Projection onto Convex Sets Algorithm for Super-Resolution Image Restoration

The Projection onto Convex Sets (POCS) algorithm for super-resolution image restoration demonstrates correct operational results through systematic validation. In this algorithm implementation, we first transform low-resolution images into high-resolution formats to enhance image quality and detail resolution. The transformation typically involves upsampling techniques combined with interpolation methods (e.g., bicubic or Lanczos interpolation) to initialize the high-resolution grid. Subsequently, the POCS algorithm iteratively applies constraint projections to restore image details and sharpness. These projections enforce physical constraints such as data consistency (matching observed low-resolution images), amplitude constraints (pixel value boundaries), and spatial domain constraints. The algorithm's efficacy has been verified through quantitative metrics including Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), confirming both correctness and effectiveness in super-resolution reconstruction tasks.