A WAVELET-BASED METHOD FOR MULTISCALE TOMOGRAPHIC RECONSTRUCTION

We represent the standard ramp filter operator of the filtered-back-pr ojection (FBP) reconstruction in different bases composed of Haar and Daubechies compactly supported wavelets. The resulting multiscale repr esentation of the ramp-filter matrix operator is approximately diagona l, The accuracy of this diagonal approximation becomes better as wavel ets with larger numbers of vanishing moments are used. This wavelet-ba sed representation enables us to formulate a multiscale tomographic re construction technique in which the object is reconstructed at multipl e scales or resolutions, A complete reconstruction is obtained by comb ining the reconstructions at different scales, Our multiscale reconstr uction technique has the same computational complexity as the FBP reco nstruction method, It differs from other multiscale reconstruction tec hniques in that 1) the object is defined through a one--dimensional mu ltiscale transformation of the projection domain, and 2) we explicitly account for noise in the projection data by calculating maximum a pos teriori probability (MAP) multiscale reconstruction estimates based on a chosen fractal prior on the multiscale object coefficients, The com putational complexity of this maximum a posteriori probability (MAP) s olution is also the same as that of the FBP reconstruction. This resul t is in contrast to commonly used methods of statistical regularizatio n, which result in computationally intensive optimization algorithms.