Review for NeurIPS paper: Learning to solve TV regularised problems with unrolled algorithms

Summary and Contributions: The paper considers the problem of accelerating TV-regularized problems. The paper first shows that assuming random Gaussian design, the analysis formulation might converge faster than the synthesis formulation based on the usual convergence rate for PGD. The paper then proposes two methods to accelerate the analysis formulation, using unrolling as done in LISTA. With regular lasso, the proximal operator is soft thresholding and back propagation is easy. With TV, backpropagation is a bit more difficult, and the paper proposes two alternatives.