1. bookVolume 11 (2011): Issue 4 (August 2011)
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
Open Access

Statistical Modeling of Low SNR Magnetic Resonance Images in Wavelet Domain Using Laplacian Prior and Two-Sided Rayleigh Noise for Visual Quality Improvement

Published Online: 21 Sep 2011
Volume & Issue: Volume 11 (2011) - Issue 4 (August 2011)
Page range: 125 - 130
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
Statistical Modeling of Low SNR Magnetic Resonance Images in Wavelet Domain Using Laplacian Prior and Two-Sided Rayleigh Noise for Visual Quality Improvement

In this paper we introduce a new wavelet-based image denoising algorithm using maximum a posteriori (MAP) criterion. For this reason we propose Laplace distribution with local variance for clean image and two-sided Rayleigh model for noise in wavelet domain. The local Laplace probability density function (pdf) is able to simultaneously model the heavy-tailed nature of marginal distribution and intrascale dependency between spatial adjacent coefficients. Using local Laplace prior and two-sided Rayleigh noise, we derive a new shrinkage function for image denoising in the wavelet domain. We propose our new spatially adaptive wavelet-based image denoising algorithm for several low signal-to-noise ratio (SNR) magnetic resonance (MR) images and compare the results with other methods. The simulation results show that this algorithm is able to truly improve the visual quality of noisy MR images with very low computational cost. In case the input MR image is blurred, a blind deconvolution (BD) algorithm is necessary for visual quality improvement. Since BD techniques are usually sensitive to noise, in this paper we also apply a BD algorithm to an appropriate subband in the wavelet domain to eliminate the effect of noise in the BD procedure and to further improve visual quality.

Keywords

Vojtíšek, L., Frollo, I., Valkovič, L., Gogola, D., Juráš, V. (2011). Phased array receiving coils for low field lungs MRI: Design and optimization. Measurement Science Review, 9, 61-67.10.2478/v10048-011-0012-3Search in Google Scholar

Song Huettel, A. W., McCarthy, G. (2009). Functional Magnetic Resonance Imaging, 2nd ed. Sunderland, MA: Sinauer Associates, Inc.Search in Google Scholar

Donoho, D. L., Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 291-294.10.1093/biomet/81.3.425Search in Google Scholar

Donoho, D. L. (1995). Denoising by soft-thresholding. IEEE Trans. on Information Theory, 41, 613-627.10.1109/18.382009Search in Google Scholar

Mihcak, M. K., Kozintsev, I., Ramchandran, K., Moulin, P. (1999). Low complexity image denoising based on statistical modeling of wavelet coefficients. IEEE Signal Proc. Letters, 6, 300-303.10.1109/97.803428Search in Google Scholar

Crouse, M. S., Nowak, R. D., Baraniuk, R. G. (1999). Analysis of multiresolution image denoising schemes using a generalized Gaussian and complexity priors. IEEE Trans. on Information Theory, 45, 909-919.10.1109/18.761332Search in Google Scholar

Malfait, M., Roose, D. (1997). Wavelet-based image denoising using a markov random field a priori model. IEEE Trans. on Image Processing, 6, 549-565.10.1109/83.56332018282948Search in Google Scholar

Crouse, M. S., Nowak, R. D., Baraniuk, R. G. (1998). Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. on Signal Processing, 46, 886-902.10.1109/78.668544Search in Google Scholar

Rabbani, H., Vafadust, M., Gazor, S. (2006). Image denoising based on a mixture of Laplace distributions with local parameters in complex wavelet domain. In IEEE Int. Conference on Image Processing, October 8-11, 2006. Atlanta, GA, 2597-2600.10.1109/ICIP.2006.313018Search in Google Scholar

Nowak, R. D. (1999). Wavelet-based rician noise removal for magnetic resonance imaging. IEEE Trans. Image Processing, 8, 1408-1419.10.1109/83.79196618267412Search in Google Scholar

Chang, S. G., Yu, B., Vetterli, M. (2000). Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Processing, 9, 1532-1546.10.1109/83.86263318262991Search in Google Scholar

Richardson, W. H. (1972). Bayesian-based iterative method of image restoration. JOSA, 62 (1), 55-59.10.1364/JOSA.62.000055Search in Google Scholar

