Imaging systems have made possible many improvements to the quality of life. I believe that with the emergence of new imaging modalities, and the enhancement of existing ones, imaging will continue to have a growing impact on life in the near future. Within this larger context, I would like to pursue research in the following areas.

Signal Processing Approaches for Imaging System Calibration
The advent of next-generation high-resolution imaging systems has posed unique challenges for system design and image formation algorithms. Imaging systems manipulate raw signal measurements resulting from physical processes to form useful imagery. Such systems utilize mathematical models for the imaging process, where the signal measurements are assumed to be made in the absence of error. When the acquired signals are not accurately described by the model, or when the measurements are contaminated with noise, the produced imagery is subject to distortions. One approach for remedying these undesired effects is to put more emphasis on the system design, which often results in expensive hardware modifications and calibration. My research interest lies in the alternative approach of applying signal processing concepts to the image formation to form useful imagery from imperfect signal measurements. The signal processing approach reduces expense and system complexity, and provides more flexibility.

I plan to investigate calibration problems in a variety of imaging modalities, and apply modern signal processing tools to decrease the time and hardware cost of the calibration procedure. I have identified scenarios in magnetic resonance imaging (MRI) where the signal processing approach can reduce system expense. One example is where the effect of field inhomogeneities must be compensated for to produce distortion-free images. Another example is in parallel MRI, where the coil sensitivities associated with multiple channel acquisitions must be properly estimated to form a useful image. In both of these applications, I have developed novel techniques that move the calibration procedure away from the physical realm and into the algorithmic realm.

A Unified Framework for Image Restoration and Enhancement
To compensate for the effects of inaccuracies in the imaging process, researchers have proposed a number of approaches to image restoration. The existing techniques are often well-motivated. However, in many cases these methods rely upon heuristics, and they sometimes fail to produce correct restorations of the image. A goal of my research is to create a more unified framework for image restoration and enhancement, from which efficient and improved methods can be derived.

I plan to systematically characterize and exploit all available assumptions in the imaging problem statement to create a more robust restoration methodology for a variety of modalities. In my thesis work within the synthetic aperture radar (SAR) autofocus paradigm, I have successfully put this methodology into practice; here, an explicit characterization of the autofocus problem structure has resulted in a new subspace-based method for correcting defocused SAR images. I have observed that a similar subspace framework can be applied to other imaging problems, particularly where there is redundancy in the data from multiple signal acquisitions of the same object, allowing powerful vector space signal processing tools to be brought to these applications.

In addition, I will exploit similarities across different imaging modalities to create a more unified framework for image restoration and enhancement. Such an approach allows tools and frameworks derived within one imaging community to be brought to another. I plan to investigate a range of practical problems in SAR, MRI, optical coherence tomography (OCT), and ultrasound through collaboration with other imaging scientists, and to develop and apply novel frameworks for these problems that will result in improved restoration procedures.