Related papers: Sequential adaptive compressed sampling via Huffma…
We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the…
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed…
Huffman Compression, also known as Huffman Coding, is one of many compression techniques in use today. The two important features of Huffman coding are instantaneousness that is the codes can be interpreted as soon as they are received and…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…
Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Common imaging techniques for detecting structural defects typically require sampling at more than twice the spatial frequency to achieve a target resolution. This study introduces a novel framework for imaging structural defects using…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the…
We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution…
The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT…
A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the…
In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names,…