Subspace-sparsifying steerable discrete cosine transform from graph fourier transform

In image compression, block-based transforms tend to be inefficient when blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. Starting from the graph Fourier transform, in this paper we present a new transform, called Subspace-Sparsifying Steer-able DCT, that can be obtained by rotating the basis vectors of the 2D DCT using a set of angles that best matches the block to be encoded. In particular, this new transform chooses the set of angles providing the sparsest image representation in the transform domain, yielding a matrix of transform coefficients that is triangular. In this way, it nearly halves the number of coefficients that need to be transmitted, obtaining a significant coding gain in comparison to the classical DCT.