Related papers: Using Wavelet Decomposition to Determine the Dimen…
We present a new method, based on fractal analysis, to characterize the output of a physical detector that is in the form of a set of real-valued, discrete physical measurements. We apply the method to gravitational-wave data from the…
We propose a new multiscale method to calculate the amplitude of the gradient of the linear polarisation vector using a wavelet-based formalism. We demonstrate this method using a field of the Canadian Galactic Plane Survey (CGPS) and show…
We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the…
The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…
In order to constrain and possibly detect unusual physics during inflation, we allow the power spectrum of primordial matter density fluctuations, P_{in}(k), to be an arbitrary function in the estimation of cosmological parameters from…
Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a…
We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…
Gravitational wave lensing, particularly microlensing by compact dark matter (DM), offers a unique avenue to probe the nature of dark matter. However, conventional detection methods are often computationally expensive, inefficient, and…
The deconvolution, or cleaning, of radio interferometric images often involves computing model visibilities from a list of clean components, in order that the contribution from the model can be subtracted from the observed visibilities.…
Gravitational lensing of gravitational waves provides a powerful probe of the mass density distribution in the universe. Wave optics effects, such as diffraction, make the lensing effect sensitive to the structure around the Fresnel scale,…
In this paper, we present a wideband subspace estimation method that characterizes the signal subspace through its orthogonal projection matrix at each frequency. Fundamentally, the method models this projection matrix as a function of…
Crystal property prediction, governed by quantum mechanical principles, is computationally prohibitive to solve exactly for large many-body systems using traditional density functional theory. While machine learning models have emerged as…
We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
Using projection between Euclidian spaces of different dimensions, the signal compression and decompression become straightforward. This encoding/decoding technique requires no preassigned measuring matrix as in compressed sensing.…
We consider a common measurement paradigm, where an unknown subset of an affine space is measured by unknown continuous quasi-convex functions. Given the measurement data, can one determine the dimension of this space? In this paper, we…