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In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
The new technique, multi-frequency imaging (MFI) is developed. In VLBI, Multi-Frequency Imaging (MFI) consists of multi-frequency synthesis (MFS) and multi-frequency analysis (MFA) of the VLBI data obtained from observations on various…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order…
This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
Bounds on the frequency domain behavior of electrically small antennas are adapted to assess the time domain distortion or fidelity achievable by simple linear time-invariant (LTI) systems. Rigorous expressions for a TM$_{01}$ spherical…
This paper studies the variation diminishing property of $k$-positive linear time-invariant (LTI) systems, which map inputs with $k-1$ sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
The performance of autonomous systems heavily relies on their ability to generate a robust representation of the environment. Deep neural networks have greatly improved vision-based perception systems but still fail in challenging…
We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are…
Full Waveform Inversion (FWI) stands as a nonlinear, high-resolution technology for subsurface imaging via surface-recorded data. This paper introduces an augmented Lagrangian dual formulation for FWI, rooted in the viewpoint that Lagrange…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
Quaternion-valued signals along with quaternion Fourier transforms (QFT)provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…
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…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…