2020/06/15 by Didem Dogan, Dogan, Didem, Figen S. Öktem +2 · 1 citation
Engineering · Medicine · Physics and Astronomy · #FOS: Electrical engineering #FOS: Physical sciences #Image and Video Processing (eess.IV) #Medical Imaging Techniques and Applications #Optics (physics.optics) #Photoacoustic and Ultrasonic Imaging #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #eess.IV #eess.SP #electronic engineering #information engineering #physics.optics
paper · pdf · doi:10.48550/arxiv.2006.08303
17 pages, 4 figures
arxiv created 2020/06/15 · openalex publication_date 2020/06/15 · arxiv updated 2020/06/16 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational imaging approaches have been developed to pass on some of the burden to a reconstruction algorithm. In various image reconstruction problems in multidimensional imaging, the measurements are in the form of superimposed convolutions. In this paper, we introduce a general framework for the solution of these problems, called here convolutional inverse problems, and develop fast image reconstruction algorithms with analysis and synthesis priors. These include sparsifying transforms, as well as convolutional or patch-based dictionaries that can adapt to correlations in different dimensions. The resulting optimization problems are solved via alternating direction method of multipliers with closed-form, efficient, and parallelizable update steps. To illustrate their utility and versatility, the developed algorithms are applied to three-dimensional image reconstruction problems in computational spectral imaging for cases with or without correlation along the third dimension. As the advent of multidimensional imaging modalities expands to perform sophisticated tasks, these algorithms are essential for fast iterative reconstruction in various large-scale problems.