414 research outputs found
A unified approach to sparse signal processing
A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i
Superresolution without Separation
This paper provides a theoretical analysis of diffraction-limited
superresolution, demonstrating that arbitrarily close point sources can be
resolved in ideal situations. Precisely, we assume that the incoming signal is
a linear combination of M shifted copies of a known waveform with unknown
shifts and amplitudes, and one only observes a finite collection of evaluations
of this signal. We characterize properties of the base waveform such that the
exact translations and amplitudes can be recovered from 2M + 1 observations.
This recovery is achieved by solving a a weighted version of basis pursuit over
a continuous dictionary. Our methods combine classical polynomial interpolation
techniques with contemporary tools from compressed sensing.Comment: 23 pages, 8 figure
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