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.