Jijun Liu

Zongjiang Tu, Chen Jiang, Yu Guan et al.

Decreasing magnetic resonance (MR) image acquisition times can potentially make MR examinations more accessible. Prior arts including the deep learning models have been devoted to solving the problem of long MRI imaging time. Recently, deep generative models have exhibited great potentials in algorithm robustness and usage flexibility. Nevertheless, none of existing schemes can be learned or employed to the k-space measurement directly. Furthermore, how do the deep generative models work well in hybrid domain is also worth being investigated. In this work, by taking advantage of the deep energy-based models, we propose a k-space and image domain collaborative generative model to comprehensively estimate the MR data from under-sampled measurement. Experimental comparisons with the state-of-the-arts demonstrated that the proposed hybrid method has less error in reconstruction accuracy and is more stable under different acceleration factors

Zhe Wang, Ahcene Ghandriche, Jijun Liu

We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger integral equation for scattering wave in inhomogeneous medium, we firstly develop an efficient approximate scheme for computing the scattered wave as well as its far-field pattern for any droplet located in the inhomogeneous background medium. By establishing the approximate relation between the far-field patterns of the scattered wave before and after the injection of a droplet, the scattered wave of the inhomogeneous medium after injecting the droplet is represented by a measurable far-field patterns, and consequently the inhomogeneity of the medium can be reconstructed from the Helmholtz equation. Finally, the reconstruction process in terms of the dual reciprocity method is proposed to realize the numerical algorithm for recovering the bulk modulus function inside a bounded domain in three dimensional space, by moving the droplet inside the bounded domain. Numerical implementations are given using the simulation data of the far-field pattern to show the validity of the reconstruction scheme, based on the mollification scheme for dealing with the ill-posedness of this inverse problem.