Row-column transforms: Low-complexity approximation of optimal non-separable transforms

This paper introduces row-column transforms (RCTs) which are 2D non-separable transforms defined with the aid of a set of 1-D linear transforms and a basis ordering permutation. We propose a novel method for the design of row-column transforms that approximate desired complex transforms (such as KLTs, SOTs, etc.) so that most of the performance of the approximated transforms is retained at significantly reduced complexity. Given a non-separable block transform of interest, our method designs an RCT by (i) optimizing a set of 1-D transforms applied to rows and columns of the signal block and (ii) finding the best transform coefficient ordering permutation. Our experimental results show that optimized RCTs closely approach the compression performance of the desired non-separable transforms while retaining the computational complexity of separable transforms.