Tie Zhou

Ji Li, Tie Zhou

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more diffraction patterns, and the modified RAAR algorithm operates in Fourier domain rather than space domain. The local convergence of the RAAR algorithm is proved by some eigenvalue analysis. Numerical simulations is presented to demonstrate the effectiveness and stability of the algorithm compared to the HIO (Hybrid Input-Output) method. The numerical performances show the global convergence of the RAAR in our tests.

Chao Wang, Tie Zhou

In this paper, we propose a hybrid method to reconstruct the absorption coefficient by fluorescence photoacoustic tomography (FPAT), which combines a squeeze iterative method (SIM) and a nonlinear optimization method. The SIM is to use two monotonic sequences to squeeze the exact coefficient, and it quickly locates near the exact coefficient. The nonlinear optimization method is utilized to attain a higher accuracy. The hybrid method inherits the advantages of each method with higher accuracy and faster convergence. The hybrid reconstruction method is also suitable for multi-measurement. Numerical experiments show that the hybrid method converges faster than the optimization method in multi-measurement case, and that the accuracy is also higher in one-measurement case.

Shousheng Luo, Jiansheng Yang, Tie Zhou

The inversion of cosh-Hilbert transform (CHT) is one of the most crucial steps for single-photon emission computed tomography with uniform attenuation from truncated projection data. Although the uniqueness of the CHT inversion had been proved \cite{Noo2007}, there is no exact and analytic inverse formula so far. Several approximated inversion algorithms of the CHT had been developed \cite{Noo2007}\cite{You2007}. In this paper, we proposed a new numerical moment-based inversion algorithm.

Chao Wang, Tie Zhou

In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and/or scattering coefficient of biological tissues. Given the scattering coefficient, an improved fixed-point iterative method is proposed to retrieve the absorption coefficient for its cheap computational cost. And we prove the convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB) method is applied. Since the reconstruction of optical coefficients involves the solution of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is improved from~\cite{Gao}. Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are the comparative methods for QPAT in two cases.

Shousheng Luo, Yanchun Zhang, Tie Zhou et al.

In this paper, we investigate how to determine a better perturbation for superiorized iteration. We propose to seek the perturbation by proximal point method. In our method, the direction and amount of perturbation are computed simultaneously. The convergence conditions are also discussed for bounded perterbation resilence iteration. Numerical experiments on simulated XCT projection data show that the proposed method improves the convergence rate and the image quality.