1-Bit Compressed Sensing with Local Sparsity Patterns

Saikiran Bulusu, Venkata Gandikota, Pramod K. Varshney

Abstract: 1-bit compressed sensing (1bCS) is a quantized signal acquisition technique to compress high-dimensional sparse signals. The goal in 1bCS is to design sensing matrices A ∈ ℝ^m×n with the fewest possible rows that enable efficient and accurate recovery of sparse signals x ∈ ℝⁿ from 1-bit measurements of the form sign(Ax). In this work, we leverage the locality in sparsity patterns observed in many real-world datasets to recover the support of signals exhibiting this sparsity pattern. Our results improve the existing bounds on the number of measurements sufficient for support recovery when the non-zero entries of a signal occur within small local neighborhoods.