,n+1)2+(c1m,n−1c0m,nc1m,n+1)2+(c1m,n−1c1m,nc0m,n+1)2+(c1m,n−1c1m,nc1m,n+1)2[5]

where θ∈{0°,45°,90°,135°} represents the four principal directions of pixel correlation.

Still taking the horizontal direction as an example, the enhancement operator reads as:

OPER0°=(1−f8)(1−f1)f4+(1−f8)f1f4+f8(1−f1)(1−f4)+f8(1−f1)f4+f8f1(1−f4)+f8f1f4=f8+f4−f8f4[6]

Similarly, the enhancement operators for the remaining orientations are obtained as:

OPER45°=f9+f5−f9f5[7]

OPER90°=f6+f2−f6f2[8]

OPER135°=f7+f3−f7f3[9]

Thus, the final enhancement value is calculated as the average of the directional enhancement operators over the four directions (0°, 45°, 90°, and 135°). Considering that, in real acquisition, the eight “nearest-neighbor” voxels are not equidistant to the central voxel, a distance weight of d=1/√2 was incorporated for the 45° and 135° directions in the computation. The final enhancement value for a given pixel (m, n) is defined as follows:

E(m,n)=mean{OPER0°,12OPER45°,OPER90°,12OPER135°}[10]

Performance evaluation

The enhanced pixel values are directly obtained through the numerical computation of the corresponding QIE operators. To quantitatively assess the performance of the proposed QIE algorithm, we compared it with four representative classical enhancement methods: HE, contrast-limited adaptive HE (CLAHE), FHE, and wavelet-based enhancement (WBE):

• HE is a global contrast-enhancement technique that redistributes pixel intensities to produce a uniform histogram.
• CLAHE was implemented with a tile grid of 16×16 pixels and a clip-limit of 0.05 to prevent over-amplification of noise (18).
• FHE was realized using a gamma value of 1.0, clip-alpha of 0.01, and full-image tiling to preserve brightness while enhancing local contrast (19).
• WBE was performed via a two-level db-wavelet decomposition; the high-frequency coefficients were amplified by a factor of 2.0, whereas the low-frequency band was attenuated by 0.2 to suppress background drift (20).

The image qualities and performance of the enhancement methods were quantitatively evaluated using the following metrics.

Entropy (21)

Entropy is a widely used metric for evaluating image quality, as it quantifies the richness of information contained within an image. It reflects the amount of uncertainty or randomness in the image data and is measured in bits. The Shannon entropy of an image is defined as:

E=∑k=0L−1P(k)∗logP(k)[11]

where P(k) denotes the probability of a pixel having gray level k, L is the total number of gray levels in the image, and E represents the entropy value of the image. Higher entropy typically indicates richer image detail and more uniform gray-level distribution.

Peak signal-to-noise ratio (PSNR)

PSNR evaluates the quality of the processed image by computing the mean squared error (MSE) between the enhanced result and the original reference image. It is defined as:

PSNR=10∗log10(MAX2MSE)[12]

where MAX represents the maximum possible pixel value. A higher PSNR value corresponds to lower distortion, indicating better preservation of image fidelity and effective noise suppression.

Structural similarity index (SSIM)

SSIM evaluates image quality by measuring similarity in three aspects: luminance, contrast, and structural consistency​. The formula is defined as:

SSIM(x,y)=(2μxμy+C1)(2σxy+C2)(μx2+μy2+C1)(σx2+σy2+C2)[13]

where μx and μy represent the local mean values of image x and y (luminance similarity); σx2 and σy2 are the variances of images (contrast similarity); σxy denotes the covariance between image x and y (structural correlation); C1 and C2 are two constants to stabilize the calculation.

