This paper presents a novel approach for speckle reduction and coherence enhancement of ultrasound images based on nonlinear coherent diffusion (NCD) model. The proposed NCD model combines three different models. According to speckle extent and image anisotropy, the NCD model changes progressively from isotropic diffusion through anisotropic coherent diffusion to, finally, mean curvature motion. This structure maximally low-pass filters those parts of the image that correspond to fully developed speckle, while substantially preserving information associated with resolved-object structures. The proposed implementation algorithm utilizes an efficient discretization scheme that allows for real-time implementation on commercial systems. The theory and implementation of the new technique are presented and verified using phantom and clinical ultrasound images. In addition, the results from previous techniques are compared with the new method to demonstrate its performance.

Visual criteria for diagnosing diffused liver diseases from ultrasound images can be assisted by computerized tissue classification. Feature extraction algorithms are proposed in this paper to extract the tissue characterization parameters from liver images. The resulting parameter set is further processed to obtain the minimum number of parameters which represent the most discriminating pattern space for classification. This preprocessing step has been applied to over 120 distinct pathology-investigated cases to obtain the learning data for classification. The extracted features are divided into independent training and test sets, and are used to develop and compare both statistical and neural classifiers. The optimal criteria for these classifiers are set to have minimum classification error, ease of implementation and learning, and the flexibility for future modifications. Various algorithms of classification based on statistical and neural network methods are presented and tested. The authors show that very good diagnostic rates can be obtained using unconventional classifiers trained on actual patient data.

We present a study of the nonlinear dynamics of electrocardiogram (ECG) signals for arrhythmia characterization. The correlation dimension and largest Lyapunov exponent are used to model the chaotic nature of five different classes of ECG signals. The model parameters are evaluated for a large number of real ECG signals within each class and the results are reported. The presented algorithms allow automatic calculation of the features. The statistical analysis of the calculated features indicates that they differ significantly between normal heart rhythm and the different arrhythmia types and, hence, can be rather useful in ECG arrhythmia detection. On the other hand, the results indicate that the discrimination between different arrhythmia types is difficult using such features. The results of this work are supported by statistical analysis that provides a clear outline for the potential uses and limitations of these features.

A novel method for reducing field inhomogeneity effects in magnetic resonance images is described in this paper. Observing that image degradation arises from B0 inhomogeneity-induced phase accrual during data acquisition, the present method numerically rewinds the accumulated phase in the k-space data based on an initial estimate of the image and a corresponding field map. The rewinding process generates a corrected k-space data set that is subsequently Fourier transformed to produce the final image. In this paper, a theoretical analysis of the method and applications of the technique to magnetic resonance imaging data are presented. The theoretical analysis of the method indicates that it is a general approach applicable to a variety of sequences. Results obtained by applying the method to experimental data acquired with single-shot echo-planar imaging, segmented echo-planar imaging with centric reordering, and spiral sequences demonstrate that it is robust in reducing image degradation induced by B0 inhomogeneity.

In magnetic resonance imaging, spatial localization is usually achieved using Fourier encoding which is realized by applying a magnetic field gradient along the dimension of interest to create a linear correspondence between the resonance frequency and spatial location following the Larmor equation. In the presence of B0 inhomogeneities along this dimension, the linear mapping does not hold and spatial distortions arise in the acquired images. In this paper, the problem of image reconstruction under an inhomogeneous field is formulated as an inverse problem of a linear Fredholm equation of the first kind. The operators in these problems are estimated using field mapping and the k-space trajectory of the imaging sequence. Since such inverse problems are known to be ill-posed in general, robust solvers, singular value decomposition and conjugate gradient method, are employed to obtain corrected images that are optimal in the Frobenius norm sense. Based on this formulation, the choice of the imaging sequence for well-conditioned matrix operators is discussed, and it is shown that nonlinear k-space trajectories provide better results. The reconstruction technique is applied to sequences where the distortion is more severe along one of the image dimensions and the two-dimensional reconstruction problem becomes equivalent to a set of independent one-dimensional problems. Experimental results demonstrate the performance and stability of the algebraic reconstruction methods.

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