Sparse orthonormal transforms for image compression

We propose a block-based transform optimization and associated image compression technique that exploits regularity along directional image singularities. Unlike established work, directionality comes about as a byproduct of the proposed optimization rather than a built in constraint. Our work classifies image blocks and uses transforms that are optimal for each class, thereby decomposing image information into classification and transform coefficient information. The transforms are optimized using a set of training images. Our algebraic framework allows straightforward extension to non-block transforms, allowing us to also design sparse lapped transforms that exploit geometric regularity. We use an EZW/SPIHT like entropy coder to encode the transform coefficients to show that our block and lapped designs have competitive rate-distortion performance. Our work can be seen as nonlinear approximation optimized transform coding of images subject to structural constraints on transform basis functions.