# Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise

arXiv: https://arxiv.org/abs/2301.03393 · HTML: https://mlsanity.com/paper/2301.03393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 85 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 15 of 15)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [A Scale Invariant Approach for Sparse Signal Recovery](https://mlsanity.com/paper/1812.08852/) (2018)
- [Limited-angle CT reconstruction via the L1/L2 minimization](https://mlsanity.com/paper/2006.00601/) (2020)
- [A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)](https://mlsanity.com/paper/1506.00060/) (2015)
- [A Novel Regularization Based on the Error Function for Sparse Recovery](https://mlsanity.com/paper/2007.02784/) (2020)
- [Image Segmentation with Adaptive Spatial Priors from Joint Registration](https://mlsanity.com/paper/2203.15548/) (2022)
- [Segmentation of Scanning Tunneling Microscopy Images Using Variational Methods and Empirical Wavelets](https://mlsanity.com/paper/1804.08890/) (2018)
- [A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity](https://mlsanity.com/paper/1504.02206/) (2015)
- [A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation](https://mlsanity.com/paper/2005.04401/) (2020)
- [Minimizing L1 over L2 norms on the gradient](https://mlsanity.com/paper/2101.00809/) (2021)
- [Analysis of The Ratio of ℓ1 and ℓ2 Norms in Compressed Sensing](https://mlsanity.com/paper/2004.05873/) (2020)
- [An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation](https://mlsanity.com/paper/2202.10115/) (2022)
- [Jump-sparse and sparse recovery using Potts functionals](https://mlsanity.com/paper/1304.4373/) (2013)
- [Edge Adaptive Hybrid Regularization Model For Image Deblurring](https://mlsanity.com/paper/2011.10260/) (2020)

## Abstract (arXiv)

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.