CGIST (Conjugate Gradient Iterative Shrinkage/Thresholding) is a Matlab based solver for L1-penalized least squares problems. This code is an implementation of the CGIST algorithm developed by Tom Goldstein (Stanford University) and Simon Setzer (Saarland University). The algorithm solves L1-penalized least squares problems using a forward-backward splitting method with an acceleration step. The acceleration step is specially designed to implicitly perform subspace optimization using the conjugate gradient method. More details on this method can be found in the paper High-Order Methods for Sparse Signal Recovery.