Wavelet-Based Method for Multiscale Tomographic Reconstruction.

摘要

We represent the standard ramp filter operator of the filtered back- projection (FBP) reconstruction in different bases composed of Haar and Daubechies compactly supported wavelets. The resulting multiscale representation of the ramp filter matrix operator is approximately diagonal. The accuracy of this diagonal approximation becomes better as wavelets with larger number of vanishing moments are used. This wavelet-based representation enables us to formulate a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. Our multiscale reconstruction technique has the same computational complexity as the FBP reconstruction method. It differs from other multiscale reconstruction techniques in that (1) the object is defined through a multiscale transformation of the projection domain, and (2) we explicitly account for noise in the projection data by calculating maximum aposteriori probability (MAP) multiscale reconstruction estimates based on a chosen fractal prior on the multiscale object coefficients. The computational complexity of this MAP solution is also the same as that of the FBP reconstruction. This is in contrast to commonly used methods of statistical regularization which result in computationally intensive optimization algorithms. The framework for multiscale reconstruction presented here can find application in object feature recognition directly from projection data, and regularization of imaging problems where the projection data are noisy.