Sparse Reconstruction in Compressed Sensing

The sparse reconstruction problem in compressed sensing remains one of the core challenges in signal processing. Traditional Matching Pursuit (MP) algorithms approximate signals by iteratively selecting optimal atoms, but computational complexity increases significantly as problem scales grow. To address this bottleneck, researchers have developed innovative block processing strategies.

The core concept involves partitioning large atom dictionaries into multiple sub-blocks, each containing structurally related atoms. The reconstruction process operates at two levels: first performing coarse-grained screening between blocks to quickly identify potential matching regions, then executing traditional MP's fine-grained search within selected blocks. This divide-and-conquer strategy substantially reduces computational burden, particularly suitable for high-dimensional signal processing.

Block design must consider inter-atom correlations, commonly implemented through frequency-band partitioning, time-domain segmentation, or spatial clustering approaches. Proper block partitioning maintains signal feature coherence while avoiding information loss from forced segmentation. Experimental results demonstrate that block-based MP algorithms can reduce computation time by 30%-50% compared to original versions while maintaining equivalent reconstruction accuracy.

This improvement not only enhances algorithm practicality but also provides a natural framework for hardware parallelization—different processing units can handle specific block computations independently. This concept has later evolved into more advanced variants like adaptive blocking and dynamic block partitioning, promoting compressed sensing applications in medical imaging and wireless communications.