Accelerated Weighted ℓ1-Minimization for MRI Reconstruction Under Tight Frames in Complex Domain

Pokala, PK and Seelamantula, CS (2020) Accelerated Weighted ℓ1-Minimization for MRI Reconstruction Under Tight Frames in Complex Domain. In: SPCOM 2020 - International Conference on Signal Processing and Communications, 19 - 24 July 2020, Bangalore.

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Abstract

We propose an improvement of the projected fast iterative soft-thresholding algorithm (pFISTA) and smoothing FISTA (SFISTA) to achieve faster convergence and improved reconstruction accuracy. The pFISTA addresses the problem of compressed sensing magnetic resonance imaging (CS-MRI) reconstruction under tight frames and considers standard ℓ1 norm minimization. The ℓ1}-norm weighs each component in a sparse vector equally. However, this is restrictive. We employ the weighted ℓ1}-regularizer, defined over a complex-domain as the sparsity-promoting function in CS-MRI reconstruction. The weighted ℓ1-regularizer assigns different weights to the components in a sparse vector to improve upon reconstruction accuracy. The optimization objective in CS-MRI is a real-valued function defined over a complex-domain and is therefore not holomorphic. We derive an algorithm, namely, projected weighted iterative soft-thresholding algorithm (pWISTA) based on Wirtinger calculus to solve the weighted ℓ1-regularized CS-MRI reconstruction under tight frames. We show that the proximal operator for the weighted ℓ1 regularizer over a complex-domain is the soft-thresholding operator, but with a different threshold for each component. We also incorporate Nesterov's momentum into the pWISTA update to obtain the projected weighted fast iterative soft-thresholding algorithm (pWFISTA), which result in accelerated optimization as shown by the experimental results.

Item Type:	Conference Paper
Publication:	SPCOM 2020 - International Conference on Signal Processing and Communications
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	06 Feb 2023 06:28
Last Modified:	06 Feb 2023 06:28
URI:	https://eprints.iisc.ac.in/id/eprint/79850

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