Wavelet regularization for frequency domain volume rendering

Volume Rendering is the process of computing the 2D projections of a given 3D data along a specified viewing direction for visualizing it on a 2D screen. Rendering of medical data (MRI, CT etc ) requires discrete evaluation of the X-ray transform which involves computing the line integrals of the 3D data along a specified viewing direction. Frequency domain methods which are based on the Fourier Projection Slice Theorem are very popular due to their low computational complexity. However these suffer from various drawbacks like high interpolation cost, high memory requirement and appearing of ghosting artefacts. In this paper we present a new frequency domain volume rendering algorithm which overcomes these drawbacks to a great extent. The proposed algorithm is based on iteratively computing the inverse Fourier transform with an L1 regularization constraint on the Wavelet coefficients of the final image. The results of our algorithm have significantly fewer ghosting artefacts as compared to the results of conventional frequency domain volume rendering.