Image Restoration Using Least Squares Filtering and Wiener Filtering Methods

In this article, we present two approaches for image restoration: least squares filtering and Wiener filtering. These methods are not only applicable to image restoration but can also be extended to other domains such as audio and signal processing. While each method has distinct advantages and limitations, both are grounded in mathematical models, making their underlying principles relatively straightforward to comprehend. The implementation typically involves creating filter functions that process degraded images through matrix operations and frequency domain transformations. The least squares approach minimizes the squared difference between the original and restored images, often implemented using linear algebra operations like matrix inversions. The Wiener filtering method incorporates statistical characteristics of both the signal and noise, requiring power spectrum estimations for optimal results. Through these methods, we can effectively restore corrupted or missing image data, generating high-quality output suitable for further analysis and research. The accompanying result plots below visually demonstrate the performance of each technique, enabling comparative analysis of their effectiveness in various degradation scenarios. These visualizations help researchers assess restoration quality metrics such as peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM).