Learned ISTA with Error-based Thresholding for Adaptive Sparse Coding

The learned iterative shrinkage thresholding algorithm (LISTA) introduces deep unfolding models with learnable thresholds in some shrinkage functions for sparse coding. Drawing on some theoretical insights, we advocate an error-based thresholding (EBT) mechanism for LISTA, which leverages a function of the layer-wise reconstruction error to suggest an appropriate threshold value for each observation on each layer. We show that the EBT mechanism well disentangles the learnable parameters in the shrinkage functions from the reconstruction errors, making them more adaptive to the various observations. With rigorous theoretical analyses, we show that the proposed EBT can lead to a faster convergence on the basis of LISTA and its variants, in addition to its higher adaptivity. Extensive experimental results confirm our theoretical analyses and verify the effectiveness of our methods.