MATLAB Implementation of Chambolle's Projection Algorithm

In the following code segment, you will find a MATLAB implementation of Chambolle's algorithm. The main program proj.m contains the core optimization routine, while the two additional files function as utility modules called during algorithm execution. This algorithm primarily utilizes projection operations to solve image denoising and reconstruction problems through variational methods. The implementation employs gradient descent with proximal operations to minimize total variation, making it particularly valuable for image processing and computer vision research. Key computational aspects include dual variable updates, divergence calculations, and thresholding operations that ensure convergence. Chambolle's projection method has been widely adopted in medical image processing, computer graphics, and digital signal processing domains due to its effectiveness in preserving edges while removing noise. Understanding this algorithm is essential for researchers and practitioners working in these technical fields. The MATLAB code structure demonstrates practical implementation of: - Dual formulation of the total variation minimization problem - Iterative projection steps with controlled step sizes - Efficient matrix operations for handling image data - Convergence criteria checking for optimal results