An Efficient OMP for Multidimensional Data Denoising and Recovery in Compressed Sensing

Compressive sensing (CS) has revolutionized sparse signal processing by enabling a faithful signal acquisition, and recovery at sampling rates far smaller than the Nyquist frequency. Its benefits include efficient data storage, low energy transmissions, and high spectral efficiency. Furthermore, CS recovery is a good solution to noise removal in many applications such as biomedical signal processing, quantitative finance, and wireless communications. However, its use in applications involving high-dimensional data is challenging. To address this, we propose a novel denoising strategy based on the orthogonal matching pursuit (OMP) algorithm, extended to multivariate data considering dataset correlations. This extension allows the algorithm to benefit from the inherent relationships between time series within the high-dimensional data, leading to more effective noise removal and improved signal reconstruction. We evaluate the performance of our OMP-based method through numerical experiments using synthetic data.