Contrast-to-noise ratio (CNR)

CNR quantifies the discriminability between two tissue classes by scaling their signal difference to the underlying noise level, thereby serving as an objective surrogate for lesion conspicuity. For two tissue classes A and B, CNR is computed as:

CNR=|μA−μB|σnoise[14]

where μA is the mean pixel value in the lesion region; μB is the mean pixel value in the background region; and σnoise presents the standard deviation (SD) of pixel values in the background region. In this study, for thoracic CT, region of interest (ROI)-A was defined as the gross tumor volume (GTV) delineated for radiotherapy and ROI-B as the intraluminal region of the thoracic aorta. For brain MRI, ROI-A comprised the GTV in brain and ROI-B was part of the normal-appearing cerebrospinal fluid (CSF). All structures were manually contoured on axial slices by an experienced radiation oncologist and subsequently reviewed by a senior specialist. To preserve inter-slice continuity, three-dimensional (3D) voxel-wise CNR was computed per patient. A higher CNR indicated superior separability between normal tissue and tumor.

Datasets

A total of 120 T2-weighted brain MR slices and 314 thoracic CT slices were retrospectively and randomly selected from 10 patients previously scanned at Peking Union Medical College Hospital. CT data were acquired on a Philips Brilliance Big Bore scanner (Philips Healthcare, Amsterdam, Netherlands) for three patients and on a GE Revolution CT scanner (GE Healthcare, Chicago, IL, USA) for the remaining two. All MR images were obtained with a GE Discovery MR750 system. Detailed acquisition parameters are summarized in Table 1. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the institutional ethics board of the Peking Union Medical College Hospital. Informed consent was provided by all the patients.

Statistical analysis

The evaluation metrics for images processed using the QIE and the algorithms used for comparison were expressed as mean ± SD. To assess the statistical significance of performance differences between the two methods, paired-samples t-tests were conducted for all comparisons. A P value less than 0.05 was considered statistically significant. All analyses, including metric extraction, computation of means, SDs, and P values, were performed using Python version 3.10.9 (Python Software Foundation, Wilmington, DE, USA).

Results

Measurement of performance

To assess the effectiveness and robustness of the QIE algorithm, a set of T2-weighted MR brain images and CT lung images from 10 patients were analyzed. The evaluation metrics, including entropy, PSNR, SSIM, and CNR, were calculated at the patient-level.

Table 2 presents the quantitative results of images processed with HE, CLAHE, FHE, WBE, and the QIE algorithm, along with their corresponding P values compared to the proposed QIE method. The proposed QIE algorithm consistently attained the highest mean entropy on both MR and CT datasets, indicating superior information content. Compared with HE, FHE, and WBE, QIE also yielded significantly higher PSNR and SSIM values (paired t-test, P<0.01 for all comparisons), reflecting better signal fidelity and structural preservation. Although CLAHE achieved the largest PSNR and an SSIM marginally above that of QIE, its Entropy remained lower. With respect to CNR, QIE had greater value than CLAHE and WBE, but lower than the HE and FHE methods; however, the difference did not reach statistical significance (P>0.05), most likely because marked inter-patient variability in tumor density and morphology introduced substantial variance into CNR estimates. Overall, these results demonstrate that QIE outperforms three widely used conventional enhancement techniques (HE, FHE, and WBE) in terms of both contrast gain and structural integrity.

Visual quality of the images

Figure 3 exemplifies, for each patient, one representative slice containing the lesion: the original CT/MR image, the HE-enhanced and the QIE-enhanced counterpart, together with the corresponding horizontal intensity profiles. To assess tumor-to-background differentiation, a 200-pixel line segment centered on the lesion was extracted; all profiles were min–max normalized to [0, 1] to permit shape comparison. Although HE elevates global brightness, it simultaneously amplifies noise, manifesting as high-frequency serrations in the profile and in patient 3, an apparent underestimation of tumor extent. In contrast, QIE yields an intermediate brightness while smoothing homogeneous regions (e.g., heart), thereby suppressing profile irregularities and providing a noise-reduced representation without sacrificing contrast.

Figure 3 Representative patient slice containing the lesion acquired as shown before and after image enhancement, and the corresponding horizontal intensity profiles. The inset is a 200×200-pixel magnified crop of the original 512×512 image. CT, computed tomography; HE, histogram equalization; MRI, magnetic resonance imaging; QIE, quantum-inspired enhancement.

