Dictionary learning from incomplete data for efficient image restoration

In real-world image processing applications, the data is high dimensional but the amount of high-quality data needed to train the model is very limited. In this paper, we demonstrate applicability of a recently presented method for dictionary learning from incomplete data, the so-called Iterative Thresholding and K residual Means for Masked data, to deal with high-dimensional data in an efficient way. In particular, the proposed algorithm incorporates a corruption model directly at the dictionary learning stage, also enabling reconstruction of the low-rank component again from corrupted signals. These modifications circumvent some difficulties associated with the efficient dictionary learning procedure in the presence of limited or incomplete data. We choose an image inpainting problem as a guiding example, and further propose a procedure for automatic detection and reconstruction of the low-rank component from incomplete data and adaptive parameter selection for the sparse image reconstruction. We benchmark the efficacy and efficiency of our algorithm in terms of computing time and accuracy on colour, 3D medical, and hyperspectral images by comparing it to its dictionary learning counterparts.