发表机构
Politehnica Bucharest; Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy（布加勒斯特理工大学; 罗马尼亚科学院格奥尔基·米霍克-卡尤斯·雅各布数学统计与应用数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种正则化循环坐标最小化方法求解非凸复合优化问题，应用于量化图像压缩，在KODAK和CLIC 2024数据集上低比特率下优于JPEG，且分类精度无明显下降。
AI 中文摘要
本文提出了一种正则化循环坐标最小化方法，用于求解目标函数由两项之和构成的非凸复合优化问题，其中一项是二次连续可微的，第二项是简单且可分离的。我们分析了该坐标最小化方法的收敛行为，特别是根据对问题的假设，我们提供了关于一阶最优性准则和目标残差的收敛速率。然后，我们展示了该算法框架可高效应用于求解量化矩阵分解问题，这类问题出现在例如有损图像压缩中。具体而言，在KODAK和CLIC 2024数据集上，我们的方法在低比特率下显著优于JPEG，在不造成过度质量下降的情况下实现了每像素比特数的节省，并且在较高比特率下仍保持可比性。此外，我们使用3种著名的卷积网络AlexNet、ResNet50和MobileNetV2，基于浮点数和整数算术表示，在分类任务中评估了原始图像和量化压缩图像。值得注意的是，在比较卷积网络的两种数值表示时，在ImageNet数据集上没有显著的精度下降。使用真实数据进行的图像压缩和分类数值结果表明，与文献中成熟的方法相比，我们的算法具有灵活性和高效性。
英文摘要
This paper presents a regularized cyclic coordinate minimization method for solving nonconvex composite optimization problems having the objective function formed as the sum of two terms, one is twice continuously differentiable and the second term is simple and separable. We analyze the convergence behaviour of our coordinate minimization method, in particular we provide convergence rates to a first-order optimality criterion and objective residual depending on the assumptions on the problem. Then, we show that our algorithmic framework can be efficiently applied for solving quantized matrix factorization problems that arise in e.g., lossy image compression. More specifically, on KODAK and CLIC 2024 datasets, our method notably outperforms JPEG at low bit rates, achieving savings in bits per pixel without excessive degradation and remains comparable at higher bit rates. Moreover, we evaluate both the original and quantized compressed images in a classification task using 3 well-known convolutional networks AlexNet, ResNet50 and MobileNetV2 based on floating point and integer arithmetic representations. Remarkably, when comparing the two numerical representations of the convolutional networks, there is no substantially accuracy degradation on ImageNet dataset. The numerical results on image compression and classification using real data show the flexibility and efficiency of our algorithm compared to well-established methods from the literature.
Comments12 pages
