Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain

• Published in: IEEE transactions on image processing Vol. 18; no. 10; pp. 2364 - 2369
• Main Authors: Yu, Hancheng, Zhao, Li, Wang, Haixian
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Computational efficiency; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Filters; Gaussian distribution; Gaussian noise; Image denoising; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Imaging, Three-Dimensional - methods; Information, signal and communications theory; joint bilateral filter; Low-frequency noise; Mathematical models; Miscellaneous; Noise; Noise reduction; Pattern Recognition, Automated - methods; PSNR; Reproducibility of Results; Sensitivity and Specificity; Shrinkage; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; spatial domain; Studies; Telecommunications and information theory; trivariate shrinkage filter; Wavelet; Wavelet coefficients; Wavelet domain; Wavelet transforms; Cost minimization; Image processing; Noise reduction; Gaussian distribution; Artefact; 1/f noise; joint bilateral filter; spatial domain; Gaussian noise; trivariate shrinkage filter; A posteriori estimation; Joint; Algorithm; Computational complexity; Color image; Noisy image; Image quality; Wavelets; Algorithm performance; Wavelet transformation; Signal processing; wavelet domain; Open market; Signal analysis; Signal to noise ratio; Image denoising
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2009.2026685

This correspondence proposes an efficient algorithm for removing Gaussian noise from corrupted image by incorporating a wavelet-based trivariate shrinkage filter with a spatial-based joint bilateral filter. In the wavelet domain, the wavelet coefficients are modeled as trivariate Gaussian distribution, taking into account the statistical dependencies among intrascale wavelet coefficients, and then a trivariate shrinkage filter is derived by using the maximum a posteriori (MAP) estimator. Although wavelet-based methods are efficient in image denoising, they are prone to producing salient artifacts such as low-frequency noise and edge ringing which relate to the structure of the underlying wavelet. On the other hand, most spatial-based algorithms output much higher quality denoising image with less artifacts. However, they are usually too computationally demanding. In order to reduce the computational cost, we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain. This filter could suppress the noise while preserve image details with small computational cost. Extension to color image denoising is also presented. We compare our denoising algorithm with other denoising techniques in terms of PSNR and visual quality. The experimental results indicate that our algorithm is competitive with other denoising techniques.