Compressive sensing recovery from non-ideally quantized measurements

The problem of signal recovery from non-ideally quantized linear measurements is considered. Quantization non-idealities due to circuit second-order effects are inevitable in practical deployments of compressive sensing and introduce distortion in the measurement process. Quantization non-idealities are commonly characterized by integral non-linearity (INL), offset and gain error metrics. These metrics are included in the signal reconstruction process to enforce quantization consistency. Signal reconstruction is formulated as a linear program. The performance of the proposed approach is assessed numerically and compared with other signal recovery techniques. It is shown that a linear program can be competitive and in some cases superior to more elaborate signal recovery approaches. It is also shown that satisfying quantization consistency does not always lead to better signal recovery in terms of signal-to-noise ratio (SNR).