Related papers: Sparse recovery for spherical harmonic expansions
We derive a compressive sampling method for acoustic field reconstruction using field measurements on a predefined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
Compressive sensing involves the inversion of a mapping $SD \in \mathbb{R}^{m \times n}$, where $m < n$, $S$ is a sensing matrix, and $D$ is a sparisfying dictionary. The restricted isometry property is a powerful sufficient condition for…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
A central limitation of multiple-acquisition magnetic resonance imaging (MRI) is the degradation in scan efficiency as the number of distinct datasets grows. Sparse recovery techniques can alleviate this limitation via randomly undersampled…
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n…
Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We study the problem of recovering sparse signals from compressed linear measurements. This problem, often referred to as sparse recovery or sparse reconstruction, has generated a great deal of interest in recent years. To recover the…
In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing…
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…
An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class…