Online data-driven dynamic image restoration using DINO-KAT models

Sparsity-based techniques have been popular for reconstructing images and videos from limited or corrupted measurements. Methods such as dictionary or transform learning have been demonstrated to be useful in applications such as denoising, inpainting, and medical image reconstruction. In this work, we propose a new framework for online or sequential adaptive reconstruction of dynamic image sequences from linear (typically undersampled) measurements. In particular, the spatiotemporal patches of the underlying dynamic image sequence are assumed to be sparse in a DIctioNary with lOw-ranK AToms (DINO-KAT), and the dictionary model and images are simultaneously and sequentially estimated from streaming measurements. The proposed online algorithm involves efficient memory usage and simple and efficient updates of the low-rank atoms, sparse coefficients, and images. Our numerical experiments show the usefulness of the proposed scheme in inverse problem settings such as video reconstruction or inpainting from limited and noisy pixels.