Approximate Message Passing With Parameter Estimation for Heavily Quantized Measurements

Abstract

Designing efficient sparse recovery algorithms that could handle noisy\nquantized measurements is important in a variety of applications -- from radar\nto source localization, spectrum sensing and wireless networking. We take\nadvantage of the approximate message passing (AMP) framework to achieve this\ngoal given its high computational efficiency and state-of-the-art performance.\nIn AMP, the signal of interest is assumed to follow certain prior distribution\nwith unknown parameters. Previous works focused on finding the parameters that\nmaximize the measurement likelihood via expectation maximization -- an\nincreasingly difficult problem to solve in cases involving complicated\nprobability models. In this paper, we treat the parameters as unknown variables\nand compute their posteriors via AMP. The parameters and signal of interest can\nthen be jointly recovered. Compared to previous methods, the proposed approach\nleads to a simple and elegant parameter estimation scheme, allowing us to\ndirectly work with 1-bit quantization noise model. We then further extend our\napproach to general multi-bit quantization noise model. Experimental results\nshow that the proposed framework provides significant improvement over\nstate-of-the-art methods across a wide range of sparsity and noise levels.\n