A fast image reconstruction algorithm based on penalized-likelihood estimate

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.

Block matching 3D random noise filtering for absorption optical projection tomography

Absorption and emission optical projection tomography (OPT), alternatively referred to as optical computed tomography (optical-CT) and optical-emission computed tomography (optical-ECT), are recently developed three-dimensional imaging techniques with value for developmental biology and ex vivo gene expression studies. The techniques' principles are similar to the ones used for x-ray computed tomography and are based on the approximation of negligible light scattering in optically cleared samples. The optical clearing is achieved by a chemical procedure which aims at substituting the cellular fluids within the sample with a cell membranes' index matching solution. Once cleared the sample presents very low scattering and is then illuminated with a light collimated beam whose intensity is captured in transillumination mode by a CCD camera. Different projection images of the sample are subsequently obtained over a 360 degrees full rotation, and a standard backprojection algorithm can be used in a similar fashion as for x-ray tomography in order to obtain absorption maps. Because not all biological samples present significant absorption contrast, it is not always possible to obtain projections with a good signal-to-noise ratio, a condition necessary to achieve high-quality tomographic reconstructions. Such is the case for example, for early stage's embryos. In this work we demonstrate how, through the use of a random noise removal algorithm, the image quality of the reconstructions can be considerably improved even when the noise is strongly present in the acquired projections. Specifically, we implemented a block matching 3D (BM3D) filter applying it separately on each acquired transillumination projection before performing a complete three-dimensional tomographical reconstruction. To test the efficiency of the adopted filtering scheme, a phantom and a real biological sample were processed. In both cases, the BM3D filter led to a signal-to-noise ratio increment of over 30 dB on severe noise-affected reconstructions revealing original-noise-hidden-image details. These results show the utility of the BM3D approach for OPT under typical conditions of very low light absorption, suggesting its implementation as an efficient alternative to other filtering schemes such as for example the median filter.