Improvement of medical image resolution using an extended 2D factorized form complex number parametric model

We showed that multidimensional parametric modeling is an interesting method to improve the spatial resolution of ultrasound images. The major issue is to estimate simultaneously the model parameters and orders. We recently proposed a least-square-based technique which is able to estimate both orders and parameters of a general N-dimensional auto-regressive (AR) model. This method has been extended to an instrumental variable-like approach accounting for the characteristics of ultrasound images. The proposed method is based on specific factorization of the regression matrix. The methodology developed may be applied to an AR model of any dimension (3 or 4D). However, we focus here on the 2D situation and show improvement of resolution of ultrasound images by this method.