Generalized Fast Iteratively Reweighted Soft-Thresholding Algorithm for Sparse Coding under Tight Frames in the Complex-Domain

Pokala, PK and Chemudupati, S and Seelamantula, CS (2020) Generalized Fast Iteratively Reweighted Soft-Thresholding Algorithm for Sparse Coding under Tight Frames in the Complex-Domain. In: Proceedings - International Conference on Image Processing, ICIP, 25-28 September 2020, Abu Dhabi; United Arab Emirates, pp. 2875-2879.

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Abstract

We present a new method for fast magnetic resonance image (MRI) reconstruction in the complex-domain under tight frames. We propose a generalized problem formulation that allows for different weight-update strategies for iteratively reweighted �1-minimization under tight frames. Further, we impose sufficient conditions on the function of the weights that leads to the reweighting strategy, which follows the interpretation originally given by Candès et al, but is more efficient than theirs. Since the objective function in complex-domain compressive sensing MRI (CS-MRI) reconstruction problem is nonholomorphic, we resort to Wirtinger calculus for deriving the update strategies. We develop an algorithm called generalized iteratively reweighted soft-thresholding algorithm (GIRSTA) and its fast variant, namely, generalized fast iteratively reweighted soft-thresholding algorithm (GFIRSTA). We provide convergence guarantees for GIRSTA and empirical convergence results for GFIRSTA. Our experiments show a remarkable performance of the proposed algorithms for complex-domain CS-MRI reconstruction considering both random sampling and radial sampling strategies. GFIRSTA outperforms state-of-the-art techniques in terms of peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). © 2020 IEEE.

Item Type:	Conference Paper
Publication:	Proceedings - International Conference on Image Processing, ICIP
Publisher:	IEEE Computer Society
Additional Information:	cited By 0; Conference of 2020 IEEE International Conference on Image Processing, ICIP 2020 ; Conference Date: 25 September 2020 Through 28 September 2020; Conference Code:165772
Keywords:	Calculations; Compressed sensing; Magnetic resonance imaging; Signal to noise ratio, Convergence results; Magnetic resonance images (MRI); Objective functions; Peak signal to noise ratio; Reconstruction problems; Soft-thresholding algorithm; State-of-the-art techniques; Structural similarity indices, Iterative methods
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	22 Jan 2021 06:42
Last Modified:	22 Jan 2021 06:42
URI:	http://eprints.iisc.ac.in/id/eprint/67729

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