Related papers: Limits of Deterministic Compressed Sensing Conside…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
In this paper we revisit the deterministic version of the Sparse Fourier Transform problem, which asks to read only a few entries of $x \in \mathbb{C}^n$ and design a recovery algorithm such that the output of the algorithm approximates…
There have been a number of studies on sparse signal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance.…
This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length $N$. For…
This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are…
Based on $\alpha$-stable random projections with small $\alpha$, we develop a simple algorithm for compressed sensing (sparse signal recovery) by utilizing only the signs (i.e., 1-bit) of the measurements. Using only 1-bit information of…
In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse…
We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the…
In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal…