Incorporating Handcrafted Filters in Convolutional Analysis Operator Learning for Ill-Posed Inverse Problems

Convolutional analysis operator learning (CAOL) enables the unsupervised training of convolutional sparsifying autoencoders, taking advantage of large datasets to obtain high quality filters. In previous works, using CAOL within model-based image reconstruction (MBIR) for ill-posed inverse problems significantly improved image reconstruction accuracy over existing MBIR using non-trained regularizers and generalized better than existing non-MBIR deep neural network approaches. This paper modifies the CAOL Procrustes filter update to allow some filters to be handcrafted. Doing so makes it possible to incorporate domain knowledge in the learning process and accelerates CAOL by learning fewer filters. We apply the proposed generalization of CAOL to MBIR for sparse-view CT. Numerical experiments show that 1) handcrafting discrete cosine transform filters can trade-off training time and reconstruction quality and 2) handcrafting filters based on finite differences can speed up training without sacrificing reconstruction quality.