Statistical image reconstruction (SIR) methods for X-ray CT produce
high-quality and accurate images, while greatly reducing patient exposure to
radiation. When further reducing X-ray dose to an ultra-low level by lowering
the tube current, photon starvation happens and electronic noise starts to
dominate, which introduces negative or zero values into the raw measurements.
These non-positive values pose challenges to post-log SIR methods that require
taking the logarithm of the raw data, and causes artifacts in the reconstructed
images if simple correction methods are used to process these non-positive raw
measurements. The raw data at ultra-low dose deviates significantly from
Poisson or shifted Poisson statistics for pre-log data and from Gaussian
statistics for post-log data. This paper proposes a novel SIR method called MPG
(mixed Poisson-Gaussian). MPG models the raw noisy measurements using a mixed
Poisson-Gaussian distribution that accounts for both the quantum noise and
electronic noise. MPG is able to directly use the negative and zero values in
raw data without any pre-processing. MPG cost function contains a reweighted
least square data-fit term, an edge preserving regularization term and a
non-negativity constraint term. We use Alternating Direction Method of
Multipliers (ADMM) to separate the MPG optimization problem into several
sub-problems that are easier to solve. Our results on 3D simulated cone-beam
data set and synthetic helical data set generated from clinical data indicate
that the proposed MPG method reduces noise and decreases bias in the
reconstructed images, comparing with the conventional filtered back projection
(FBP), penalized weighted least-square (PWLS) and shift Poisson (SP) method for
ultra-low dose CT (ULDCT) imaging.

本文提出了一种新的统计影像重建方法，称为 MPG (混合泊松 - 高斯) 方法，其可以应对 X-ray CT 在超低剂量下的成像问题，并且证明此方法可以降低图像重建中的噪声和偏差。

使用混合泊松高斯噪声模型进行 X 射线 CT 图像的统计重建

Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise  Model for X-Ray CT

Due to the potential risk of inducing cancers, radiation dose of X-ray CT
should be reduced for routine patient scanning. However, in low-dose X-ray CT,
severe artifacts usually occur due to photon starvation, beamhardening, etc,
which decrease the reliability of diagnosis. Thus, high quality reconstruction
from low-dose X-ray CT data has become one of the important research topics in
CT community. Conventional model-based denoising approaches are, however,
computationally very expensive, and image domain denoising approaches hardly
deal with CT specific noise patterns. To address these issues, we propose an
algorithm using a deep convolutional neural network (CNN), which is applied to
wavelet transform coefficients of low-dose CT images. Specifically, by using a
directional wavelet transform for extracting directional component of artifacts
and exploiting the intra- and inter-band correlations, our deep network can
effectively suppress CT specific noises. Moreover, our CNN is designed to have
various types of residual learning architecture for faster network training and
better denoising. Experimental results confirm that the proposed algorithm
effectively removes complex noise patterns of CT images, originated from the
reduced X-ray dose. In addition, we show that wavelet domain CNN is efficient
in removing the noises from low-dose CT compared to an image domain CNN. Our
results were rigorously evaluated by several radiologists and won the second
place award in 2016 AAPM Low-Dose CT Grand Challenge. To the best of our
knowledge, this work is the first deep learning architecture for low-dose CT
reconstruction that has been rigorously evaluated and proven for its efficacy.

为了应对 X-ray CT 低剂量扫描中复杂噪声的问题，提出了一种基于方向小波变换和深度卷积网络的去噪算法，实验结果证实该算法能够有效去除噪声并在 CT 重建中取得良好效果。