A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints | Semantic Scholar (2024)

A new generalized thresholding algorithm useful for inverse problems with sparsity constraints that penalizes small coefficients over a wider range and applies less bias to the larger coefficients, much like hard thresholding but without discontinuities is proposed.

A type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization.

Under the restricted isometry property (RIP), it is proved that the optimal thresholding based algorithms are globally convergent to the solution of sparse optimization problems.

A minimax-concave penalty-based formulation, which offers an unbiased estimate of the sparse signal, is considered, which outperforms in terms of the probability-of-error-in-support (PES)-a strong support recovery metric, by at least three-fold.

The cardinality minimization problem is converted to the sum-of-ratio problem and the new model is solved with an optimization algorithm proposed for finding the optimal solution to the ratio problem.

This work introduces a parametrized quasi-soft thresholding operator and uses it to obtain new algorithms for compressed sensing and matrix completion and shows that the new algorithms can effectively improve the accuracy.

The proposed two-term penalty function consisting of a synthesis between the ¿i-norm and the penalty function associated with the Non-Negative Garrote (NNG) thresholding rule is non-convex and shows good performance for the denoising and deconvolution problems.

Empirical results indicate that the NT-type algorithms for signal recovery from noisy measurements are robust and very comparable to several mainstream algorithms for sparse signal recovery.

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It is proved that replacing the usual quadratic regularizing penalties by weighted 𝓁p‐penalized penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem.

This article obtains parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems, and sketches three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models.

The methodology for updating weights proposed in this work consists in considering those weights as Lagrange multipliers, being able in this way to apply classical Lagrange relaxation algorithms for the update process.

This paper presents a formula that characterizes the allowed undersampling of generalized sparse objects, and proves that this formula follows from state evolution and present numerical results validating it in a wide range of settings.

A fast algorithm is derived for the constrained TV-based image deblurring problem with box constraints by combining an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA).

The development of the recovery of the recovered frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods is retrace and two models recently studied independently by the authors for the Recovery of vector valued functions from incomplete data are reviewed.

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