Deep dictionary-transform learning for image reconstruction

Various dictionaries and transforms are known to sparsify images, and have been exploited in algorithms for image reconstruction from limited data. Methods that simultaneously reconstruct the image and learn dictionaries or sparsifying transforms for image patches, called blind compressed sensing methods, have shown promising performance. Motivated by such adaptive algorithms, this paper proposes an approach to train dictionary-transform based methods for image reconstruction by minimizing a minimum absolute reconstruction error criterion. Each "layer" of the algorithm consists of applying (convolving) trained transforms, thresholdings, and dictionaries to images, followed by a simple least squares update of the images. Numerical experiments illustrate the usefulness and speed-ups provided by such trained algorithms compared to related schemes.