Comparison of Image Denoising: Wiener Filter vs. Least Squares Filter

This article explores the comparative performance of Wiener filtering and least squares filtering in image denoising applications. We provide a detailed discussion of the advantages and limitations of both methods, along with their respective suitability under different scenarios. Wiener filtering operates as a statistical approach based on noise modeling, typically implemented using frequency domain operations with power spectrum estimates. While effective at noise reduction, it often introduces image blurring due to its linear nature. In contrast, least squares filtering represents a nonlinear methodology that minimizes the squared error between the original and filtered images. This approach maintains better edge preservation and detail retention through iterative optimization techniques. The implementation typically involves constructing regularization terms and solving optimization problems using gradient descent or conjugate gradient methods. Furthermore, we discuss selection criteria for choosing between these filtering techniques and provide guidance on parameter adjustment strategies based on practical requirements. These adjustments may involve modifying regularization parameters, iteration counts, or noise variance estimates to achieve optimal results in specific image processing applications.