Regularized coordinate minimization for nonconvex composite optimization with application to quantized image compression

Abstract

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.