An analytical inversion formula for the exponential Radon transform with an imaginary attenuation coefficient was developed in 2007 (2007 Inverse Problems 23 1963-71). The inversion formula in that paper suggested that it is possible to obtain an exact MRI (magnetic resonance imaging) image without acquiring low-frequency data. However, this un-measured low-frequency region (ULFR) in the k-spac...

Recovery rate is essential to the estimation of the portfolio's loss and economic capital. Neglecting the randomness of the distribution of recovery rate may underestimate the risk. The study introduces two kinds of models of distribution, Beta distribution estimation and kernel density distribution estimation, to simulate the distribution of recovery rates of corporate loans and bonds. As is k...

Over-exposure and perspective distortion are two of the main factors underlying inaccurate feature extraction. First, based on Steger's method, we propose a method for correcting curvilinear structures (lines) extracted from over-exposed images. A new line model based on the Gaussian line profile is developed, and its description in the scale space is provided. The line position is analytically...

ABSTRACT The use of distances between Time-Frequency Representations (TFRs) has recently led to a time-frequency formulation of the problem of non-stationary signals classification. In this paper, we propose a new method based upon the optimization of the TFR, remaining in the Cohen’s group. We show that a radially gaussian kernel and a Fisher-like contrast criterion provide improved classifica...

Measuring the diffusion properties of crossing fibers is very challenging due to the high number of model parameters involved and the intrinsically low SNR of Diffusion Weighted MR Images. Noise filtering aims at suppressing the noise while pertaining the data distribution. We propose an adaptive version of the Linear Minimum Mean Square Error (LMMSE) estimator to achieve this. Our filter appli...

Ž . Temporal complexity of early ventricular fibrillation VF is re-assessed through measuring the correlation dimension Ž . D , entropy K and high-dimensional component s from electrocardiogram ECG recordings using the Gaussian kernel 2 2 algorithm. Seven representative ECG traces of induced VF among 53 pig subjects are selected for analysis. VF is found to have 80–90% low-dimensional determini...

Gaussian kernel smoothing has been widely used in 3D whole brain imaging analysis as a way to increase signal-to-noise ratio. Gaussian kernel is isotropic in Euclidian space. However, data obtained on the convoluted brain cortex fails to be isotropic in the Euclidean sense. On the curved surface, a straight line between two points is not the shortest distance so one may incorrectly assign less ...

In this paper, we apply kernel PCA for speech enhancement and derive pre-image iterations for speech enhancement. Both methods make use of a Gaussian kernel. The kernel variance serves as tuning parameter that has to be adapted according to the SNR and the desired degree of de-noising. We develop a method to derive a suitable value for the kernel variance from a noise estimate to adapt pre-imag...

The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore exte...

The importance of the support vector machine and its applicability to a wide range of problems is well known. The strength of the support vector machine lies in its kernel. In our recent paper, we have shown how the Laplacian kernel overcomes some of the drawbacks of the Gaussian kernel. However this was not a total remedy for the shortcomings of the Gaussian kernel. In this paper, we design a ...