Sparse approximations is a research area in mathematics and computer science that focuses on developing methods for representing and approximating data with a minimal number of variables or features. The goal is to find a compact representation of the data that captures its essential characteristics while reducing complexity and computational cost. Sparse approximations have applications in signal processing, machine learning, image processing, and many other fields where efficient and accurate data representation is important. Common techniques used in sparse approximations include compressed sensing, dictionary learning, and sparse coding.