[Paper Review] Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CT

Qiaoqiao Ding, Yong Long+2 more|arXiv (Cornell University)|Jan 19, 2018

Medical Imaging Techniques and Applications2 references19 citations

TL;DR

This paper proposes a novel statistical image reconstruction method, MPG (Mixed Poisson-Gaussian), for ultra-low-dose X-ray CT that directly models raw measurements using a mixed Poisson-Gaussian distribution to handle both quantum and electronic noise. By avoiding pre-processing of non-positive values and using ADMM to solve a reweighted least squares cost function with edge-preserving regularization, MPG reduces noise and bias more effectively than FBP, PWLS, and SP methods in simulated and clinical data.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of non-positive raw measurements in ultra-low-dose CT (ULDCT) caused by electronic noise at low photon counts.
• To develop a statistical image reconstruction framework that accurately models both quantum (Poisson) and electronic (Gaussian) noise in raw CT data.
• To eliminate the need for pre-processing steps like replacing negative values, which distort statistical properties and introduce bias.
• To improve image quality by reducing noise and bias in ULDCT reconstructions compared to conventional methods such as FBP, PWLS, and SP.
• To enable robust reconstruction under varying electronic noise levels using a unified statistical model and efficient optimization.

Proposed method

• The MPG method models raw CT measurements using a mixed Poisson-Gaussian distribution that accounts for both quantum noise and electronic noise in the detector system.
• It formulates a reweighted least squares data-fidelity term based on the likelihood of the mixed Poisson-Gaussian distribution to enable tractable optimization.
• The method incorporates an edge-preserving regularization term and a non-negativity constraint to enhance image quality and preserve anatomical details.
• An Alternating Direction Method of Multipliers (ADMM) algorithm is employed to decompose the complex optimization problem into simpler, solvable sub-problems.
• The algorithm is initialized with FBP or PWLS reconstructions and iteratively updates variables to minimize the MPG cost function.
• The approach directly uses negative and zero values in raw data without replacement or clipping, preserving statistical integrity.

Experimental results

Research questions

• RQ1 Can a statistical image reconstruction method effectively model raw CT measurements that include negative and zero values due to electronic noise at ultra-low doses?
• RQ2 How does the mixed Poisson-Gaussian noise model compare to standard Poisson or shifted Poisson models in preserving image accuracy under ultra-low-dose conditions?
• RQ3 To what extent can the MPG method reduce noise and bias in reconstructed images compared to FBP, PWLS, and SP methods in low-dose scenarios?
• RQ4 How robust is the MPG method to varying levels of electronic noise in clinical and simulated data?
• RQ5 Can the MPG method maintain image quality when the number of projection views is reduced, enabling further dose reduction?

Key findings

• For a 3D cone-beam data set with $ I_i = 5 \times 10^3 $, MPG achieved the lowest RMSE of 64.4 HU, outperforming FBP (126.2), PWLS (145.1), and SP (70.7).
• In the same data set, MPG achieved the highest SNR of 16.2 dB, significantly outperforming FBP (-0.8 dB), PWLS (9.1 dB), and SP (15.4 dB).
• On synthetic helical data with $ I_i = 10^4 $ and $ \sigma^2 = 60^2 $, MPG reduced RMSE to 75.5 HU, compared to 83.0 HU for SP and 126.2 HU for FBP.
• With $ \sigma^2 = 60^2 $, MPG achieved an SNR of 14.8 dB, outperforming SP (14.0 dB), PWLS (6.9 dB), and FBP (-3.1 dB).
• MPG reduced the percentage of non-positive measurements from 6.9% to effectively usable data by preserving information instead of discarding or replacing values.
• Visual results showed that MPG produced images with less noise and lower bias than FBP, PWLS, and SP, especially under high electronic noise conditions.