Finding the most sparse solution to the underdetermined system $\mathbf{y}=\mathbf{Ax}$, given a tolerance, is known to be NP-hard. A popular way to approximate a sparse solution is by using Greedy Pursuit algorithms, and Orthogonal Matching Pursuit (OMP) is one of the most widely used such solutions. For this paper, we implemented an efficient implementation of OMP that leverages Cholesky inverse properties as well as the power of Graphics Processing Units (GPUs) to deliver up to 200x speedup over the OMP implementation found in Scikit-Learn.

翻译：在给定容差条件下，寻找欠定系统 $\mathbf{y}=\mathbf{Ax}$ 的最稀疏解被证明是NP难问题。逼近稀疏解的一种常用方法是采用贪婪追踪算法，其中正交匹配追踪（OMP）是此类方案中应用最广泛的算法之一。本文实现了一种高效的OMP算法，该算法利用Cholesky逆矩阵特性及图形处理器（GPU）的强大算力，相较于Scikit-Learn中的OMP实现可获得高达200倍的加速比。