Abstract:
We often work with discrete-domain analog image samples due to digital imaging systems. All imaging devices blur the input image before sampling to form output pixels due to physical constraints.
This paper reconstructs binary shape images from few blurred samples. Medical imaging, shape processing, and image segmentation use this problem. Our method represents analog shape images in a discrete grid finer than the sampling grid.
We recover a Hankel structure-formed rank r matrix from pixels. We propose efficient ADMM-based lowrank matrix recovery algorithms for noiseless and noisy environments.
We analyze the noiseless recovery sample size. We study the problem in the random sampling framework and show that with O(r log_4(n_1_n_2_)) random samples (where the image size is assumed to be n_1_n_2), we can guarantee the perfect reconstruction with high probability under mild conditions.
When the input noise is bounded, the reconstruction error is bounded in the noisy case, proving the robustness of the proposed recovery. Simulations show that our method outperforms total variation minimization in noiseless settings.
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