Sequential Interval Passing for Compressed Sensing

The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal reconstruction using techniques such as linear programming (LP) and iterative message passing schemes. The interval passing algorithm (IPA) is an attractive CS approach due to its low complexity when compared to LP. In this paper, we propose a sequential IPA that is inspired by sequential belief propagation decoding of low-density-parity-check (LDPC) codes used for forward error correction in channel coding. In the sequential setting, each check node (CN) in the Tanner graph of an LDPC measurement matrix is scheduled one at a time in every iteration, as opposed to the standard ``flooding'' interval passing approach in which all CNs are scheduled at once per iteration. The sequential scheme offers a significantly lower message passing complexity compared to flooding IPA on average, and for some measurement matrix and signal sparsity, a complexity reduction of 36% is achieved. We show both analytically and numerically that the reconstruction accuracy of the IPA is not compromised by adopting our sequential scheduling approach.