Based on transformed $\ell_1$ regularization, transformed total variation
(TTV) has robust image recovery that is competitive with other nonconvex total
variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its
performance, we propose a TTV-regularized Mumford--Shah model with fuzzy
membership function for image segmentation. To solve it, we design an
alternating direction method of multipliers (ADMM) algorithm that utilizes the
transformed $\ell_1$ proximal operator. Numerical experiments demonstrate that
using TTV is more effective than classical TV and other nonconvex TV variants
in image segmentation.

使用基于转换的 l1 正则化的转换总变差 (TTV)，提出了带模糊成员函数的 TTV 正则化 Mumford--Shah 模型进行图像分割，并通过交替方向乘子法设计了求解算法。数值实验表明，在图像分割中使用 TTV 比传统的 TV 和其他非凸 TV 变体更有效。

一种带有转换总变差的图像分割模型

An Image Segmentation Model with Transformed Total Variation

Although deep convolutional neural networks have achieved rapid development,
it is challenging to widely promote and apply these models on low-power
devices, due to computational and storage limitations. To address this issue,
researchers have proposed techniques such as model compression, activation
sparsity induction, and hardware accelerators. This paper presents a method to
induce the sparsity of activation maps based on Transformed $\ell1$
regularization, so as to improve the research in the field of activation
sparsity induction. Further, the method is innovatively combined with
traditional pruning, constituting a dual sparse training framework. Compared to
previous methods, Transformed $\ell1$ can achieve higher sparsity and better
adapt to different network structures. Experimental results show that the
method achieves improvements by more than 20\% in activation map sparsity on
most models and corresponding datasets without compromising the accuracy.
Specifically, it achieves a 27.52\% improvement for ResNet18 on the ImageNet
dataset, and a 44.04\% improvement for LeNet5 on the MNIST dataset. In
addition, the dual sparse training framework can greatly reduce the
computational load and provide potential for reducing the required storage
during runtime. Specifically, the ResNet18 and ResNet50 models obtained by the
dual sparse training framework respectively reduce 81.7\% and 84.13\% of
multiplicative floating-point operations, while maintaining accuracy and a low
pruning rate.

本研究论文介绍了一种基于转换的 l1 正则化方法来诱导激活图的稀疏性，以改善激活稀疏诱导领域的研究。同时，本方法与传统修剪结合，构成了双稀疏训练框架。实验结果表明，该方法在大多数模型和相应数据集上可以实现超过 20% 的激活图稀疏度提升，同时不影响准确性。另外，双稀疏训练框架能够大大减少计算负载并降低运行时所需的存储。