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In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation Ax=b, where A is an m×n full-rank matrix, b is a column-vector of dimension m, and m (the number of equations) is larger tha ...
In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation Ax=b, where A is an m×n full-rank matrix, b is a column-vector of dimension m, and m (the number of equations) is larger tha ...
A novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated ...
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ℓ1 minimisation. The problem is to identify a dictionary \dico from a set of training samples \Y knowing that \Y=\dico\X ...
This paper proposes a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an l1 regularization. Ho ...
Institute of Electrical and Electronics Engineers2013
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ℓ1-minimisation. The problem can also be seen as factorising a \ddim×\nsig matrix $Y=(y_1 \ldots y_\nsig), , y_n\in \R^\ ...
Institute of Electrical and Electronics Engineers2010
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ell1 minimisation, or more precisely the problem of identifying a dictionary dico from a set of training samples Y knowing that $ ...
We develop an algorithm for the solution of indefinite least-squares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorizatio ...
Society for Industrial and Applied Mathematics1998
This work studies the mean-square stability of stochastic gradient algorithms without resorting to slow adaptation approximations or to the widely used, yet rarely applicable, independence assumptions. This is achieved by reducing the study of the mean-squ ...
We derive a stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitz, and product of two Toeplitz matrices). The algorithm is based on a modified fast QR factorization of ...
Society for Industrial and Applied Mathematics1998
