A review of optimisation and least-square problem methods on field programmable gate array-based orthogonal matching pursuit implementations

Orthogonal matching pursuit (OMP) is the most efficient algorithm used for the reconstruction of compressively sampled data signals in the implementation of compressive sensing. OMP operates in an iteration-based nature, which involves optimisation and least-square problem (LSP) as the main processes. However, optimisation and LSP processes comprise complex mathematical operations that are computationally demanding, and software-based implementations are slow, power-consuming, and unfit for real-time applications. To fill the research gap, we reviewed the optimisation and LSP techniques implemented on the FPGA platform as the hardware accelerator. Aspects that contributed to the performance, algorithm, and methods involved in the implemented works were discussed and compared. The methods were found to be improved when modified or combined. However, the best approach still depends on the requirement of the system to be developed, and this review is significant as a reference.