相关论文: Geometry and Symmetry in Short-and-Sparse Deconvol…

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…

The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…

Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether…

Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be…

We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…

Deconvolution of the telescope Point Spread Function (PSF) is necessary for even moderate dynamic range imaging with interferometric telescopes. The process of deconvolution can be treated as a search for a model image such that the…

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…

This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…

We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things…

Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed since signal identifiability is a key concern, and there have been…

We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.…

In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider…