Image denoising with spline interpolation based on singular value decomposition and other evaluation methods

Abstract

In this thesis, we construct two new algorithms for image denoising, namely, spline and spline-wavelet, which combine spline interpolation and wavelets together with nonlinear filtering based on block singular value decomposition. Those two approaches are compared with other existing methods, which involve BlockSvd filter, wavelet (global thresholding) filter, median filter, average filter, and adaptive filter. The performance of these approaches differs little from each other. Generally speaking, median filter is very suitable for processing images to reduce "salt and pepper" noise. But for zero-mean Gaussian and speckle noises, an adaptive filter and spline-wavelet methods are more stable and slightly superior to other filters in most conditions and for most images. The proposed algorithms were tested under different types of images and a wide range of signal to noise ratios (SNR). The numerical results demonstrate that these methods can be used in different and useful ways for reducing image noise.