A three-step framework for noisy image segmentation in brain MRI

TL;DR

Brain MRI segmentation is challenged by intensity inhomogeneity, noise, and artifacts. The authors propose SegMIC2T, a three-step framework that combines cartoon-texture decomposition, a modified MICO bias-correction model, and clustering-based segmentation, solved via a multi-block ADMM with multiaffine constraints. A quadratic surrogate of KL divergence is used for the texture penalty, and convergence of the ADMM scheme is analyzed under a sufficiently large penalty parameter $\rho$, with empirical evidence of convergence. Numerical experiments on BrainWeb data show SegMIC2T attaining superior segmentation metrics, particularly for CSF, compared with MICO and TVMICO across varied noise and bias levels. The work advances robust brain MRI segmentation by integrating noise localization, bias correction, and efficient optimization, with promising directions for higher-dimensional extensions and alternative basis representations.

Abstract

Magnetic Resonance Imaging (MRI) is essential for noninvasive generation of high-quality images of human tissues. Accurate segmentation of MRI data is critical for medical applications like brain anatomy analysis and disease detection. However, challenges such as intensity inhomogeneity, noise, and artifacts complicate this process. To address these issues, we propose a three-step framework exploiting the idea of Cartoon-Texture evolution to produce a denoised and debiased MR image. The first step involves identifying statistical information about the nature of the noise using a suitable image decomposition. In the second step, a multiplicative intrinsic component model is applied to a smother version of the image, simultaneously reconstructing the bias and removing noise using noise information from the previous step. At the final step, standard clustering techniques are used to create an accurate segmentation. Additionally, we present a convergence analysis of the ADMM scheme for solving the nonlinear optimization problem with multiaffine constraints resulting from the second step. Numerical tests demonstrate the effectiveness of our framework, especially in noisy brain segmentation, both from a qualitative and a quantitative viewpoint, compared to similar methods.

Figures (6)

• Figure 1: The original brain MRI coming from BrainWeb database (slice n. 91), followed by (from left to right) its corrupted version with noise and bias, the ground truth of the brain selected ROIs: cerebrospinal fluid in dark grey, gray matter in grey, and white matter in white. The last two images depict cartoon and texture components of the MRI scan, respectively.
• Figure 2: History of the objective function value and the change in the reconstructed MRI scan for 8 different instances of the multiaffine-constrained problem.
• Figure 3: Workflow of the SegMIC2T algorithm performed on slice060 with low (top row) and moderate (bottom row) level of the combined artifacts. We indicate the noise percentage with np and with bl the bias level, respectively.
• Figure 4: The first row shows the ground-truth of the BrainWeb slice n. 91 and the binary masks of the three tissues, CSF, GM, and WM. The second row exhibits the corresponding MRI slice corrupted by the following three combinations of the noise percentage, np, and bias level, bl, (from left to right): $5\%$ noise and $0-$level bias, $7\%$ noise and $20-$level bias, and $9\%$ noise and $40-$level bias. The third and fourth rows present the segmentation results produced by MICO, and SegMIC2T, respectively.
• Figure 5: Comparison of MICO, TVMICO and SegMIC2CT on the segmentation of slice064 with slight and moderate combined artifacts. np: noise percentage, bl: bias level.

Theorems & Definitions (10)

• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 4
• proof
• Remark 2