Task-Driven Dictionary Learning

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.Comment: final draft post-refereein

Restoration of error-diffused images using projection onto convex sets

In this paper, a novel inverse halftoning method is proposed to restore a continuous tone image from a given half-tone image. A set theoretic formulation is used where three sets are defined using the prior information about the problem. A new space-domain projection is introduced assuming the halftoning is performed using error diffusion, and the error diffusion filter kernel is known. The space-domain, frequency-domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution