Sparsifying orthogonal transforms with compact bases for data compression

Learned Sparsifying orthogonal transforms (SOTs) have proven to be a powerful tool for image and video processing. In this paper, we propose a variant of SOT, named compact bases SOT, or CB-SOT, which has several promising features for data compression: (i) as an input-adaptive transform, it can sparsely represent the input data very well; (ii) the transform matrix is orthogonal; (iii) unlike SOT, the transform matrix is compact, since a large amount of entries are zero. We formulate CB-SOT as a constrained optimization problem and solve it efficiently using alternating iteration. Experiments on images show that the proposed algorithm empirically converges well and CB-SOT produces better performance of energy compaction, indicating its potential for data compression.