Modular Forward Models and Algorithms for Regularized Reconstruction of Time-Space Scalar and Vector Fields

The framework of model-based iterative reconstruction (MBIR) is a versatile but powerful technique for solving a wide variety of inverse problems in imaging. In MBIR, image reconstruction works by finding the solution that minimizes a cost function consisting of the sum of a forward model and a prior model term. The physics of imaging is captured by the forward model and image sparsity is modeled by the prior model. The challenge lies in the design of physically accurate forward models and optimization algorithms for reconstruction. First, we solve the inverse problem associated with traditional X-ray computed tomography imaging of time-varying samples that uses a linear and sparse model for the forward problem. We formulate a 4D MBIR algorithm for reconstruction that when combined with an interlaced view sampling strategy achieves dramatic improvements in spatial and temporal resolution of reconstructions. However, this algorithm cannot be used for more complex forms of non-sparse or non-linear tomographic imaging systems. In the area of magnetic imaging using vector field electron tomography (VFET), traditional algorithms do not permit us to directly reconstruct the sample\u27s magnetization due to the non-sparse and complex nature of the forward problem. We formulate the first algorithm ever to perform 3D reconstruction of the sample\u27s magnetization using the MBIR framework. Next, we solve the inverse problem in X-ray phase contrast tomography (XPCT) using a non-linear forward model that accounts for X-ray refraction and diffraction. We show that our algorithm accurately reconstructs the sample and does not adversely constrain the experimental conditions by using a linear approximation to the forward model. Both the algorithms designed for VFET and XPCT use modular forward models that permit us to solve the original inverse problem by iteratively solving multiple but simpler optimization problems using efficient algorithms. We generalize this approach and call it the framework of plug-and-play forward models for MBIR. We show that plug-and-play forward modeling allows us to solve complex inverse problems using independent software modules that solve simpler inverse problems