arXiv subjects

Yizhuang Song

Publications and source records attributed to Yizhuang Song.

3 recordsLinked to original sources

arXiv2026

A hybrid statistical sampling and iterative regularization method in sparse-view computed tomography

Sparse-view computed tomography (CT) is an effective method to reduce the radiation exposure in medical imaging. To reduce the severe streaking artifacts that occur in reconstructed images due to violation of the Nyquist/Shannon sampling criterion, regularization is widely used to minimize the cost function. However, the iterative methods may lead to the accumulation and propagation of errors, which adversely affects the restoration of image details and textures. In this paper, we propose a hybrid model that integrates statistical sampling with iterative regularization to simultaneously shorten the sampling time and enhance the reconstruction quality. The proposed method is validated using three datasets: the Shepp-Logan phantom, the actual walnut X-ray projections provided by the Finnish Inverse Problems Society, and the clinical lung CT images.

physics.med-ph↗

arXiv2022

A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography

This paper proposes a nonlinear weighted anisotropic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the detected objects) into the EIT reconstruction process, aiming to preserve the conductivity profiles (to be detected). We study the NWATV image reconstruction by employing a novel soft thresholding based reformulation included in the alternating direction method of multipliers (ADMM). To evaluate the proposed approach, 2D and 3D numerical experiments and human EIT lung imaging are carried out. It is demonstrated that the properties of the internal inhomogeneity are well preserved and improved with the proposed regularization approach, in comparison to traditional total variation (TV) and recently proposed fidelity embedded regularization approaches. Owing to the simplicity of the proposed method, the computational cost is significantly decreased compared with the well established primal-dual algorithm. Meanwhile, it was found that the proposed regularization method is quite robust to the measurement noise, which is one of the main uncertainties in EIT.

math.AP↗

arXiv2022

Convergence analysis of the harmonic $B_z$ algorithm with single injection current in MREIT

Magnetic resonance electrical impedance tomography (MREIT) aims to recover the electrical conductivity distribution of an object using partial information of magnetic flux densities inside the tissue which can be measured using an MRI scanner, with the advantage that a higher spatial resolution of conductivity image can be provided than existing EIT techniques involving surface measurements. Traditional MREIT reconstruction algorithms use two data sets obtained with two linearly independent injected currents. However, injection of two currents is often not possible in applications such as transcranial electrical stimulation. Recently, we proposed an iterative conductivity reconstruction algorithm called the single current harmonic $B_z$ algorithm that demonstrated satisfactory performance in numerical and phantom tests. In this paper, we provide a rigorous mathematical analysis of the convergence of the iterative sequence for realizing this algorithm. We prove that, applying some mild conditions on the exact conductivity, the iterative sequence converges to the true solution within an explicit error bound. Such theoretical results substantiate the reasonability and efficiency of the proposed algorithm. We also provide more numerical evidence to validate these theoretical results.

math.AP↗