This paper presents a very efficient algorithm for image denoising based on wavelets and multifractals for singularity detection. A challenge of image denoising is how to preserve the edges of an image when reducing noise. By modeling the intensity surface of a noisy image as statistically self-similar multifractal processes and taking advantage of the multiresolution analysis with wavelet transform to exploit the local statistical self-similarity at different scales, the pointwise singularity strength value characterizing the local singularity at each scale was calculated. By thresholding the singularity strength, wavelet coefficients at each scale were classified into two categories: the edge-related and regular wavelet coefficients and the irregular coefficients. The irregular coefficients were denoised using an approximate minimum mean-squared error (MMSE) estimation method, while the edge-related and regular wavelet coefficients were smoothed using the fuzzy weighted mean (FWM) filter aiming at preserving the edges and details when reducing noise. Furthermore, to make the FWM-based filtering more efficient for noise reduction at the lowest decomposition level, the MMSE-based filtering was performed as the first pass of denoising followed by performing the FWM-based filtering. Experimental results demonstrated that this algorithm could achieve both good visual quality and high PSNR for the denoised images.

It was recently reported that the real-time flat panel detector-based cone-beam computed tomography (CBCT) breast imaging can help improve the detectability of small breast tumors with an X-ray dose comparable to that of the conventional mammography. In this paper, an efficient denoising algorithm is proposed to further reduce the X-ray exposure level required by a CBCT scan to acquire acceptable image quality. The proposed wavelet-based denoising algorithm possesses three significant characteristics: 1) wavelet coefficients at each scale are classified into two categories: irregular coefficients, and edge-related and regular coefficients; 2) noise in irregular coefficients is reduced as much as possible without producing artifacts to the denoised images; and 3) for the edge-related and regular coefficients, if they are at the first decomposition level, they are further denoised, otherwise, no modifications are made to them so as to obtain good visual quality for diagnosis. By applying the proposed denoising algorithm to the filtered projection images, the X-ray exposure level necessary for the CBCT scan can be reduced by up to 60% while obtaining clinically acceptable image quality. This denoising result indicates that in the clinical application of CBCT breast imaging, the patient radiation dose can be significantly reduced.

In recent years, wavelets have attracted great attention in both still image compression and video coding, and several novel wavelet-based image compression algorithms have been developed so far, one of which is Shapiro's embedded zerotree wavelet (EZW) image compression algorithm. However, there are still some deficiencies in this algorithm. In this paper, after the analysis of the deficiency in EZW, a new algorithm based on quantized coefficient partitioning using morphological operation is proposed. Instead of encoding the coefficients in each subband line-by-line, regions in which most of the quantized coefficients are significant are extracted by morphological dilation and encoded first. This is followed by using zerotrees to encode the remaining space which has mostly zeros. Experimental results show that the proposed algorithm is not only superior to the EZW, but also compares favorably with the most efficient wavelet-based image compression algorithms reported so far.