Quasi Monte Carlo-based isotropic distribution of gradient directions for improved reconstruction quality of 3D EPR imaging

Abstract

In continuous wave (CW) electron paramagnetic resonance imaging (EPRI), high quality of reconstructed image along with fast and reliable data acquisition is highly desirable for many biological applications. An accurate representation of uniform distribution of projection data is necessary to ensure high reconstruction quality. The current techniques for data acquisition suffer from nonuniformities or local anisotropies in the distribution of projection data and present a poor approximation of a true uniform and isotropic distribution. In this work, we have implemented a technique based on Quasi-Monte Carlo method to acquire projections with more uniform and isotropic distribution of data over a 3D acquisition space. The proposed technique exhibits improvements in the reconstruction quality in terms of both mean-square-error and visual judgment. The effectiveness of the suggested technique is demonstrated using computer simulations and 3D EPRI experiments. The technique is robust and exhibits consistent performance for different object configurations and orientations.

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging

“…Further, since the distribution of the data is structured, the reconstruction is sensitive to the alignment of the sampling grid and the distribution of information content. Therefore, the reconstruction may possess an orientational bias, and rotating the object for a given sampling may change the reconstruction quality considerably [17]. As a result, the reconstruction quality may vary with the number of acquired projections, configuration of the object to be imaged, and the orientation of the sampling grid relative to the phantom.…”

“…Bak et al [27] has numerically analyzed the performances of various powder averaging methods to compare their insensitivities to the orientation of the object from which the spectra is observed and reported that the performance of so called REPULSION technique, which is similar to the one presented here, is on par or superior to the other popular techniques. More importantly, most of these other methods are only valid for S 2 and their extension to S 3 is not obvious, which is also the case for the distribution based on two successive Fibonacci numbers, whose feasibility for 3D spatial EPRI has been recently reported [17]. In recent years, spherical designs [28] have received a great deal of attention because they generate optimal distributions (in terms of zero integration error) for any integrand that can be approximated by a polynomial of limited degree.…”

“…In every iteration, particles are moved in the direction d to reduce the net U of the system. (17) where is the tangential component of force acting on the ith particle due to the rest of the particles, and β is a constant controlling the amount of displacement for the particles. The antipodal symmetry introduced in the initialization was kept intact during the gradient descent by tying the antipodal points together and moving them in pairs.…”

“…2. The computation of Voronoi cells, also used to assign relative weight to each projection before applying the FBP, over S 3 is similar to a previously reported procedure for S 2 [17].…”

“…Equal solid angle (ESA)-based sampling for 3D EPRI has been presented earlier [8] which results in an estimated reduction of 30% in the acquisition time over equal linear angle (ELA)-based sampling. A further improvement in the reconstruction has been observed [17] by obtaining a more uniform distribution of the gradient.…”