Gonzalo Vegas-Sánchez-Ferrero

Automatic noise estimation in images using local statistics. Additive and multiplicative cases

In this paper, we focus on the problem of automatic noise parameter estimation for additive and multiplicative models and propose a simple and novel method to this end. Specifically we show that if the image to work with has a sufficiently great amount of low-variability areas (which turns out to be a typical feature in most images), the variance of noise (if additive) can be estimated as the mode of the distribution of local variances in the image and the coefficient of variation of noise (if multiplicative) can be estimated as the mode of the distribution of local estimates of the coefficient of variation. Additionally, a model for the sample variance distribution for an image plus noise is proposed and studied. Experiments show the goodness of the proposed method, specially in recursive or iterative filtering methods.

Unsupervised 4D myocardium segmentation with a Markov Random Field based deformable model

A stochastic deformable model is proposed for the segmentation of the myocardium in Magnetic Resonance Imaging. The segmentation is posed as a probabilistic optimization problem in which the optimal time-dependent surface is obtained for the myocardium of the heart in a discrete space of locations built upon simple geometric assumptions. For this purpose, first, the left ventricle is detected by a set of image analysis tools gathered from the literature. Then, the segmentation solution is obtained by the Maximization of the Posterior Marginals for the myocardium location in a Markov Random Field framework which optimally integrates temporal-spatial smoothness with intensity and gradient related features in an unsupervised way by the Maximum Likelihood estimation of the parameters of the field. This scheme provides a flexible and robust segmentation method which has been able to generate results comparable to manually segmented images for some derived cardiac function parameters in a set of 43 patients affected in different degrees by an Acute Myocardial Infarction.

Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods - based on a single noise level for the whole image - fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.

A local fuzzy thresholding methodology for multiregion image segmentation

Thresholding is a direct and simple approach to extract different regions from an image. In its basic formulation, thresholding searches for a global value that maximizes the separation between output classes. The use of a single hard threshold value is precisely the source of important segmentation errors in many scenarios like noisy images or uneven illumination. If no connectivity or closed objects are considered, the method is prone to produce isolated pixels. In this paper a new multiregion thresholding methodology is presented to overcome the common drawbacks of thresholding methods when images are corrupted with artifacts and noise. It is based on relating each pixel in the image to different output centroids via a fuzzy membership function, avoiding any initial hard decision. The starting point of the technique is the definition of the output centroids using a clustering method compatible with most thresholding techniques in the literature. The method makes use of the spatial information through a local aggregation step where the membership degree of each pixel is modified by local information that takes into account the memberships of the surrounding pixels. This makes the method robust to noise and artifacts. The general formulation of the proposed methodology allows the design of spatial aggregations for multiple applications, including the possibility of including heuristic information via a fuzzy inference rule base.

Anisotropic Diffusion Filter With Memory Based on Speckle Statistics for Ultrasound Images

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.

On the influence of interpolation on probabilistic models for ultrasonic images

The influence of the cartesian interpolation of ultrasound data over the final image statistical model is studied. When fully formed speckle is considered and no compression of the data is done, we show that the interpolated final image can be modeled following a Gamma distribution, which is a good approximation for the weighted sum of Rayleigh variables. The importance of taking into account the interpolation stage to statistically model ultrasound images is pointed out. The interpolation model here proposed can be easily extended to more complex distributions.

Spatially variant noise estimation in MRI: A homomorphic approach

The reliable estimation of noise characteristics in MRI is a task of great importance due to the influence of noise features in extensively used post-processing algorithms. Many methods have been proposed in the literature to retrieve noise features from the magnitude signal. However, most of them assume a stationary noise model, i.e., the features of noise do not vary with the position inside the image. This assumption does not hold when modern scanning techniques are considered, e.g., in the case of parallel reconstruction and intensity correction. Therefore, new noise estimators must be found to cope with non-stationary noise. Some methods have been recently proposed in the literature. However, they require multiple acquisitions or extra information which is usually not available (biophysical models, sensitivity of coils). In this work we overcome this drawback by proposing a new method that can accurately estimate the non-stationary parameters of noise from just a single magnitude image. In the derivation, we considered the noise to follow a non-stationary Rician distribution, since it is the most common model in real acquisitions (e.g., SENSE reconstruction), though it can be easily generalized to other models. The proposed approach makes use of a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is then estimated by a low pass filtering with a Rician bias correction. Results in real and synthetic experiments evidence the better performance and the lowest error variance of the proposed methodology when compared to the state-of-the-art methods.

A Markov Random Field Approach for Topology-Preserving Registration: Application to Object-Based Tomographic Image Interpolation

This paper proposes a topology-preserving multiresolution elastic registration method based on a discrete Markov random field of deformations and a block-matching procedure. The method is applied to the object-based interpolation of tomographic slices. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy based on intensity- and gradient-related features, the smoothness of the transformation is favored by an appropriate prior on the field, and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori configuration. Additionally, the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters. In order to obtain an unbiased interpolation result, the registration is performed both in the forward and backward directions, and the resulting transformations are combined by using the local information content of the deformation. The method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso. Quantitative comparisons offer an overall improvement in performance with respect to related works in the literature. Additionally, the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant.

Probabilistic-driven oriented speckle reducing anisotropic diffusion with application to cardiac ultrasonic images

A novel anisotropic diffusion filter is proposed in this work with application to cardiac ultrasonic images. It includes probabilistic models which describe the probability density function (PDF) of tissues and adapts the diffusion tensor to the image iteratively. For this purpose, a preliminary study is performed in order to select the probability models that best fit the stastitical behavior of each tissue class in cardiac ultrasonic images. Then, the parameters of the diffusion tensor are defined taking into account the statistical properties of the image at each voxel. When the structure tensor of the probability of belonging to each tissue is included in the diffusion tensor definition, a better boundaries estimates can be obtained instead of calculating directly the boundaries from the image. This is the main contribution of this work. Additionally, the proposed method follows the statistical properties of the image in each iteration. This is considered as a second contribution since state-of-the-art methods suppose that noise or statistical properties of the image do not change during the filter process.

About the background distribution in MR data: a local variance study

A model for the distribution of the sample local variance (SLV) of magnetic resonance data is proposed. It is based on a bimodal Gamma distribution, whose maxima are related to the signal and background areas of the image. The model is valid for single- and multiple-coil systems. The proposed distribution allows us to characterize some signal/background properties in MR data. As an example, the model is used to study the effect of the background size over noise estimation techniques and a method to test the validity of background-based noise estimators is presented.