Related papers: Beamforming in the Reproducing Kernel Domain Based…
A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper,…
Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…
Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
Designing unimodular waveforms with a desired beampattern, spectral occupancy and orthogonality level is of vital importance in the next generation Multiple-Input Multiple-Output (MIMO) radar systems. Motivated by this fact, in this paper,…
In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $\mathbb{S}^d \subset \mathbb{R}^{d+1}$. The reproducing kernel is given by an integral representation using the truncated power function…
In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on…
This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…
Audio zooming, a signal processing technique, enables selective focusing and enhancement of sound signals from a specified region, attenuating others. While traditional beamforming and neural beamforming techniques, centered on creating a…
Spatial aliasing affects spaced microphone arrays, causing directional ambiguity above certain frequencies, degrading spatial and spectral accuracy of beamformers. Given the limitations of conventional signal processing and the scarcity of…
We present a single-stage casual waveform-to-waveform multichannel model that can separate moving sound sources based on their broad spatial locations in a dynamic acoustic scene. We divide the scene into two spatial regions containing,…
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…
Ambisonics is a method for capturing and rendering a sound field accurately, assuming that the acoustics of the playback room does not significantly influence the sound field. However, in practice, the acoustics of the playback room may…
We give a derivation of the non-Markovian quantum state diffusion equation of Di{\'o}si and Strunz starting from a model of a quantum mechanical system coupled to a bosonic bath. We show that the complex trajectories arises as a consequence…
In this work, we introduce a spatio-temporal kernel for Gaussian process (GP) regression-based sound field estimation. Notably, GPs have the attractive property that the sound field is a linear function of the measurements, allowing the…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of $L^p(\Rd), 1\le p\le \infty$, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity.…
While existing end-to-end beamformers achieve impressive performance in various front-end speech processing tasks, they usually encapsulate the whole process into a black box and thus lack adequate interpretability. As an attempt to fill…