Comparative Analysis of Greedy Iterative Algorithms for Compressed Sensing MRI Reconstruction

Abstract

Thisstudypresentsacomparativeanalysisoffivesparserecoveryalgorithms—Orthogonal Matching Pursuit(OMP), Basis Pursuit (BP), IterativeHardThresholding(IHT),CompressiveSamplingMatchingPursuit(CoSaMP),andSubspacePursuit(SP)—toaccelerate Mag- neticResonanceImaging(MRI)viaCompressedSensing(CS).Employingapatch-basedframework withaDiscrete Cosine Transform(DCT) dictionaryandaGaussiansensingmatrix, performance was evaluatedusing PSNR,SSIM, MSE, and executiontime.ResultsdemonstratethatCoSaMPachievesthehighestreconstructionquality(27.25dBPSNR),followedcloselybySPandOMP,whileBPoffersthefastestexecution atthecostofaccuracy.Thisresearchhighlightsthecriticaltrade-offsbetweenre construction qualityand computationalefficiency,providinga guide for algorithm selection in real-time and hardware-oriented MRI systems.

Introduction

This paper presents a comparative study of compressed sensing (CS)-based MRI reconstruction algorithms aimed at reducing MRI scan time while maintaining high image quality. Since conventional MRI requires complete sampling of k-space, scans are time-consuming and susceptible to patient motion artifacts. Compressed sensing addresses this challenge by reconstructing images from significantly fewer measurements by exploiting the sparsity of medical images in an appropriate transform domain.

The study compares five widely used sparse recovery algorithms:

• Orthogonal Matching Pursuit (OMP)
• Basis Pursuit (BP/ISTA)
• Iterative Hard Thresholding (IHT)
• Compressive Sampling Matching Pursuit (CoSaMP)
• Subspace Pursuit (SP)

The proposed framework preprocesses DICOM MRI images by normalizing and resizing them to 128 × 128 pixels, then divides them into 8 × 8 non-overlapping patches. Each patch is transformed into a sparse representation using a Discrete Cosine Transform (DCT) dictionary, while compressed measurements are obtained through a normalized Gaussian sensing matrix. Sparse coefficients are reconstructed using the five algorithms, and the recovered patches are combined to produce the final MRI image.

Performance is evaluated using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Mean Squared Error (MSE), reconstruction error, and execution time. The study also investigates reconstruction quality, convergence behavior, computational complexity, and suitability for hardware implementation, particularly fixed-point implementations for real-time systems.

Experimental results show that CoSaMP achieves the best reconstruction quality with the highest PSNR (27.25 dB), followed by OMP and SP, which effectively preserve structural details and image edges. BP (ISTA) provides the fastest execution time but produces smoother images with lower reconstruction accuracy, while IHT offers a balance between computational efficiency and image quality.

Conclusion

This study presented a comprehensive comparative analysis of five sparse recovery algorithms—Orthogonal Matching Pursuit (OMP),BasisPursuit(BP)usingISTA,IterativeHardThresholding(IHT),CompressiveSamplingMatchingPursuit(CoSaMP), and Subspace Pursuit (SP)—within a unified compressed sensing framework for MRI reconstruction. TheexperimentalevaluationdemonstratesthatCoSaMPachievesthehighestreconstructionaccuracy,consistentlyoutperform- ing other methods in terms of PSNR (27.25 dB) and SSIM (0.775).Subspace Pursuit (SP) provides a robust balance between accuracy and computational efficiency, making it a highly practical choice for real-time applications.While OMP produces competitivereconstructionquality,itsiterativenatureincurssignificantlyhigherexecutiontime,suggestinganeedfordedicated hardware acceleration.Furthermore, optimization-based methods like BP offer high speed but fail to match the reconstruction fidelity of greedy algorithms in patch-based configurations. These results highlight that the selection of a reconstruction algorithm must be guided by application-specific requirements, particularly thecritical trade-off betweenimage fidelity andcomputational latency.For clinicalscenarios requiring high-quality reconstruction, CoSaMP is preferred, whereas SP is more suitable when computational throughput is equally prioritized. Futureworkcanextendthisframeworkinseveralpromisingdirections: • Hardware Acceleration:Implementing these algorithms on GPU or FPGA platforms (using HLS or Verilog) to achieve nanosecond-level execution speeds for real-time clinical deployment. • AdvancedSparsity: Incorporatingadaptiveorlearneddictionaries,suchasK-SVD,tofurtherenhancetherepresentation of complex anatomical structures. • DeepLearningIntegration: Combiningthephysics-basedCSframeworkwithDeepLearning(e.g., ResidualU-Nets)to improve performance in highly undersampled and noisy scenarios. • Real-worldValidation: Evaluatingthesystemonactualk-spaceundersampledMRIdatafromclinicalscannerstovalidate its practical applicability under varied noise conditions.

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Copyright

Copyright © 2026 SVR Manimala, Venkatapuram Pragnan Reddy, Thatipamula Mishal, Adavi Venkata Sai Manoj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.