# Convergence Analysis of MAP based Blur Kernel Estimation

arXiv: https://arxiv.org/abs/1611.07752 · HTML: https://mlsanity.com/paper/1611.07752/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2016.

## Built on by (most cited first, 9 of 9)

- [Iterative Filter Adaptive Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2108.13610/) (2021)
- [Single Image Defocus Deblurring Using Kernel-Sharing Parallel Atrous Convolutions](https://mlsanity.com/paper/2108.09108/) (2021)
- [Realistic Blur Synthesis for Learning Image Deblurring](https://mlsanity.com/paper/2202.08771/) (2022)
- [MSSNet: Multi-Scale-Stage Network for Single Image Deblurring](https://mlsanity.com/paper/2202.09652/) (2022)
- [Gaussian Kernel Mixture Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2111.00454/) (2021)
- [Blind Image Deblurring with Unknown Kernel Size and Substantial Noise](https://mlsanity.com/paper/2208.09483/) (2022)
- [Deep Hybrid Camera Deblurring for Smartphone Cameras](https://mlsanity.com/paper/2312.13317/) (2023)
- [SR-R2KAC: Improving Single Image Defocus Deblurring](https://mlsanity.com/paper/2307.16242/) (2023)
- [GS-RealBlur: A Flexible Data Acquisition Framework for Real-World Image Deblurring](https://mlsanity.com/paper/2607.15401/) (2026)

## Abstract (arXiv)

One popular approach for blind deconvolution is to formulate a maximum a posteriori (MAP) problem with sparsity priors on the gradients of the latent image, and then alternatingly estimate the blur kernel and the latent image. While several successful MAP based methods have been proposed, there has been much controversy and confusion about their convergence, because sparsity priors have been shown to prefer blurry images to sharp natural images. In this paper, we revisit this problem and provide an analysis on the convergence of MAP based approaches. We first introduce a slight modification to a conventional joint energy function for blind deconvolution. The reformulated energy function yields the same alternating estimation process, but more clearly reveals how blind deconvolution works. We then show the energy function can actually favor the right solution instead of the no-blur solution under certain conditions, which explains the success of previous MAP based approaches. The reformulated energy function and our conditions for the convergence also provide a way to compare the qualities of different blur kernels, and we demonstrate its applicability to automatic blur kernel size selection, blur kernel estimation using light streaks, and defocus estimation.