Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some s...

Non-negative matrix factorization (NMF) is an appealing technique for many audio applications, such as automatic music transcription, source separation and speech enhancement. Sparsity constraints are commonly used on the NMF model to discover a small number of dominant patterns. Recently, group sparsity has been proposed for NMF based methods, in which basis vectors belonging to a same group a...

Many bioinformatics problems deal with chemical concentrations that should be non-negative. Non-negative matrix factorization (NMF) is an approach to take advantage of non-negativity in data. We have recently developed sparse NMF algorithms via alternating nonnegativity-constrained least squares in order to obtain sparser basis vectors or sparser mixing coefficients for each sample, which lead ...

In this paper we consider the problem of minimizing a convex differentiable function subject to sparsity constraints. Such constraints are non-convex and the resulting optimization problem is known to be hard to solve. We propose a novel generalization of this problem and demonstrate that it is equivalent to the original sparsity-constrained problem if a certain weighting term is sufficiently l...

In this paper, we focus on learning product graphs from multi-domain data. We assume that the graph is formed by Cartesian of two smaller graphs, which refer to as factors. pose problem estimating factor Laplacian matrices. To capture local interactions in data, seek sparse factors and a smoothness model for propose an efficient iterative solver then extend infer multi-component with applicatio...

We consider a class of sparsity-inducing optimization problems whose constraint set is regularizer-compatible, in the sense that, becomes easy-to-project-onto after coordinate transformation induced by regularizer. Our model general enough to cover, as special cases, ordered LASSO Tibshirani and Suo (Technometrics 58:415–423, 2016) its variants with some commonly used nonconvex regularizers. Th...

Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard” sparsity. In many cases, we can represent this additional information in a structured sparsity model. Recent research has shown ...