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.
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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.
Song Huettel A. W. McCarthy G. (2009). Functional Magnetic Resonance Imaging 2nd ed. Sunderland MA: Sinauer Associates Inc.
Donoho D. L. Johnstone I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 291-294.
Donoho D. L. (1995). Denoising by soft-thresholding. IEEE Trans. on Information Theory 41 613-627.
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.
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.
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.
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.
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.
Nowak R. D. (1999). Wavelet-based rician noise removal for magnetic resonance imaging. IEEE Trans. Image Processing 8 1408-1419.
Chang S. G. Yu B. Vetterli M. (2000). Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Processing 9 1532-1546.
Richardson W. H. (1972). Bayesian-based iterative method of image restoration. JOSA 62 (1) 55-59.
Lucy L. B. (1974). An iterative technique for the rectification of observed distributions. Astronomical Journal 79 (6) 745-754.
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.
Stockham T. G. Cannon T. M. Ingebretsen R. B. (1975). Blind deconvolution through digital signal processing. In Proc. IEEE 63 (4) 678-692.
Cannon M. (1976). Blind deconvolution of spatially invariant image blurs with phase. IEEE Trans. on Acoustic Speech and Signal Processing 24 (1) 58-63.
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.
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.
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.
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.
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.
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.
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.
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.
Sroubek F. Flusser J. (2005). Multichannel blind deconvolution of spatially misaligned images. IEEE Trans. Image Processing 14 (7) 874-883.
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.
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.
Greenspan H. Oz G. Kiryati N. Peled S. (2002). MRI inter-slice reconstruction using super resolution. Magnetic Resonance Imaging 20 (5) 437-446.