Simultaneous Sensing Error Recovery and Tomographic Inversion Using an Optimization-Based Approach

Abstract

Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental conditions, which are often beyond the capabilities of the state-of-the-art reconstruction techniques such as regularizations. Because they can lead to reduced spatial resolution and even misinterpretation of the underlying sample structures, these errors present a fundamental obstacle to full realization of the capabilities of next-generation physical imaging. In this work, we develop efficient and explicit recovery schemes of the most common experimental error: movement of the center of rotation during the experiment. We formulate new physical models to capture the experimental setup, and we devise new mathematical optimization formulations for reliable inversion of complex samples. We demonstrate and validate the efficacy of our approach on synthetic data under known perturbations of the center of rotation.

Accelerating error correction in tomographic reconstruction

“…We formulate the center of rotation drifts based on the model proposed in ref. 27 (see "Methods"). Briefly, we note that each center of rotation drift is parameterized by a scalar parameter (thus, the center of rotation drifts for a complete scan is represented by a vector of these parameters).…”

“…In some cases, multiscale methods are employed that downsample the projections and align them at the lower resolution prior to working with the full-scale data 26 . Optimization-based methods seek to minimize some cost function that accounts for the drifts and reconstruction simultaneously, in which gradient-based methods are often employed as the underlying solver 23,[27][28][29][30] .…”

libEnsemble: A Library to Coordinate the Concurrent Evaluation of Dynamic Ensembles of Calculations

“…As an example, we note that controlled environment inverse problems such as those arising from 3D tomographic imaging can already saturate current resources [37]. Efficiently accounting for imperfect experimental conditions and understanding key uncertainties necessitate performing not just one expensive inversion but many inversions for ensembles data that are adaptively refined [38,39].…”

Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography

“…N = 64), which are variations of the Shepp-Logan Phantom (see Figure 4.1 for two representative samples). Given N θ and N τ , we then simulate their corresponding sinograms f based on standard discrete Radon transform [6]. Next we add 0.1% Gaussian noise to each sinogram, respectively.…”