Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based...

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting coupling of non-vanishing components. These ...

The image information acquisition ability of a conventional camera is usually much lower than the Shannon Limit since it does not make use of the correlation between pixels of image data. Applying a random phase modulator to code the spectral images and combining with compressive sensing (CS) theory, a spectral camera based on true thermal light ghost imaging via sparsity constraints (GISC spec...

Quantities of interest appearing in concrete applications often possess sparse expansions with respect to a preassigned frame. Recently, there were introduced sparsity measures which are typically constructed on the basis of weighted l1 norms of frame coefficients. One can model the reconstruction of a sparse vector from noisy linear measurements as the minimization of the functional defined by...

We study a deep linear network expressed under the form of a matrix factorization problem. It takes as input a matrix X obtained by multiplying K matrices (called factors and corresponding to the action of a layer). Each factor is obtained by applying a fixed linear operator to a vector of parameters satisfying a sparsity constraint. In machine learning, the error between the product of the est...

Background subtraction has been widely investigated in recent years. Most previous work has focused on stationary cameras. Recently, moving cameras have also been studied since videos from mobile devices have increased significantly. In this paper, we propose a unified and robust framework to effectively handle diverse types of videos, e.g., videos from stationary or moving cameras. Our model i...

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically relevant computed controls but adds more challenges to the numerical solution of these problems. The needed L1-terms as well as additional inclusion of box cont...

Finding a sparse representation of a possibly noisy signal can be modeled as a variational minimization with `q-sparsity constraints for q less than one. Especially for real-time and on-line applications, one requires fast computations of these minimizers. However, there are no sufficiently fast algorithms, and to circumvent this limitation, we consider minimization up to a constant factor. We ...

Deformable models integrate bottom-up information derived from image appearance cues and top-down priori knowledge of the shape. They have been widely used with success in medical image analysis. One limitation of traditional deformable models is that the information extracted from the image data may contain gross errors, which adversely affect the deformation accuracy. To alleviate this issue,...

We propose new families of models and algorithms for high-dimensional nonparametric learning with joint sparsity constraints. Our approach is based on a regularization method that enforces common sparsity patterns across different function components in a nonparametric additive model. The algorithms employ a coordinate descent approach that is based on a functional soft-thresholding operator. T...