Discussion

This study presents a novel QIE algorithm for improving the contrast of medical images, grounded in principles of QSP. To our knowledge, there is currently no existing literature applying the QIE algorithm to CT or MR images. The proposed approach demonstrates superior performance compared to four classical enhancement methods across multiple quantitative evaluation metrics. Due to the simplicity and clarity of its mathematical formulation, the QIE algorithm ensures computational efficiency and is highly reproducible.

Experimental results indicate that the QIE algorithm surpasses all other algorithms in improving entropy. Entropy, a key indicator of information richness, has been used to evaluate the quality of CT or MR images in many studies (22-24). In this study, the results of entropy from the QIE algorithm reached values of 4.37 for CT image sets and 6.45 for MR image sets, which is better than the results obtained by classical enhancement methods for the same set of images. The increase in entropy across both imaging modalities suggests improved detail preservation and enhanced visual differentiation of anatomical structures.

PSNR and SSIM are important evaluation metrics in the fields of image compression, denoising, and enhancement. Many studies use these two indicators to assess the overall image quality and structural fidelity (25,26). Higher PSNR values indicate reduced noise and distortion, whereas the near-unity SSIM scores reflect outstanding preservation of structural similarity to the original images (27,28). In this study, the QIE algorithm demonstrated improvements in both PSNR and SSIM compared to the HE, FHE, and WBE methods; however, these values were lower than those achieved by CLAHE, likely because CLAHE’s tile-wise intensity redistribution suppresses local noise more aggressively. This result suggests that further refinement of the QIE operator—such as incorporating adaptive, region-aware quantum-state weights—could reconcile contrast amplification with noise control and represents a promising direction for future work. Overall, the present results indicate that QIE does not introduce artifacts commonly associated with aggressive contrast enhancement techniques, such as over-smoothing or edge degradation.

In terms of CNR, the QIE algorithm achieved moderate performance, ranking higher than CLAHE and WBE but lower than HE and FHE in both imaging cohorts. However, the difference failed to reach statistical significance. This absence of significance is attributable to pronounced inter-patient heterogeneity in tumor density and morphology, which inflated the between-subject variance of the CNR numerator and reduced the power to detect a true effect. Although QIE did not outperform all conventional methods in CNR, it consistently demonstrated the highest entropy values and competitive PSNR and SSIM scores, indicating superior information content and structural preservation. These findings suggest that QIE enhances image quality in a way that may still improve visual lesion discernibility, even if not fully captured by CNR alone. Future work will explore adaptive ROI selection strategies and larger, multi-center datasets to better evaluate whether the observed CNR differences achieve statistical significance and clinical relevance.

Moreover, the across-the-board gains in entropy, PSNR, and SSIM achieved by QIE carry readily foreseeable clinical translational potential. The entropy increment widens the gray-level gap between lesions and normal parenchyma, affording higher visual conspicuity that could reduce miss rates in early-stage lung cancer or diminutive brain metastasis screening. The PSNR improvement corresponds to less noise power, promising shorter reading times and less visual fatigue—benefits that are particularly welcome in high-throughput emergency workflows. Enhanced SSIM preserves anatomical edge sharpness without overshoot, and is expected to diminish inter-observer variability when radiation oncologists delineate the GTV, thereby allowing tighter planning target volume margins and lower dose to adjacent organs-at-risk. Although the present study did not include a reader panel, these quantitative advances show a clear hypothesis for multi-reader receiver operating characteristic (ROC) trials in the next step that will further verify QIE’s real-world value in improving diagnostic confidence.

