469 research outputs found
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
Computational Methods for Sparse Solution of Linear Inverse Problems
The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications
Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing
Compressed sensing aims at reconstructing sparse signals from significantly
reduced number of samples, and a popular reconstruction approach is
-norm minimization. In this correspondence, a method called orthonormal
expansion is presented to reformulate the basis pursuit problem for noiseless
compressed sensing. Two algorithms are proposed based on convex optimization:
one exactly solves the problem and the other is a relaxed version of the first
one. The latter can be considered as a modified iterative soft thresholding
algorithm and is easy to implement. Numerical simulation shows that, in dealing
with noise-free measurements of sparse signals, the relaxed version is
accurate, fast and competitive to the recent state-of-the-art algorithms. Its
practical application is demonstrated in a more general case where signals of
interest are approximately sparse and measurements are contaminated with noise.Comment: 7 pages, 2 figures, 1 tabl
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