Adaptive filters based on local estimates

Adaptive schemes for noise filtering and edge detection of digital signals are developed which are based on the minimum mean square error (MMSE) estimate of the information bearing signal corrupted by additive noise. The MMSE estimate is computed using the local statistics of the input signal and noise. The output is fed back to the input and the difference between the input and the output is used as the noise estimator. The local statistics of signal and noise are computed through a moving signal window and a moving noise window, which are over the input signal and the noise estimator, respectively. These schemes change their performance according to the local SNR (signal-to-noise ratio) adaptively and have almost optimal filtering performance at homogeneous (low-SNR) regions of the signal and preserve edge information at edge (high-SNR) regions as well as the median filter. Two kinds of adaptive filtering algorithms and an edge-detection algorithm are considered.<>