Regularized Computed Tomography using Complex Wavelets

Reconstructing low-dose computed tomography (CT) images is an unstable inverse problem, due to the presence of noise. To address this problem, we propose a new regularized reconstruction method that combines features from the Filtered Back-Projection (FBP) algorithm and regularization theory. The filtering part of FBP comprises Fourier-domain inversion followed by noise suppression based on thresholding procedure in complex wavelet domain. The proposed method exploits the properties of dual tree complex wavelet transform (DT-CWT) to remove blurring and noise without the need for assuming a specific noise model. Furthermore, it uses an adaptive shrinkage function based on median, mean and standard deviation of wavelet coefficients to suppress noise while preserving the sharpness of the reconstructed image. The efficacy of the proposed method was assessed with projections simulated from Shepp-Logan Phantom. Simulation results confirm that the proposed method produces consistently good reconstruction in terms of suppressing noise and preserving resolution in the reconstructed images.