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We develop a projected Nesterov’s proximal-gradient (PNPG) scheme for reconstructing sparse signals from compressive Poisson-distributed measurements with the mean signal intensity that follows an affine model with known intercept. The objective function to be minimized is a sum of convex data fidelity (negative log-likelihood (NLL)) and regularization terms. We apply sparse signal regularization where the signal belongs to a nonempty closed convex set within the domain of the NLL and signal sparsity is imposed using total-variation (TV) penalty. We present analytical upper bounds on the regularization tuning constant. The proposed PNPG method employs projected Nesterov’s acceleration step, function restart, and an adaptive step-size selection scheme that aims at obtaining a good local majorizing function of the NLL and reducing the time spent backtracking. We establish O(k⁻²) convergence of the PNPG method with step-size backtracking only and no restart. Numerical examples demonstrate the performance of the PNPG method.
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This content will become publicly available on January 1, 2026
Adaptive and Self-Tuning SBL With Total Variation Priors for Block-Sparse Signal Recovery
This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the hyper-parameter space of the sparse signal. The main contributions are two-fold. 1) We extend the TV penalty beyond the immediate neighbor, thus enabling better capture of the signal structure. 2) A dynamic framework is provided to learn the regularization weights for the TV penalty based on the statistical dependencies between the entries of tentative blocks, thus eliminating the need for fine-tuning. The superior performance of the proposed method is empirically demonstrated by extensive computer simulations with the state-of-art benchmarks. The proposed solution exhibits both excellent performance and robustness against sparsity model mismatch.
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- Award ID(s):
- 2225617
- PAR ID:
- 10599159
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Signal Processing Letters
- Volume:
- 32
- ISSN:
- 1070-9908
- Page Range / eLocation ID:
- 1555 to 1559
- Subject(s) / Keyword(s):
- Compressive sensing block-sparsity total variation SBL ADMM
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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