An Application of Wavelet Shrinkage to Tomography
This chapter introduces a wavelet-based method for reconstructing images from certain types of tomographic data. “Tomography” actually refers to a broad class of problems which have in common the fact that their data may be described as noisy observations or approximations of line integrals. The chapter considers that denoise using only wavelet shrinkage methods, but many approaches fit the general framework. It assumes the characteristics of the noise present in the modalities associated with these geometries may be quite different. Furthermore, certain edge-enhancing filters from the engineering literature have been seen to take similar advantage of the wavelet-induced sparseness in other areas of application. The indirectness of tomographic data necessitates an additional step in the typical wavelet-denoising process used with direct data. The wavelet-vaguelette decomposition, first introduced by D. L. Donoho, is a tool specifically designed for the problematic inversion step.