Lucy, L. B. (1974). An iterative technique for the rectification of observed distributions. Astronomical Journal, 79 (6), 745-754.10.1086/111605Search in Google Scholar

Fish, D. A., Brinicombe, A. M., Pike, E. R. (1995). Blind deconvolution by means of the Richardson-Lucy algorithm. J. of the Optical Society of America A, 12 (1), 58-65.10.1364/JOSAA.12.000058Search in Google Scholar

Stockham, T. G., Cannon, T. M., Ingebretsen, R. B. (1975). Blind deconvolution through digital signal processing. In Proc. IEEE, 63 (4), 678-692.10.1109/PROC.1975.9800Search in Google Scholar

Cannon, M. (1976). Blind deconvolution of spatially invariant image blurs with phase. IEEE Trans. on Acoustic, Speech, and Signal Processing, 24 (1), 58-63.10.1109/TASSP.1976.1162770Search in Google Scholar

Rabbani, H. (2008). Statistical modeling of low SNR magnetic resonance images in wavelet domain using Laplacian prior and two-sided Rayleigh noise for visual quality improvement. In International Conference on Information Technology and Applications in Biomedicine (ITAB 2008), May 30-31, 2008. IEEE, 116-119.10.1109/ITAB.2008.4570560Search in Google Scholar

Rabbani, H., Vafadust, M. (2008). Image/video denoising based on a mixture of Laplace distributions with local parameters in multidimensional complex wavelet domain. Signal Processing, 88 (1), 158-173.10.1016/j.sigpro.2007.07.016Search in Google Scholar

Rabbani, H., Nezafat, R., Gazor, S. (2009). Waveletdomain medical image denoising using bivariate Laplacian mixture model. IEEE Trans. on Biomedical Engineering, 56 (12), 2826-2837.10.1109/TBME.2009.202887619695984Search in Google Scholar

Selesnick, I. W., Kingsbury, N., Baraniuk, R. G. (2005). The dual-tree complex wavelet transforms - a coherent framework for multiscale signal and image processing. IEEE Signal Proc. Magazine, 9, 123-151.10.1109/MSP.2005.1550194Search in Google Scholar

Kingsbury, N. G. (2000). A dual-tree complex wavelet transform with improved orthogonality and symmetry properties. In 2000 Int. Conference on Image Processing, Vol. 2, September 10-13, 2000. IEEE, 375-378.10.1109/ICIP.2000.899397Search in Google Scholar

Geman, S., Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6 (6), 721-741.10.1109/TPAMI.1984.4767596Search in Google Scholar

Derin, H., Elliott, H. (1987). Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. on Pattern Analysis and Machine Intelligence, 9, 39-55.10.1109/TPAMI.1987.4767871Search in Google Scholar

Molina, R., Katsaggelos, A. K., Abad, J., Mateos, J. (1997). A Bayesian approach to blind deconvolution based on dirichlet distributions. In IEEE Int. Conference on Acoustics, Speech and Signal Processing (ICASSP-97), Vol. 4, April 21-24, 1997. IEEE, 2809-2812.10.1109/ICASSP.1997.595373Search in Google Scholar

Sroubek, F., Flusser, J. (2005). Multichannel blind deconvolution of spatially misaligned images. IEEE Trans. Image Processing, 14 (7), 874-883.10.1109/TIP.2005.849322Search in Google Scholar

Babacan, S., Molina, R., Katsaggelos, A. (2008). Parameter estimation in TV image restoration using variational distribution approximation. IEEE Trans. Image Processing, 17 (23), 326-339.10.1109/TIP.2007.916051Search in Google Scholar

Levin, A., Weiss, Y., Durand, F., Freeman, W. T. (2009). Understanding and evaluating blind deconvolution algorithms. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2009), June 20-25, 2009. IEEE, 1964-1971.10.1109/CVPR.2009.5206815Search in Google Scholar

Greenspan, H., Oz, G., Kiryati, N., Peled, S. (2002). MRI inter-slice reconstruction using super resolution. Magnetic Resonance Imaging, 20 (5), 437-446.10.1016/S0730-725X(02)00511-8Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo