Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

Regularized Compression of A Noisy Blurred Image

Both regularization and compression are important issues in image processing and have been widely approached in the literature. The usual procedure to obtain the compression of an image given through a noisy blur requires two steps: first a deblurring step of the image and then a factorization step of the regularized image to get an approximation in terms of low rank nonnegative factors. We examine here the possibility of swapping the two steps by deblurring directly the noisy factors or partially denoised factors. The experimentation shows that in this way images with comparable regularized compression can be obtained with a lower computational cost