Efficient algorithms for convolutional inverse problems in multidimensional imaging

Computational imaging is the process of indirectly forming images from measurements using image reconstruction algorithms that solve inverse problems. In many inverse problems in multidimensional imaging such as spectral and depth imaging, the measurements are in the form of superimposed convolutions related to the unknown image. In this thesis, we first provide a general formulation for these problems named as convolutional inverse problems, and then develop fast and efficient image reconstruction algorithms that exploit sparse models in analysis and synthesis forms. These priors involve sparsifying transforms or data-adaptive dictionaries that are patch-based and convolutional. The numerical performance of the developed algorithms is evaluated for a three-dimensional image reconstruction problem in spectral imaging. The results demonstrate the superiority of the convolutional dictionary prior over others. The developed algorithms are also extended to the compressive setting with compressed convolutional measurements.