Image Reconstruction

MRI is basically a Fourier transform-based imaging technique. Although the Fourier reconstruction algorithm is optimal in the minimum-norm, least-squares sense, it suffers from a number of practical problems, most notably, limited resolution and Gibbs ringing artifact, when the number of encodings measured is small. These problems have limited the speed, efficiency, and quantitative accuracy of MRI. Although these problems are tolerable to a large extent in conventional anatomical imaging, they have become an important obstacle for functional and metabolic imaging.

Over the past decade, the investigators of the Image Reconstruction Core have made great effort to address the image reconstruction problem from different angles, resulting in several very promising ideas and techniques that can use prior (or side) information effectively to compensate for the lack of sufficient measured imaging data, thus giving rise to much higher resolution and imaging speeds than the Fourier transform-based counterparts do.

The P41 grant brings together this group of investigators to further address the prior-driven image reconstruction problem systematically and jointly. The overall goal is to develop, implement, and validate a set of novel, advanced image reconstruction algorithms for several specific imaging applications to effectively support the research and application projects of the proposed Resource Center.

The overall project is organized according to the diagram above, which is tightly integrated with the Data Acquisition core, the Image Processing core, and the Application Projects. A distinct, novel feature of this image reconstruction core is the emphasis of using prior information. So, in contrast to the traditional image reconstruction paradigm, we assume that input to this module includes both measured data and prior/side information. Depending on the nature of the prior/side information available for a particular imaging experiment, the image reconstruction module invokes either a deterministic image model or a statistical image model to find an optimal reconstruction that is consistent with the measured data.

A powerful deterministic model to be further investigated in this Core is the generalized series model which uses prior/side information to construct a set of shaped (spatiotemporal) basis functions for efficient (parsimonious) representation of the desired image function, making highly sparse sampling of the data space possible. This model is particularly suitable for dynamic imaging in which dynamic image data and side information can be collected simultaneously for determination of the model parameters.

For another large class of imaging problems (e.g., anatomically-constrained spectroscopic imaging, perfusion-weighted imaging, diffusion tensor imaging), the a priori anatomical information is uncertain and it is best formulated as a statistical prior of the desired image function. With this prior, Bayesian inference aims to produce the most probable reconstruction, given the measured data. Therefore, in contrast to the generalized series model that handles prior and measured data in a deterministic way, Bayesian inference provides a probabilistic framework to use uncertain prior information and noisy measured data in a principled way. When effective prior is available, Bayesian image reconstruction methods can indeed overcome conventional limits of image quality, SNR and resolution.

This Core project will exploit these properties of Bayesian inference and develop practical and effective Bayesian image reconstruction methods. We expect that the generalized series and the Bayesian methods, when fully developed, will provide a set of powerful image reconstruction algorithms to effectively support the research and application projects of the proposed Center.

The proposed work in this Core is organized into three inter-dependent projects.