Maximum Entropy Image Restoration

In this article, we explore how to implement image restoration using the maximum entropy algorithm. The maximum entropy algorithm is a mathematical model grounded in information theory that predicts unknown data by modeling given datasets. In image processing applications, this algorithm can restore lost information from corrupted images, thereby recovering the original appearance of degraded visuals. The core principle involves selecting the probability distribution that best aligns with actual conditions when given a set of known information constraints. This approach enables inference of unknown information based on available data, achieving the objective of image restoration. We will detail the algorithm's fundamental principles and applications, including implementation aspects such as entropy calculation using logarithmic functions (e.g., -sum(p.*log(p)) in MATLAB) and optimization techniques like Lagrange multipliers for constraint handling. Practical case studies demonstrate its application in reconstructing blurred or noisy images through iterative convergence toward maximum entropy solutions.