The advantages of QIE are attributed to its quantum-inspired design, which leverages probabilistic amplitude encoding and multi-pixel correlate via simulated quantum states (29). Unlike traditional methods that primarily rely on global or local histogram statistics (5), QIE simulates the nonlinear and context-aware enhancement behaviors inspired by quantum mechanics, thereby enabling more adaptive and perceptually meaningful improvements in image quality. From a clinical perspective, the enhanced visualization of anatomical details has the potential to assist radiologists in more accurate identification, thereby improving diagnostic accuracy and facilitating more informed treatment planning. The robustness and generalizability of the QIE algorithm, as demonstrated across two image modalities and anatomical regions, underscore its potential applicability in various medical imaging contexts.

Nonetheless, this study has several limitations. The principal limitation of the present work is the small number of patients, resulting in only 10 independent imaging sessions despite the large slice count. This limited anatomical and pathological breadth cannot capture inter-site variations in scanner models, reconstruction kernels, or disease subtypes, and thus constrains the external validity of our findings. Consequently, the reported performance metrics may not generalize to other field strengths of MRI or pathologies. Future studies will aim to expand the evaluation to data from a broader spectrum of anatomical variants, multiple imaging platforms, and image modalities. In addition, beyond standalone enhancement, QIE can be readily integrated into existing artificial intelligence (AI) pipelines: its closed-form, derivative-friendly operator enables feature preprocessing for end-to-end convolutional neural network (CNN) or Transformer training, whereas the negligible parameter count introduces no additional memory bottlenecks. For quantum-hardware execution, QIE requires only single-qubit rotations and two-qubit controlled gates—both native to present IBM-Q and IonQ Noisy Intermediate-Scale Quantum (NISQ) processors—and fits within ≤12 qubits per 3×3 neighborhood, making a Digital Imaging and Communications in Medicine (DICOM)-compatible proof-of-concept feasible once quantum RAM interfaces mature. Future work will therefore pursue (I) large-scale validation of QIE as an AI preprocessing module and (II) experimental porting to available quantum processors to benchmark runtime vs. classical simulation.

Conclusions

This study presents a QIE algorithm that integrates quantum-inspired mechanisms into classical image processing frameworks. The proposed method effectively enhances image contrast while preserving structural details in both CT and MR images. Quantitative evaluations using Entropy, PSNR, and SSIM confirm the algorithm’s superior performance compared to traditional approaches such as HE. These results highlight the potential of QIE as a robust and generalizable tool for medical image enhancement. Future work will extend the application of this algorithm to other imaging modalities, assess its utility as a preprocessing step for commercial AI models, and explore its deployment on actual quantum computing platforms as the technology matures.

Acknowledgments

None.

Footnote

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1474/dss

Funding: This work was supported by National Key R&D Program of China, Ministry of Science and Technology of the People’s Republic of China (No. 2022YFC2404606).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1474/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. The study was approved by the institutional ethics board of the Peking Union Medical College Hospital. Informed consent was obtained from all the patients.

