205 research outputs found
Recovery under Side Constraints
This paper addresses sparse signal reconstruction under various types of
structural side constraints with applications in multi-antenna systems. Side
constraints may result from prior information on the measurement system and the
sparse signal structure. They may involve the structure of the sensing matrix,
the structure of the non-zero support values, the temporal structure of the
sparse representationvector, and the nonlinear measurement structure. First, we
demonstrate how a priori information in form of structural side constraints
influence recovery guarantees (null space properties) using L1-minimization.
Furthermore, for constant modulus signals, signals with row-, block- and
rank-sparsity, as well as non-circular signals, we illustrate how structural
prior information can be used to devise efficient algorithms with improved
recovery performance and reduced computational complexity. Finally, we address
the measurement system design for linear and nonlinear measurements of sparse
signals. Moreover, we discuss the linear mixing matrix design based on
coherence minimization. Then we extend our focus to nonlinear measurement
systems where we design parallel optimization algorithms to efficiently compute
stationary points in the sparse phase retrieval problem with and without
dictionary learning
Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm
The goal of this paper is to develop a novel numerical method for efficient
multiplicative noise removal. The nonlocal self-similarity of natural images
implies that the matrices formed by their nonlocal similar patches are
low-rank. By exploiting this low-rank prior with application to multiplicative
noise removal, we propose a nonlocal low-rank model for this task and develop a
proximal alternating reweighted minimization (PARM) algorithm to solve the
optimization problem resulting from the model. Specifically, we utilize a
generalized nonconvex surrogate of the rank function to regularize the patch
matrices and develop a new nonlocal low-rank model, which is a nonconvex
nonsmooth optimization problem having a patchwise data fidelity and a
generalized nonlocal low-rank regularization term. To solve this optimization
problem, we propose the PARM algorithm, which has a proximal alternating scheme
with a reweighted approximation of its subproblem. A theoretical analysis of
the proposed PARM algorithm is conducted to guarantee its global convergence to
a critical point. Numerical experiments demonstrate that the proposed method
for multiplicative noise removal significantly outperforms existing methods
such as the benchmark SAR-BM3D method in terms of the visual quality of the
denoised images, and the PSNR (the peak-signal-to-noise ratio) and SSIM (the
structural similarity index measure) values
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