Convolutional Inverse Problems in Imaging with Convolutional Sparse Models

Dogan, Didem; Oktem, Figen S.

doi:10.1364/cosi.2019.jw2a.9

Cited by 2 publications

(3 citation statements)

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“…In fact, for linear shift-variant systems whose response slowly varies across the field of view, time, depth, or spectral dimensions, the system operator can often be approximated by a linear combination of regular convolution operators [8,9]. In this paper, we focus on the solution of this type of inverse problems, which are called here convolutional inverse problems [10]. Such inverse problems are encountered in various computational imaging modalities such as computational photography, wide-field astronomical imaging, three-dimensional microscopy, spectral imaging, ultrafast imaging, radio interferometric imaging, magnetic resonance imaging, and ultrasound imaging [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we focus on the solution of this type of inverse problems, which are called here convolutional inverse problems [10]. Such inverse problems are encountered in various computational imaging modalities such as computational photography, wide-field astronomical imaging, three-dimensional microscopy, spectral imaging, ultrafast imaging, radio interferometric imaging, magnetic resonance imaging, and ultrasound imaging [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In the analysis case, multidimensional discrete derivative operators or sparsifying transforms can be utilized such as discrete cosine transform (DCT), wavelets, or their Kronecker-product forms [5,7,21]. In the synthesis case, convolutional or patch-based dictionaries can be utilized, which can also be adapted to correlations in different dimensions [10,[22][23][24][25][26][27][28][29][30][31]. Based on the available prior knowledge about the image of interest, there may be correlations either all through the image data or only in certain dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithms for Convolutional Inverse Problems in Multidimensional Imaging

Dogan,

Oktem

2020

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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.

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