In this paper, we focus on the problem of speckle removal by means of anisotropic diffusion and, specifically, on the importance of the correct estimation of the statistics involved. First, we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed, which is the case of a previously reported filter, namely, SRAD. Then, we focus on the problem of estimation of the coefficient of variation of both signal and noise and of noise itself. Our experiments indicate that neighborhoods used for parameter estimation do not need to coincide with those used in the diffusion equations. Then, we show that, as long as the estimates are good enough, the filter proposed here and the SRAD perform fairly closely, a fact that emphasizes the importance of the correct estimation of the coefficients of variation

A new method for noise filtering in images that follow a Rician model-with particular attention to magnetic resonance imaging-is proposed. To that end, we have derived a (novel) closed-form solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are developed. These methods use information of the sample distribution of local statistics of the image, such as the local variance, the local mean, and the local mean square value. Accordingly, the dynamic estimation of noise leads to a recursive version of the LMMSE, which shows a good performance in both noise cleaning and feature preservation. This paper also includes the derivation of the probability density function of several local sample statistics for the Rayleigh and Rician model, upon which the estimators are built.

Ultrasound (US) imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle, which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods. With the aim of alleviating the effect of speckle, many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection. Most of the state-of-the-art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature. However, the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes. This loss of information is even magnified due to the iterative process of some speckle filters, e.g., diffusion filters, which tend to produce over-filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process. In this paper, we propose an anisotropic diffusion filter with a probabilistic-driven memory mechanism to overcome the over-filtering problem by following a tissue selective philosophy. In particular, we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues, by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved. Results both in synthetic and real US images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures, which are removed by the state-of-the-art filters.

A new and complementary method to assess image quality is presented. It is based on the comparison of the local variance distribution of two images. This new quality index is better suited to assess the non-stationarity of images, therefore it explicitly focuses on the image structure. We show that this new index outperforms other methods for the assessment of image quality in medical images