Wavelet Transform Based Impulsive Noise Removal: A Smart Non-Linear Filtering Algorithm

摘要

In many applications where operations based on computing signal or image derivatives are applied, impulsive noise in the signal or image can result in serious errors. Noise elimination is a main concern in Signal and Image Processing. Wavelets introduce new classes of basis functions for Time-Frequency signal analysis and have properties particularly suited to the transient (impulse like) components. Due to its Time-Frequency localization one can detect and remove impulsive noises. The conventional linear filters, which consist of convolving the signal with a constant matrix to obtain a linear combination of neighborhood values may produce poor feature localization resulting in incomplete noise suppression. The linear filters consider any low frequency structure to be noise, but they fail to efficiently remove impulsive noises. To mitigate this problem novel non-linear filter using wavelet transform is proposed. The proposed non-linear algorithm recognizes high-amplitude, high -frequency and low-amplitude, low-frequency structures as signals. This recursive nonlinear filter is composed of conditional rules, which are applied independently, in any order. It identifies noisy items by inspection of their surrounding neighborhood, and replaces their values with most conservative ones out of their neighbors' values. The simulation was performed using MATLAB 5.1.The results are presented with various parameters like percentage of image spoiled, percentage of noise removed, Peak Signal to Noise Ratio (PSNR) in dB and execution time in sec. The performance of the proposed algorithm is compared with the conventional median filter.