Image denoising employing local mixture models in sparse domains

In this study, the authors fit three univariate mixture distributions to the image coefficients in four sparse domains [ordinary discrete wavelet transform (DWT), discrete complex wavelet transform (DCWT), discrete contourlet transform (DCOT) and discrete curvelet transform (DCUT)]. By estimating the parameters of these mixture priors locally using adjacent coefficients in the same scale, the authors characterise the heavy-tailed nature and the intrascale statistical dependency of these coefficients. Using these mixture-local-priors, the authors derive estimators using maximum a posteriori (MAP) and minimum mean squared error (MMSE) for image denoising. Using the proposed shrinkage functions in these sparse domains for various window sizes from our simulations, we conclude that: (i) among these transforms the DCWT is preferred both in terms of performance and computational cost; (ii) the best window size for denoising depends on the noise level and type of image; (iii) incorporating interscale dependency into the denoising process results in some improvement only for uncrowded images, and (iv) the MMSE estimators outperform the MAP estimators if the input peak signal-to-noise ratio (PSNR) is greater than 28 dB and the MAP estimators are preferred for PSNR smaller than 22 dB.