Image Restoration Using Wiener Filtering and Inverse Filtering with Custom MATLAB Implementation

This project involves implementing image restoration techniques using custom MATLAB code for both Wiener filtering and inverse filtering, deliberately avoiding reliance on MATLAB's built-in functions. Wiener filtering serves as an image restoration method that operates in the frequency domain to minimize noise impact by estimating the original signal through statistical approaches. The implementation typically requires calculating the power spectra of both the original image and noise, followed by applying the Wiener filter transfer function: H_w(u,v) = [H*(u,v) / (|H(u,v)|² + K)] where H(u,v) represents the degradation function and K is the noise-to-signal ratio. Inverse filtering employs a reverse filtering technique that attempts to recover details lost due to blurring by applying the inverse of the degradation function: G(u,v)/H(u,v), where G(u,v) is the Fourier transform of the degraded image. However, practical implementation requires careful handling of frequency components where H(u,v) approaches zero to avoid amplification of noise. By developing custom programs for these filtering methods, we gain deeper insight into the algorithmic principles, including frequency domain operations, Fourier transforms, and noise modeling. The implementation process involves key steps such as converting images to frequency domain using fft2(), designing filter transfer functions, handling division operations with thresholding to prevent instability, and converting results back to spatial domain using ifft2(). This hands-on approach not only enhances programming skills but also allows for algorithm customization and optimization based on specific image characteristics and noise conditions, thereby strengthening understanding and application of digital image processing concepts.