Joint sparsity-based optimization of a set of orthonormal 2-D separable block transforms

We propose an iterative method for the optimization of a set of 2-D separable transforms for a given training data set. The method outputs orthonormal transforms, each one being optimal for a subset of the data with respect to a sparsity-based objective function. The vertical and horizontal directions of the transform may be different, thus allowing directional-adapted transforms (in contrast to the usual DCT). Additionally, we relate the reconstruction error and the sparsity cost terms through the quantization step. To prove the validity of our approach, experimental results concerning coding applications are provided.