Image Reconstruction Based on POCS (Projection Onto Convex Sets)

In the MATLAB environment, we can implement image reconstruction using the Projection Onto Convex Sets (POCS) algorithm. This iterative reconstruction method progressively enhances image quality through cyclic projections between constraint sets. The implementation typically involves defining convex sets representing prior knowledge (such as support constraints, positivity constraints, or frequency-domain constraints) and alternating projections between them. Key MATLAB functions like fft2/ifft2 for Fourier transforms and imfilter for constraint enforcement are commonly employed. Algorithm parameters including iteration count, constraint thresholds, and relaxation factors can be adjusted based on specific image characteristics and reconstruction requirements to optimize results. The reconstruction process can be further enhanced by integrating complementary image processing techniques such as Wiener filtering for noise reduction or regularization methods for artifact suppression. Implementing POCS in MATLAB provides practical insights into iterative reconstruction algorithms and demonstrates effective application of convex optimization principles in digital image processing.