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. Frangioni JV. New technologies for human cancer imaging. J Clin Oncol 2008;26:4012-21. [Crossref] [PubMed]
2. Salmon E, Bernard Ir C, Hustinx R. Pitfalls and Limitations of PET/CT in Brain Imaging. Semin Nucl Med 2015;45:541-51. [Crossref] [PubMed]
3. Mileto A, Guimaraes LS, McCollough CH, Fletcher JG, Yu L. State of the Art in Abdominal CT: The Limits of Iterative Reconstruction Algorithms. Radiology 2019;293:491-503. [Crossref] [PubMed]
4. Despotović I, Goossens B, Philips W. MRI segmentation of the human brain: challenges, methods, and applications. Comput Math Methods Med 2015;2015:450341. [Crossref] [PubMed]
5. Radhika R, Mahajan R. Medical image enhancement: a review. In: Proceedings of International Conference on Data Science and Applications: ICDSA 2021, Volume 1. Singapore: Springer Singapore; 2021:105-18.
6. Zhang G, Yan P, Zhao H, Zhang X. A contrast enhancement algorithm for low-dose CT images based on local histogram equalization. In: 2008 2nd International Conference on Bioinformatics and Biomedical Engineering. IEEE; 2008:2462-5.
7. Magudeeswaran V, Ravichandran CG, Thirumurugan P. Brightness preserving bi-level fuzzy histogram equalization for MRI brain image contrast enhancement. Int J Imaging Syst Technol 2017;27:153-61.
8. Li Z, Jia Z, Yang J, Kasabov N. An efficient and high quality medical CT image enhancement algorithm. Int J Imaging Syst Technol 2020;30:939-949.
9. Ramesh S, Tomesh T, Riesenfeld SJ, Chong FT, Pearson AT. Quantum computing for oncology. Nat Cancer 2024;5:811-6. [Crossref] [PubMed]
10. Pakela JM, Tseng HH, Matuszak MM, Ten Haken RK, McShan DL, El Naqa I. Quantum-inspired algorithm for radiotherapy planning optimization. Med Phys 2020;47:5-18. [Crossref] [PubMed]
11. Eldar YC, Oppenheim AV. Quantum signal processing. IEEE Signal Process Mag 2002;19:12-32.
12. Manju A, Nigam MJ. Applications of quantum inspired computational intelligence: a survey. Artificial Intelligence Review 2014;42:79-156.
13. Wang Z, Xu M, Zhang Y. Review of quantum image processing. Arch Comput Methods Eng 2022;29:737-61.
14. Zhang Y, Lu K, Gao Y, Wang M. NEQR: a novel enhanced quantum representation of digital images. Quantum Inf Process 2013;12:2833-60.
15. Rubio Y, Montiel O, Sepulveda R. Quantum inspired algorithm for microcalcification detection in mammograms. Information Sciences 2019;480:305-23.
16. Lehr JL, Capek P. Histogram equalization of CT images. Radiology 1985;154:163-9. [Crossref] [PubMed]
17. Senthilkumaran N, Thimmiaraja J. Histogram equalization for image enhancement using MRI brain images. In: 2014 World Congress on Computing and Communication Technologies. IEEE; 2014:80-3.
18. Reza AM. Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement. J VLSI Signal Process Syst Signal Image Video Technol 2004;38:35-44.
19. Sheet D, Garud H, Suveer A, Mahadevappa M, Chatterjee J. Brightness preserving dynamic fuzzy histogram equalization. IEEE Transactions on Consumer Electronics 2010;56:2475-80.
20. Matsuda Y, Ogawa M, Yano M. Shape retrieval with geometrically characterized contour partitions. IEEE Access 2015;3:1161-78.
21. Gull SF, Skilling J. Maximum entropy method in image processing. IEE Proceedings F (Communications, Radar and Signal Processing) 1984;131:646-59.
22. Petrongolo M, Zhu L. Noise Suppression for Dual-Energy CT Through Entropy Minimization. IEEE Trans Med Imaging 2015;34:2286-97. [Crossref] [PubMed]
23. Yadav PS, Gupta B, Lamba SS. A new approach of contrast enhancement for Medical Images based on entropy curve. Biomed Signal Process Control 2024;88:105625.
24. Kumar R, Bhandari AK. Spatial mutual information based detail preserving magnetic resonance image enhancement. Comput Biol Med 2022;146:105644. [Crossref] [PubMed]
25. Hore A, Ziou D. Image quality metrics: PSNR vs. SSIM. In: 2010 20th International Conference on Pattern Recognition. IEEE; 2010:2366-9.
26. Al Najjar Y. Comparative analysis of image quality assessment metrics: MSE, PSNR, SSIM and FSIM. International Journal of Science and Research 2024;13:110-4. (IJSR).
27. Sara U, Akter M, Uddin MS. Image quality assessment through FSIM, SSIM, MSE and PSNR—a comparative study. Journal of Computer and Communications 2019;7:8-18.
28. Setiadi DRIM. PSNR vs SSIM: imperceptibility quality assessment for image steganography. Multimed Tools Appl 2021;80:8423-44.
29. Dunjko V, Taylor JM, Briegel HJ. Quantum-Enhanced Machine Learning. Phys Rev Lett 2016;117:130501. [Crossref] [PubMed]