Related papers: Iterative Cauchy Thresholding: Regularisation with…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…
In the framework of sparsity-enforcing regularisation for linear inverse problems, we consider the minimisation of a square-root Lasso cost function. To solve this problem we devise a simple modification (called SQRT-ISTA) of the Iterative…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…
A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…
We propose a batchwise monotone algorithm for dictionary learning. Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose…
Modern large scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component…
We propose a sparse coefficient estimation and automated model selection procedure for autoregressive (AR) processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
We propose novel iterative learning control algorithms to track a reference trajectory in resource-constrained control systems. In many applications, there are constraints on the number of control actions, delivered to the actuator from the…
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…