Fan-Beam Convolution-backprojection Algorithm For Image Reconstruction Based On The Wavelet

It is well known that the Radon transformation is the CT technology mathematical foundation. Image reconstruction is reconstructing (or inversion) the image function from the Radon transform of the image function (also called projection data). The convolution back-projection reconstruction is used in CT widely because of the advantages of simple algorithm,higher image resolution, comfortable accuracy and less time consuming. As a useful tool, the wavelet transform has widely applied in the image processing.In this paper, we can obtain the fan-beam convolution-backprojection algorithm for image reconstruction based on the wavelet inversion formula of the Radon transform by one-dimensional wavelet transform on Radon transform. Our algorithm is the same simple as the classical convolution-backprojection algorithm. what's more, the algorithm can be used to reconstruct global image as well as local image, and is easier to implement utilizing less margin data. In our algorithm we use the special selection Lemaric-Meyer wavelet to improve the local reconstruction precision. Furtherly,we study the relation between the parameter's selection and the reconstruction to optimize the window function ,thus obtain the best local reconstruction with less margin data. Also,we make the error analysis and the numerical simulation ,and establish the corresponding formula.