Lasso-Based Fast Residual Recovery For Modulo Sampling

In practice, Analog-to-Digital Converter (ADC) is used to perform sampling. A practical bottleneck of ADC is its lower dynamic range, leading to loss of information. To address this issue, researchers suggested folding operation on the signal using a modulo operator before passing it as an input to ADC. Though this process preserves the signal information, an unfolding algorithm is required to get the true samples from the folded samples. Noise robustness and computational time are two key parameters of an unfolding algorithm. In this paper, we propose a fast and robust algorithm for unfolding. Specifically, we first show that the first-order difference of the residual samples (the difference between the folded and true samples) is sparse by deriving an upper bound on its sparsity, and can be recovered from its partial Fourier measurements by formulating a sparse recovery problem. We demonstrate that the proposed algorithm is robust to noise and computationally efficient compared to the existing methods.