Reconstruction of Binary Shapes From Blurred Images via Hankel-Structured Low-Rank Matrix Recovery


We are increasingly dealing with discrete-domain samples of analogue images due to the popularity of digital imaging technologies.. As a result of physical constraints, all imaging equipment blur input images before generating pixels. Reconstruction of binary images from a few blurred samples is the topic of this paper It has uses in medical imaging, form processing and picture segmentation. The analogue form image is represented in a discrete grid much finer than the sampling grid in our method. Using a Hankel structure, we describe the task as recovering a rank r matrix from the pixels. We also offer efficient ADMM-based techniques for recovering the lowrank matrix in both noiseless and noisy environments. Additionally, we analyse the number of samples needed for a successful recovery in the absence of noise. The random sampling framework is used to examine the problem, and we find that under mild conditions, we can ensure perfect reconstruction with a high probability using O(r log 4 (n 1 n 2)) random samples. When the input noise is bounded, we further demonstrate that the suggested recovery is robust to noise in the noisy environment. Results from simulations show that in noiseless situations, our strategy outperforms the standard total variation minimization.

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