Proximal Methods for Hierarchical Sparse Coding

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally organize in a prespecified arborescent structure, leading to a better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Reconstructive Sparse Code Transfer for Contour Detection and Semantic Labeling

We frame the task of predicting a semantic labeling as a sparse reconstruction procedure that applies a target-specific learned transfer function to a generic deep sparse code representation of an image. This strategy partitions training into two distinct stages. First, in an unsupervised manner, we learn a set of generic dictionaries optimized for sparse coding of image patches. We train a multilayer representation via recursive sparse dictionary learning on pooled codes output by earlier layers. Second, we encode all training images with the generic dictionaries and learn a transfer function that optimizes reconstruction of patches extracted from annotated ground-truth given the sparse codes of their corresponding image patches. At test time, we encode a novel image using the generic dictionaries and then reconstruct using the transfer function. The output reconstruction is a semantic labeling of the test image. Applying this strategy to the task of contour detection, we demonstrate performance competitive with state-of-the-art systems. Unlike almost all prior work, our approach obviates the need for any form of hand-designed features or filters. To illustrate general applicability, we also show initial results on semantic part labeling of human faces. The effectiveness of our approach opens new avenues for research on deep sparse representations. Our classifiers utilize this representation in a novel manner. Rather than acting on nodes in the deepest layer, they attach to nodes along a slice through multiple layers of the network in order to make predictions about local patches. Our flexible combination of a generatively learned sparse representation with discriminatively trained transfer classifiers extends the notion of sparse reconstruction to encompass arbitrary semantic labeling tasks.Comment: to appear in Asian Conference on Computer Vision (ACCV), 201

Multi-task Image Classification via Collaborative, Hierarchical Spike-and-Slab Priors

Promising results have been achieved in image classification problems by exploiting the discriminative power of sparse representations for classification (SRC). Recently, it has been shown that the use of \emph{class-specific} spike-and-slab priors in conjunction with the class-specific dictionaries from SRC is particularly effective in low training scenarios. As a logical extension, we build on this framework for multitask scenarios, wherein multiple representations of the same physical phenomena are available. We experimentally demonstrate the benefits of mining joint information from different camera views for multi-view face recognition.Comment: Accepted to International Conference in Image Processing (ICIP) 201

Multimodal Multipart Learning for Action Recognition in Depth Videos

The articulated and complex nature of human actions makes the task of action recognition difficult. One approach to handle this complexity is dividing it to the kinetics of body parts and analyzing the actions based on these partial descriptors. We propose a joint sparse regression based learning method which utilizes the structured sparsity to model each action as a combination of multimodal features from a sparse set of body parts. To represent dynamics and appearance of parts, we employ a heterogeneous set of depth and skeleton based features. The proper structure of multimodal multipart features are formulated into the learning framework via the proposed hierarchical mixed norm, to regularize the structured features of each part and to apply sparsity between them, in favor of a group feature selection. Our experimental results expose the effectiveness of the proposed learning method in which it outperforms other methods in all three tested datasets while saturating one of them by achieving perfect accuracy