Analysis of general weights in weighted ℓ1−2 minimization through applications

Sastry, Challa Subrahmanya (2023) Analysis of general weights in weighted ℓ1−2 minimization through applications. Digital Signal Processing, 133. p. 103833. ISSN 1051-2004

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Abstract

The weighted ℓ1−2 minimization has recently attracted some attention due to its capability to deal with highly coherent matrices. Notwithstanding the availability of its stable recovery guarantees, there appear to be some issues not addressed in the literature, which are (i). convergence of the solver for the weighted ℓ1−2 minimization analytically, and (ii). detailed analysis of relevance of general weights to applications. While establishing the convergence of the solver of the weighted ℓ1−2 minimization, we demonstrate the significance of general weights, w∈(0,1), empirically through some applications, including the reconstruction of magnetic resonance images. In particular, we show that the general weights attain significance when we do not have fully accurate or fully corrupt information about the support of the signal to be reconstructed from its linear measurements. We conclude the work by discussing a numerical scheme that chooses the partial support and the weights iteratively.

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IITH Creators:

IITH Creators	ORCiD
Sastry, Challa Subrahmanya	UNSPECIFIED

Item Type:

Article

Uncontrolled Keywords:

Compressed sensing; Reconstruction in MRI; Weighted minimization; ℓ1−2 minimization; Magnetic resonance; Magnetic resonance imaging; Compressed sensing; Reconstruction in MRI; Weighted minimization; ℓ1−2 minimization

Subjects:

Mathematics
Mathematics > Numerical analysis

Divisions:

Department of Mathematics

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

27 Aug 2023 11:59

Last Modified:

27 Aug 2023 11:59

URI:

http://raiithold.iith.ac.in/id/eprint/11646