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

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

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Performance of current face recognition algorithms reduces significantly when they are applied to low-resolution face images. To handle this problem, super-resolution techniques can be applied either in the pixel domain or in the face subspace. Since face images are high dimensional data which are mostly redundant for the face recognition task, feature extraction methods that reduce the dimension of the data are becoming standard for face analysis. Hence, applying superresolution in this feature domain, in other words in face subspace, rather than in pixel domain, brings many advantages in computation together with robustness against noise and motion estimation errors. Therefore, we propose new superresolution algorithms using Bayesian estimation and projection onto convex sets methods in feature domain and present a comparative analysis of the proposed algorithms with those already in the literature.