Sparse orthonormal transforms for image compression

Abstract

We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOT) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multi-resolution, block, lapped, etc.) with significantly better n-term approximation performance.For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. Index Termssparse orthonormal transform, sparse lapped transform, sparse multi-resolution transform, transform optimization, image compression, nonlinear approximation 2

Image coding with incomplete transform competition for HEVC

“…Afterwards, the transform is updated given the hard-thresholded coefficients c i and the x i . A detailed resolution of this equation is described in [5], as well as the relation between λ and the hard-thresholding parameter.…”

“…They can be considered as a special case of sparse orthonormal transforms [5] in which only one basis vector is retained and considered: consequently, a signal that has been transformed using an incomplete transform has only one coefficient different from zero in the transform domain.…”

“…The incomplete transform design is based upon the sparse orthogonal transforms model proposed and detailed in [5]. The original method describes how to derive one optimal transform iteratively for some training data and an initial transform by using a metric that includes a sparsity constraint.…”

Anisotropic multiscale sparse learned bases for image compression

“…Chen A similar idea is followed by Sezer et al 1 where a library of bases is optimized on a training set to maximize the sparsity of the transform vectors. We can likewise refer to the well-known wavelets, which are very effective at describing the edges of an image.…”

Sparse optimization with directional DCT bases for image compression

“…In [4], the authors replace the DCT in the JPEG scheme by other transforms, better adapted to the local statistics of each block. In a similar way, Sezer et al optimize a library of bases on a training set to maximize the sparsity of the transformed vectors (see [5]). We can likewise refer to the well-known wavelets [6], curvelets [7], contourlets [8] and bandelets [9], which are very effective at describing the edges of an image.…”