Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography.

We propose a novel multiscale penalized weighted least-squares (PWLS) method for restoration of low-dose computed tomography (CT) sinogram. The method utilizes wavelet transform for the multiscale or multi-resolution analysis on the sinogram. Specifically the Mallat-Zhong's wavelet transform is applied to decompose the sinogram to different resolution levels. At each decomposed resolution level, a PWLS criterion is applied to restore the noise-contaminated wavelet coefficients, where the penalty is adaptive to each resolution scale and the weight is adaptive to each scale and each location. The proposed PWLS method is based on the observation that (1) the noisy sinogram of low-dose CT after logarithm transform can be modeled as signal-dependent Gaussian variables and the sample variance depends on the sample mean; and (2) the noise restoration can be more effective when it is adaptive to different resolution levels. The effectiveness of the proposed multiscale PWLS method is validated by an experimental study. The gain by multiscale approach over single-scale means is quantified by noise-resolution tradeoff measures.