相关论文: Sparse reconstruction by convex relaxation: Fourie…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…
We consider the following basic inference problem: there is an unknown high-dimensional vector $w \in \mathbb{R}^n$, and an algorithm is given access to labeled pairs $(x,y)$ where $x \in \mathbb{R}^n$ is a measurement and $y = w \cdot x +…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
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…
The problem central to sparse recovery and compressive sensing is that of stable sparse recovery: we want a distribution of matrices A in R^{m\times n} such that, for any x \in R^n and with probability at least 2/3 over A, there is an…
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…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities.…