A spatially selective filter based on the undecimated wavelet transform that is robust to noise estimation error

Xu, Y. et al. (see IEEE T-IP, vol.3, no.6, 1994) proposed an effective wavelet based spatially selective denoising algorithm. The performance of the algorithm depends on the noise power estimation. Pan, Q. et al. (see IEEE T-SP, vol.47, no.12, 1999) tried to improve the performance via a small modification. However, our simulation shows that both of these methods are sensitive to noise estimation. We analyze the sensitivity of these two methods and introduce a new spatially selective noise filter based on the UDWT (undecimated wavelet transform) that uses spatial correlation thresholding. Theoretic analysis and simulations show our algorithm improves the denoising effect. They also show that our proposed method is robust to errors in the noise power estimate. Because our approach is robust, we can relax the requirements for the estimation of the threshold without sacrificing performance, and so our method is more computationally efficient. We also put some perspective on the impact of employing nonorthogonal representations. Simulation results show the effectiveness of our proposed algorithm.