Basis Pursuit

Basis pursuit is an optimization technique used to find the sparsest solution to an underdetermined system of linear equations, aiming to recover a signal from incomplete or noisy measurements. Current research focuses on improving the efficiency and robustness of basis pursuit algorithms, particularly in high-dimensional settings, exploring connections to lattice problems and developing novel approaches like combinatorial methods and multiresolution techniques such as samplets. These advancements have significant implications for various fields, including signal processing, machine learning, and robust principal component analysis, enabling more accurate and efficient data analysis in the presence of noise and incomplete information.