Multiscale Penalized Weighted Least-Squares Sinogram Restoration for Low-Dose X-Ray Computed Tomography

In this paper, 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 multiresolution 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 updated by an exponential relationship between the data variance and mean at each scale and location. The proposed PWLS method is based on the observations that 1) noise in the CT sinogram after logarithm transform and calibration can be modeled as signal-dependent variables and the sample variance depends on the sample mean by an exponential relationship; and 2) noise reduction can be more effective when it is adaptive to different resolution levels. The effectiveness of the proposed multiscale PWLS method is validated by both computer simulations and experimental studies. The gain by multiscale approach over single scale means is quantified by noise-resolution tradeoff measures.