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Optimal Sampling Rates in Infinite-Dimensional Compressed Sensing

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Sparsity & [and] dictionaries - algorithms & [and] design

Karin Schnass

With the flood of information available today the question how to deal with high dimensional data/signals, which are cumbersome to handle, to calculate with and to store, is highly important. One approach to reducing this flood is to find sparse signal rep ...

EPFL2009

Recovery of Compressible Signals in Unions of Subspaces

Volkan Cevher

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquisition of sparse or compressible signals; instead of taking periodic samples, we measure inner products with All < N random vectors and then recover the signal via a sparsity-s ...

2009

Compressive sensing recovery of spike trains using a structured sparsity model

Volkan Cevher

The theory of Compressive Sensing (CS) exploits a well-known concept used in signal compression – sparsity – to design new, efficient techniques for signal acquisition. CS theory states that for a length-N signal x with sparsity level K, M = O(K log(N/K)) ...

2009

Recovery of clustered sparse signals from compressive measurements

Volkan Cevher

We introduce a new signal model, called (K,C)-sparse, to capture K-sparse signals in N dimensions whose nonzero coefficients are contained within at most C clusters, with C < K < N. In contrast to the existing work in the sparse approximation and compress ...

2009

Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine

Laurent Jacques

The theory of Compressed Sensing (CS) is based on reconstructing sparse signals from random linear measurements. As measurement of continuous signals by digital devices always involves some form of quantization, in practice devices based on CS encoding mus ...

2009

Dequantizing Compressed Sensing with non-Gaussian Constraints

Laurent Jacques

2009

Sampling Bounds for Sparse Support Recovery in the Presence of Noise

Michael Christoph Gastpar

It is well known that the support of a sparse signal can be recovered from a small number of random projections. However, in the presence of noise all known sufficient conditions require that the per-sample signal-to-noise ratio (SNR) grows without bound w ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Semantic coding by supervised dimensionality reduction

Pascal Frossard, Effrosyni Kokiopoulou

This paper addresses the problem of representing multimedia information under a compressed form that permits efficient classification. The semantic coding problem starts from a subspace method where dimensionality reduction is formulated as a matrix factor ...

2008

Average case analysis of sparse recovery with Thresholding: New bounds based on average dictionary coherence

Pierre Vandergheynst, Mohammad Golbabaee

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also ...

2008

Sparse signal recovery using Markov random fields

Volkan Cevher

Compressive Sensing (CS) combines sampling and compression into a single sub-Nyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a g ...

2008