Abstract
In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning.
Highlights
It has become commonplace to talk about the recent “information explosion” or “data deluge”.These expressions refer to a much faster growth in data production compared to all available data storage and to the even more evident divergence between the volume of data produced and the general data processing capacity
Its noiseless counterpart can be obtained by taking the limit σn2 → 0, which leads to P(y|u) = δ(y − u)
We proposed an online algorithm for Compressed Sensing
Summary
It has become commonplace to talk about the recent “information explosion” or “data deluge” These expressions refer to a much faster growth in data production compared to all available data storage and to the even more evident divergence between the volume of data produced and the general data processing capacity. The Nyquist rate [6,7] is a concept present in virtually all signal acquisition protocols used in consumer electronics and medical imaging devices, among others [2] It implies the necessity of a high sampling frequency, which means an especially high demand if we consider the pervasive high definition registers. We consider the scenario of a signal generated by an unknown distribution and its recovery by means of a Bayesian online CS scheme.
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