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In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In the important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the… (More)
A simple yet highly efficient artificial intelligence technique utilizing a genetic algorithm is used to register time-separated pairs of MRI data sets. To encourage others to try the approach, the algorithm is presented by way of a simple example to a 2-D data set; it is equally applicable to 3-D data. The technique is reliably found to reduce mismatch in… (More)
We address the problem of recovering a low-rank matrix that has a small fraction of its entries arbitrarily corrupted. This problem is recently attracting attention as nontrivial extension of the classical PCA (principal component analysis) problem with applications in image processing and model/system identification. It was shown that the problem can be… (More)
In this paper, we propose a novel online scheme for the sparse adaptive filtering problem. It is based on a formulation of the adaptive filtering problem as a minimization of the sum of (possibly nonsmooth) convex functions. Our proposed scheme is a time-varying extension of the so-called Douglas-Rachford splitting method. It covers many existing adaptive… (More)
We study the problem of optimizing over parameters the maximal real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic cellular decomposition in terms of Number-of-Roots-invariant.
We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic decomposition into cells in terms of Number-of-Roots-invariant.