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Sparse representations has shown to be a very powerful model for real world signals, and has enabled the development of applications with notable performance. Combined with the ability to learn a dictionary from signal examples, sparsity-inspired algorithms are often achieving state-of-the-art results in a wide variety of tasks. Yet, these methods have traditionally been restricted to small dimensions mainly due to the computational constraints that the dictionary learning problem entails. In the context of image processing, this implies handling small image patches. In this work we show how to efficiently handle bigger dimensions and go beyond the small patches in sparsity-based signal and image processing methods. We build our approach based on a new cropped wavelet decomposition, which enables a multi-scale analysis with virtually no border effects. We then employ this as the base dictionary within a double sparsity model to enable the training of adaptive dictionaries. To cope with the increase of training data, while at the same time improving the training performance, we present an Online Sparse Dictionary Learning (OSDL) algorithm to train this model effectively, enabling it to handle millions of examples. This work shows that dictionary learning can be up-scaled to tackle a new level of signal dimensions, obtaining large adaptable atoms that we call trainlets

Over the last decade, a number of algorithms have shown promising results in removing additive white Gaussian noise from natural images, and though different, they all share in common a patch based strategy by locally denoising overlapping patches. While this lowers the complexity of the problem, it also causes noticeable artifacts when dealing with large smooth areas. In this paper we present a patch-based denoising algorithm relying on a sparsity-inspired model (K-SVD), which uses a multi-scale analysis framework. This allows us to overcome some of the disadvantages of the popular algorithms. We look for a sparse representation under an already sparsifying wavelet transform by adaptively training a dictionary on the different decomposition bands of the noisy image itself, leading to a multi-scale version of the K-SVD algorithm. We then combine the single scale and multi-scale approaches by merging both outputs by weighted joint sparse coding of the images. Our experiments on natural images indicate that our method is competitive with state of the art algorithms in terms of PSNR while giving superior results with respect to visual quality.

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Computer Aided Diagnosis (CADx) systems are designed to assist doctors in medical image interpretation. However, a CADx is often thought of as a "black box" whose diagnostic decision is not intelligible to a radiologist. Therefore, a system that uses semantic image interpretation, and mimics human image analysis, has clear benefits. In this paper, we propose a system which automatically generates textual description of medical image findings, such as lesions.Having found a lesion, a radiologist examines its visual appearance characteristics to make a final diagnosis. The visual appearance is usually described in terms of semantic descriptors such as: shape, orientation, margin, boundary type, contrast enhancement, localization, mass effect on surrounding tissues, and others.The estimation of semantic descriptor values requires explicit or implicit representation by a diverse set of image measurements that describe each one of the semantic descriptors quantitatively. We use various image measurements to calculate the informative features, such as histograms of pixel values, shape and texture descriptors and others.We pose the problem of semantic description of a lesion as learning to map a set of image based informative features to a set of semantic descriptor values. A lesion is described by a set of J semantic descriptors. Semantic description of the i-th lesion is an assignment where each j-th semantic descriptor can have one of the possible discrete values corresponding to the radiological lexicon. Following the standard practice in structured learning, the energy function of the above assignment is a sum of unary and pair-wise terms [1]: