Image noise reduction using wavelet-based mathematical morphology
Morphological filters are well known for their potential in image noise reduction. Peters recently proposed an attractive morphological image cleaning (MIC) algorithm that preserves thin features while removing noise by discarding regions in a sequence of residual images (the differences between the original image and morphologically smoothed versions) that it judges to contain noise and recombining the processed smooth residuals to form a cleaned image. The MIC algorithm proves to be effective on dense, low-amplitude, random or patterned noise. However, the MIC algorithm suffers from high computational cost and degraded performance for high-amplitude noise. This thesis presents a novel denoising method, wavelet-based morphological image cleaning (WMIC) algorithm, which is effective for images corrupted by noise of various amplitudes. In addition, the computational complexity of the new algorithm is much lower than Peters? MIC algorithm. These improvements are achieved by exploiting the dual spatial and frequency localization property of wavelets. Experimental results show that for low-amplitude noise, the WMIC algorithm is competitive with the median filter in removing impulse noise and the Wiener filter in suppressing continuous noise; for high-amplitude noise (especially mixed noise), the WMIC algorithm surpasses the median filter and the Wiener filter in overall performance. In this thesis, we first introduce mathematical morphology and previous morphology-based work in image noise reduction with an emphasis on Peters? MIC algorithm. After the drawbacks of Peter? MIC algorithm are discussed, we explore a wavelet domain peer. The basic theorem of wavelet transform follows. Then we propose the WMIC algorithm and give a detailed description of the implementation. Experimental results and discussions are presented at the end.