Improved Coherence Index-Based Bound in Compressive Sensing
This work addresses the reliability of sparse signal reconstruction in compressive sensing, offering incremental improvements to coherence-based bounds for practitioners in signal processing and related fields.
The paper tackles the problem of improving uniqueness conditions for sparse signal reconstruction in compressive sensing by deriving a less conservative coherence index-based lower bound for signal sparsity, specifically for matching pursuit algorithms and generalizing it to l0-norm minimization in two orthonormal bases.
Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible calculation, coherence index is one of very few CS metrics with a considerable practical importance. In this paper, we propose an improvement of the coherence based uniqueness relation for the matching pursuit algorithms. Starting from a simple and intuitive derivation of the standard uniqueness condition based on the coherence index, we derive a less conservative coherence index-based lower bound for signal sparsity. The results are generalized to the uniqueness condition of the $l_0$-norm minimization for a signal represented in two orthonormal bases.