Automatic rank estimation of Parafac decomposition and application to multispectral image wavelet denoising

There are two main contributions in this paper. Firstly, we estimate the rank for the truncation of the Parafac decomposition in an optimal sense. For this, we propose a least squares criterion and justify the choice of the fast Nelder-Mead method to minimize this criterion. Secondly, we combine the truncation of the Parafac decomposition with multidimensional wavelet packet transform. A single rank value is estimated for each decomposition level, which simplifies the implementation. We exemplify the proposed method with an application to multispectral image denoising: we study the performance of the proposed method based on Parafac decomposition, compared to ForWaRD.