Wavelet-based interpolation algorithm for MRI images

Three-dimensional (3D) visualization is a common tool that is used to make a correct diagnostic in medicine. However, in most medical data acquisition systems the information is obtained in a two-dimensional (2D) form. In this paper, an interpolation algorithm that works with a set of 2D images to create a reliable 3D model of a desired part of the body is presented. In most cases, the popular interpolation methods produce noticeable smoothing in the data generated that may cause the loss of important details. It is also important to perform noise reduction from the images that will serve as reference points to the interpolation. In order to deal with these two problems, we propose the use of the wavelet transform. One of the principal characteristics of the wavelet transform is the space-frequency decomposition that can be used to differentiate between the high detail areas and the smooth ones. The proposed approach then decompose the reference images into desired wavelet level to perform the analysis. Afterwards, the approximation coefficients are used to define the location of the interpolation area. The wavelet coefficients related to high frequency (vertical, horizontal, and diagonal) are used to locate the detail areas mentioned above. It is important to note that this is achieved by the use of a dynamic thresholding method that varies with the wavelet level and type of coefficients. Finally. we apply a linear or cubic spline interpolation depending on the number of reference images. (C) 2003 Elseviet B.V. All rights reserved.