Related papers: Sparse Phase Retrieval via Sparse PCA Despite Mode…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of $m$ measurements, $y_k = |\mathbf a_k^* \mathbf x|$ for $k = 1, \dots, m$, is it possible to recover $\mathbf x \in \mathbb{C}^n$ (i.e., length-$n$…
We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
In this paper, we introduce a new detection algorithm for large-scale wireless systems, referred to as post sparse error detection (PSED) algorithm, that employs a sparse error recovery algorithm to refine the estimate of a symbol vector…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
This paper studies the problem of support recovery of sparse signals based on multiple measurement vectors (MMV). The MMV support recovery problem is connected to the problem of decoding messages in a Single-Input Multiple-Output (SIMO)…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
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…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
Phase retrieval refers to the problem of recovering a signal $\mathbf{x}_{\star}\in\mathbb{C}^n$ from its phaseless measurements $y_i=|\mathbf{a}_i^{\mathrm{H}}\mathbf{x}_{\star}|$, where $\{\mathbf{a}_i\}_{i=1}^m$ are the measurement…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…
Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing…
We address the problem of recovering a sparse $n$-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery…