相关论文: Phase retrieval with sparse phase constraint

The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…

Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…

Phase unwrapping is the process of recovering a continuous phase signal from an original signal wrapped in the ($-\pi$,$\pi$] interval. It is a critical step of coherent signal processing, with applications such as synthetic aperture radar,…

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…

In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…

We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…

Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex…

Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…

The overdetermination of the mathematical problem underlying ptychography is reduced by a host of experimentally more desirable settings. Furthermore, reconstruction of the sample-induced phase shift is typically limited by uncertainty in…

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting…

We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization…

We study convex relaxation algorithms for phase retrieval on imaging problems. We show that structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can be exploited to both speed-up convergence…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…