Related papers: Finite Impulse Response Filters for Simplicial Com…
In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper…
This paper focuses on fast direct solvers for integral equations in the low-to-moderate-frequency regime obtained by leveraging preconditioned first kind or second kind operators regularized with Laplacian filters. The spectral errors…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
We introduce optical polarization-insensitive high pass filters based on total internal reflection of light at the interface of two dielectric media (1D) and Bragg reflection of a multilayer stack (2D) in transmission mode. The wavevectors…
Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is more flexible than other notions used so far in the…
We introduce a "loosely coherent" method for detection of continuous gravitational waves that bridges the gap between semi-coherent and purely coherent methods. Explicit control over accepted families of signals is used to increase…
This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles,…
Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding…
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal…
Shape- and scale-selective digital-filters, with steerable finite/infinite impulse responses (FIR/IIRs) and non-recursive/recursive realizations, that are separable in both spatial dimensions and adequately isotropic, are derived. The…
We propose a new class of passive nonlinear finite impulse response operators. This class is constructed by the action of finite impulse response filters in a lifted space. This allows for efficient control synthesis through constrained…
It is usual in helioseismology to remove unwanted instrumental low-frequency trends by applying high-pass filters to the time series. However, the choice of the filter is very important because it can keep the periodic signals throughout…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…