Chambolle-Pock algorithm

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Chambolle-Pock algorithm is an <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> used to solve <a href="/facts/Convex_optimization/7D6U4MTN">convex optimization</a> problems. It was introduced by Antonin Chambolle and Thomas Pock in 2011 and has since become a widely used method in various fields, including <a href="/facts/Digital_image_processing/zenalNCf">image processing</a>, <a href="/facts/Computer_vision/Tl2Yyk66">computer vision</a>, and <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>.
The Chambolle-Pock algorithm is specifically designed to efficiently solve convex optimization problems that involve the minimization of a non-smooth <a href="/facts/Loss_function/xv5ozuhl">cost function</a> composed of a data fidelity term and a regularization term. This is a typical configuration that commonly arises in ill-posed imaging <a href="/facts/Inverse_problem/Fe01pQ9E">inverse problems</a> such as <a href="/facts/Image_reconstruction/j1KqwH9e">image reconstruction</a>, <a href="/facts/Noise_reduction/9jrDQnAN">denoising</a> and <a href="/facts/Inpainting/5fHD96N8">inpainting</a>.
The algorithm is based on a primal-dual formulation, which allows for simultaneous updates of primal and <a href="/facts/Duality_(mathematics)/8jGuyQIU">dual</a> variables. By employing the <a href="/facts/Proximal_operator/KHXpHWHC">proximal operator</a>, the Chambolle-Pock algorithm efficiently handles non-smooth and non-convex regularization terms, such as the <a href="/facts/Total_variation/tyY5fTz9">total variation</a>, specific in imaging framework.

Chambolle-Pock algorithm open-in-new

Chambolle-Pock algorithm