In medical images, noise suppression is a particularly delicate and difficult task. A trade off between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. Image processing specialists usually lack the biomedical expertise to judge the diagnostic relevance of the denoising results. For example, in ultrasound images, speckle noise may contain information useful to medical experts ; the use of speckled texture for a diagnosis was discussed in  and . Also, biomedical images show extreme variability and it is necessary to operate on a case by case basis . This motivates the construction of robust and versatile denoising methods that are applicable to various circumstances, rather than being optimal under very specific conditions. The notion of robustness in multiscale denoising was addressed in . In this paper, we propose one robust method that adapts itself to various types of image noise as well as to the preference of the medical expert: a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction.
In image denoising, one often faces uncertainty about the presence of a given “feature of interest” (e.g., an image edge) in a noisy observation. Due to the sparsity of the wavelet representation, the Middleton’s optimum coupled detection and estimation approach  seems well suited for wavelet domain image denoising. To the authors’ knowledge such approaches have received little attention so far in wavelet domain filtering. Bayesian methods , ,  take the uncertainty of the signal presence into account implicitly, assuming a Bernoulli process on the wavelet coefficients  and using Gaussian mixture models for the probability density functions of the wavelet coefficients. Related hereto, but more sophisticated, spatially adaptive methods usually employ complex algorithms, based on hidden Markov tree models ,  or Markov random field prior models , , . Other recent trends in wavelet-based image denoising include applying different types of filtering in supposedly smooth and supposedly heterogeneous or “edged” image regions , , spatially adaptive thresholding  and locally adaptive Wiener filtering .
outputs of MATLAB Code :
peaksnr before = 23.68
snr before = 13.80
peaksnr after = 27.809641756910743
snr after = 17.936949104490768
ssimValues before = 0.221784578748779
ssimValues after = 0.464511041250099
denoised image :
second input image :
noisy image :
denoised image :
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