Towards Neurally Augmented ALISTA

It is well-established that many iterative sparse reconstruction algorithms such as ISTA can be unrolled to yield a learnable neural network for improved empirical performance. Recently, ALISTA has been introduced, combining the strong empirical performance of a fully learned approach like LISTA, while retaining theoretical guarantees of classical compressed sensing algorithms and significantly reducing the number of parameters to learn. However, these parameters are trained to work in expectation, often leading to suboptimal reconstruction of individual targets. In this work we therefore introduce Neurally-Augmented-ALISTA, which computes step sizes and thresholds individually for each target vector during reconstruction. This adaptive approach is theoretically motivated by revisiting the recovery guarantees of ALISTA and is able to outperform existing algorithms in sparse reconstruction.