818 research outputs found
Approximate Message Passing under Finite Alphabet Constraints
In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which
the sparse original signal is drawn from a finite alphabet. To solve this
problem we propose an iterative message passing algorithm, which capitalises
not only on the sparsity but by means of a prior distribution also on the
discrete nature of the original signal. In our numerical experiments we test
this algorithm in combination with a Rademacher measurement matrix and a
measurement matrix derived from the random demodulator, which enables
compressive sampling of analogue signals. Our results show in both cases
significant performance gains over a linear programming based approach to the
considered BPDN problem. We also compare the proposed algorithm to a similar
message passing based algorithm without prior knowledge and observe an even
larger performance improvement.Comment: 4 pages, 2 figures, to appear in IEEE International Conference on
Acoustics, Speech, and Signal Processing ICASSP 201
Recovery of binary sparse signals from compressed linear measurements via polynomial optimization
The recovery of signals with finite-valued components from few linear
measurements is a problem with widespread applications and interesting
mathematical characteristics. In the compressed sensing framework, tailored
methods have been recently proposed to deal with the case of finite-valued
sparse signals. In this work, we focus on binary sparse signals and we propose
a novel formulation, based on polynomial optimization. This approach is
analyzed and compared to the state-of-the-art binary compressed sensing
methods
Quantized Compressed Sensing for Partial Random Circulant Matrices
We provide the first analysis of a non-trivial quantization scheme for
compressed sensing measurements arising from structured measurements.
Specifically, our analysis studies compressed sensing matrices consisting of
rows selected at random, without replacement, from a circulant matrix generated
by a random subgaussian vector. We quantize the measurements using stable,
possibly one-bit, Sigma-Delta schemes, and use a reconstruction method based on
convex optimization. We show that the part of the reconstruction error due to
quantization decays polynomially in the number of measurements. This is in line
with analogous results on Sigma-Delta quantization associated with random
Gaussian or subgaussian matrices, and significantly better than results
associated with the widely assumed memoryless scalar quantization. Moreover, we
prove that our approach is stable and robust; i.e., the reconstruction error
degrades gracefully in the presence of non-quantization noise and when the
underlying signal is not strictly sparse. The analysis relies on results
concerning subgaussian chaos processes as well as a variation of McDiarmid's
inequality.Comment: 15 page
Discrete Signal Reconstruction by Sum of Absolute Values
In this letter, we consider a problem of reconstructing an unknown discrete
signal taking values in a finite alphabet from incomplete linear measurements.
The difficulty of this problem is that the computational complexity of the
reconstruction is exponential as it is. To overcome this difficulty, we extend
the idea of compressed sensing, and propose to solve the problem by minimizing
the sum of weighted absolute values. We assume that the probability
distribution defined on an alphabet is known, and formulate the reconstruction
problem as linear programming. Examples are shown to illustrate that the
proposed method is effective.Comment: IEEE Signal Processing Letters (to appear
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