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1-Bit Compressive Sensing via Approximate Message Passing with Built-in Parameter Estimation

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Document pages: 12 pages

Abstract: 1-bit compressive sensing aims to recover sparse signals from quantized 1-bitmeasurements. Designing efficient approaches that could handle noisy 1-bitmeasurements is important in a variety of applications. In this paper we usethe approximate message passing (AMP) to achieve this goal due to its highcomputational efficiency and state-of-the-art performance. In AMP the signal ofinterest is assumed to follow some prior distribution, and its posteriordistribution can be computed and used to recover the signal. In practice, theparameters of the prior distributions are often unknown and need to beestimated. Previous works tried to find the parameters that maximize either themeasurement likelihood or the Bethe free entropy, which becomes increasinglydifficult to solve in the case of complicated probability models. Here wepropose to treat the parameters as unknown variables and compute theirposteriors via AMP as well, so that the parameters and the signal can berecovered jointly. This leads to a much simpler way to perform parameterestimation compared to previous methods and enables us to work with noisy 1-bitmeasurements. We further extend the proposed approach to the generalquantization noise model that outputs multi-bit measurements. Experimentalresults show that the proposed approach generally perform much better than theother state-of-the-art methods in the zero-noise and moderate-noise regimes,and outperforms them in most of the cases in the high-noise regime.

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