Gap compensation during PET image reconstruction by constrained, total variation minimization.

PURPOSE: Positron emission tomography (PET) is a noninvasive molecular imaging tool with various clinical and preclinical applications. The polygonal structure of small-diameter PET scanners that are designed for specific purposes can lead to gaps between the detector modules and result in loss of PET data during measurement. In the current study, the authors applied the compressed sensing (CS)-based total variation (TV) minimization method to PET image reconstructions to reduce the artifacts caused by gaps in small-diameter PET systems. METHODS: The first step in each iteration estimates whether an image is consistent with the measured PET data using the existing common reconstruction algorithms (ART, OSEM, and RAMLA). The second step recovers sparsity in the gradient domain of the image by minimizing the TV of an estimated image. The authors evaluated the gap-compensable reconstruction algorithms with uniform disk and Shepp-Logan phantoms by simulating sinograms which contained Poisson random noise and a data loss due to detector gaps. In addition, these methods were applied to real high resolution research tomography (HRRT)-like sinograms of human brain and uniform phantom. A comparison with other methods for gap compensation prior to or during image reconstruction was also made. Quantitative evaluations were performed by computing the uniformity, root mean squared error, and difference between the reconstructed images of nongapped and gapped sinograms. RESULTS: The simulation results showed that the gap-compensable methods incorporating TV minimization could control gap artifacts, as well as Poisson random noise. In particular, OSEM-TV and RAMLA-TV showed distinct potential via the properties of convergence and robustness to different noise levels and gap angle. CONCLUSIONS: A TV minimization strategy incorporated into commonly used PET reconstruction algorithms was useful for reducing the occurrence of artifacts due to gaps between detector modules in small-diameter PET scanners.

Ramp-preserving denoising for conductivity image reconstruction in magnetic resonance electrical impedance tomography.

In magnetic resonance electrical impedance tomography, among several conductivity image reconstruction algorithms, the harmonic B(z) algorithm has been successfully applied to B(z) data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in B(z) data. Especially, in in vivo animal and human experiments where injection current amplitudes are limited within a few milliampere at most, measured B(z) data tend to have a low SNR. In addition, magnetic resonance (MR) signal void in outer layers of bones and gas-filled organs, for example, produces salt-pepper noise in the MR phase and, consequently, B(z) images. The B(z) images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in B(z) images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. In this paper, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing. After validating the proposed denoising method through numerical simulations, we applied it to in vivo animal imaging experiments. Both numerical simulation and experimental results show significant improvements in the quality of reconstructed conductivity images.