Compressed Sensing with Incremental Sparse Measurements

TL;DR

This paper introduces an incremental measurement decoding method for sparse signals that improves reconstruction success by leveraging identified components and adaptively adding measurements, validated through extensive simulations.

Contribution

It presents a novel incremental measurement approach that enhances sparse signal reconstruction when initial decoding fails due to insufficient measurements.

Findings

High reconstruction accuracy with incremental measurements

Efficient decoding process demonstrated through simulations

Improved recovery success over fixed measurement schemes

Abstract

This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a fixed number of sparse measurements. Often, it may fail as the number of sparse measurements may be not enough, possibly due to an underestimate of the signal sparsity. However, we observe that even if this first recovery fails, many component samples of the sparse signal have been identified. Hence, it is natural to further employ incremental measurements tuned to the unidentified samples with known locations. This approach has been proven very efficiently by extensive simulations.