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Register a new userNoisy One-bit Compressed Sensing with Side-Information
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Added by
Swatantra Kafle
Publication date
2020
fields
Electronic Engineering
and research's language is
English
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We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based method for signal reconstruction from noisy one-bit compressed measurements is proposed, which is then extended for the case where the receiver has access to a signal that aids signal reconstruction, i.e., side-information. Two different scenarios of side-information are considered-a) side-information consisting of support information only, and b) side information consisting of support and amplitude information. SI is either a noisy version of the signal or a noisy estimate of the support of the signal. We develop reconstruction algorithms from one-bit measurements using noisy SI available at the receiver. Laplacian distribution and Bernoulli distribution are used to model the two types of noises which, when applied to the signal and the support, yields the SI for the above two cases, respectively. The Expectation-Maximization algorithm is used to estimate the noise parameters using noisy one-bit compressed measurements and the SI. We show that one-bit compressed measurement-based signal reconstruction is quite sensitive to noise, and the reconstruction performance can be significantly improved by exploiting available side-information at the receiver.
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Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h in H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called one-bit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain the first scheme that achieves almost optimal measurements and sublinear decoding time for one-bit compressed sensing in the non-uniform case. For a large range of parameters, we improve the state of the art in both the number of measurements and the decoding time.
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