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This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
We consider the problem of high-dimensional misspecified phase retrieval. This is where we have an $s$-sparse signal vector $\mathbf{x}_*$ in $\mathbb{R}^n$, which we wish to recover using sampling vectors…
This paper develops a novel algorithm, termed \emph{SPARse Truncated Amplitude flow} (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval…
The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…
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…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…
We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals…
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…
A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method, referred to as nGpFBMP, performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It…