Inverse Surfacelet Transform for Image Reconstruction With Constrained Conjugate Gradient Methods

Abstract

Image reconstruction is the transformation process from a reducedorder representation to the original image pixel form. In materials characterization, it can be utilized as a method to retrieve material composition information. In our previous work, a surfacelet transform was developed to efficiently represent boundary information in material images with surfacelet coefficients. In this paper, new constrainedconjugategradient based image reconstruction methods are proposed as the inverse surfacelet transform. With geometric constraints on boundaries and internal distributions of materials, the proposed methods are able to reconstruct material images from surfacelet coefficients as either lossy or lossless compressions. The results between the proposed and other optimization methods for solving the leastsquare error inverse problems are compared.