In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

Recent advances of kernel methods have yielded a framework for representing probabilities using a reproducing kernel Hilbert space, called kernel embedding of distributions. In this paper, we propose a Monte Carlo filtering algorithm based on kernel embeddings. The proposed method is applied to state-space models where sampling from the transition model is possible, while the observation model ...

Since the development of pulse compression in the mid-1950’s the concept has become an indispensable feature of modern radar systems. A matched filter is used on reception to maximize the signal to noise ratio of the received signal. The actual waveforms that are transmitted are chosen to have an autocorrelation function with a narrow peak at zero time shift and the other values, referred to as...

Probabilistic distance measures are important quantities in many research areas. For example, the Chernoff distance (or the Bhattacharyya distance as its special example) is often used to bound the Bayes error in a pattern classification task and the Kullback-Leibler (KL) distance is a key quantity in the information theory literature. However, computing these distances is a difficult task and ...

A reproducing-kernel Hilbert space approach to image interpolation is introduced. In particular, the reproducing kernels of Sobolev spaces are shown to be exponential functions. These functions, in turn, give rise to alternative interpolation kernels that outperform presently available designs. Both theoretical and experimental results are presented.

In this paper, we consider (random) sampling of signals concentrated on a bounded Corkscrew domain ? metric measure space, and reconstructing approximately from their (un)corrupted data taken set contained in ?. We establish weighted stability bi-Lipschitz type for scheme the reproducing kernel space. The provides weak robustness to scheme, however due nonconvexity signals, it does not imply un...