Subspace-based Image Noise Reduction Filter

In this paper, subspace-based filters are developed for restoration of images corrupted by additive white Gaussian
noise (AWGN). The fundamental principle of the subspacebased
technique is to decompose the vector space of the noisy image into signal-plus-noise subspace and the noise subspace. Noise reduction is achieved by removing the noise subspace and estimating the clean image from the remaining image subspace. Linear estimation of the clean image is performed using two methods, namely using SSDC esimator and SFDC estimator. The SSDC is derived by minimizing image distortion while maintaining the residual noise energy below some given threshold. On the other hand, SFDC is derived by minimizing the energy of image distortion while keeping the energy of the residual noise in each spectral component below some given threshold. The performance of the subspace-based filters are tested with simulated images and compared with Wiener filter and waveletbased filter. The results shows that the filters outperformed Wiener filter in terms of PSNR at low noise level.