Fast and efficient union of sparse orthonormal transform for image compression

Sparse coding has been widely used in image processing. Overcomplete-based sparse coding is powerful to represent data as a small number of bases, but with time-consuming optimization methods. Orthogonal sparse coding is relatively fast and well-suitable in image compression like analytic transforms with better performance than the existing analytic transforms. Thus, there have been many attempts to design image transform based on orthogonal sparse coding. In this paper, we introduce an extension of sparse orthonormal transform (SOT) based on unions of orthonormal bases (UONB) for image compression. Different from UONB, we allocate image patches to one orthonormal dictionary according to their direction. To accelerate the method, we factorize our dictionaries into the discrete cosine transform matrix and another orthonormal matrix. In addition, for more effective implementation, calculation of direction is also conducted in DCT domain. As expected, our framework fulfills the goal of improving compression performance of SOT with fast implementation. Through experiments, we verify that proposed method produces similar performance to overcomplete dictionary outperforms SOT in compression with rather faster speed. The proposed methods are from twice to four times faster than the SOT and hundreds of times faster than UONB.