Three-dimensional blind deconvolution by CP-parameterized kernels
Abstract
We consider the problem of reconstructing a kernel k and image u in a blind deconvolution problem from convolutional data g = k*u. We particularly focus on the 3D case, i.e., on volumetric images. The problem is approached by imposing a semiparametric CP decomposition for the kernel and a variational TV penalty for the image. We also discuss a motion blur ambiguity effect, i.e., a nonuniqueness issue of the kernel in the blind deconvolution problem that may appear in certain videos of moving objects. The blind deconvolution algorithm uses an alternating minimization approach with TV regularization for u and a CP decomposition step for the kernel. These are implemented with positivity projection, kernel normalization, and\textbackslash or causal support projection steps. Several numerical examples for 3D MRI images, hyperspectral images, and a grayscale test video show the effectiveness of the method.
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BibTeX
@misc{sanogo2026threedimensional,
title = {{Three-dimensional blind deconvolution by CP-parameterized kernels}},
author = {Fatoumata Sanogo and Stefan Kindermann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25394},
eprint = {2609.25394},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25394},
}
RIS
TY - UNPB
TI - Three-dimensional blind deconvolution by CP-parameterized kernels
AU - Fatoumata Sanogo
AU - Stefan Kindermann
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25394
UR - https://arxiv.org/abs/2609.25394
AB - We consider the problem of reconstructing a kernel k and image u in a blind deconvolution problem from convolutional data g = k*u. We particularly focus on the 3D case, i.e., on volumetric images. The problem is approached by imposing a semiparametric CP decomposition for the kernel and a variational TV penalty for the image. We also discuss a motion blur ambiguity effect, i.e., a nonuniqueness issue of the kernel in the blind deconvolution problem that may appear in certain videos of moving objects. The blind deconvolution algorithm uses an alternating minimization approach with TV regularization for u and a CP decomposition step for the kernel. These are implemented with positivity projection, kernel normalization, and\textbackslash or causal support projection steps. Several numerical examples for 3D MRI images, hyperspectral images, and a grayscale test video show the effectiveness of the method.
ER -