Related papers: Filters for anisotropic wavelet decompositions
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
We demonstrate an integrated photonic circuit based on feed forward photonic meshes that can be programmed and reconfigured to perform arbitrary spectral filter functions. We investigate a subset of the available filter functions,…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
In this paper, we have studied continuous fractional wavelet transform (CFrWT) in $n$-dimensional Euclidean space $\mathbb{R}^n$ with dilation parameter $\boldsymbol a=(a_{1},a_{2},\ldots,a_{n}),$ such that none of $a_{i}'s$ are zero.…
Beamforming with desired directivity patterns using compact microphone arrays is essential in many audio applications. Directivity patterns achievable using traditional beamformers depend on the number of microphones and the array aperture.…
We proved that for any matrix dilation and for any positive integer $n$, there exists a compactly supported tight wavelet frame with approximation order $n$. Explicit methods for construction of dual and tight wavelet frames with a given…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
TFDWT is an open-source Python library that allows the construction of TensorFlow Layers for Fast Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT) in end-to-end backpropagation learning networks. By definition,…
We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized…
Adaptive optics methods have long been used to perform complex light shaping at the output of a multimode fiber (MMF), with the specific aim of controlling the emitted beam in the near-field. Gaining control of other emission properties,…
In this article, we introduce the notion of Quaternion Boostlet Transform (QBT), a hypercomplex framework designed to unify the analysis of multi-component wavefields by merging the algebraic richness of quaternions with the relativistic,…
In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is…
Flicker artifacts, arising from unstable illumination and row-wise exposure inconsistencies, pose a significant challenge in short-exposure photography, severely degrading image quality. Unlike typical artifacts, e.g., noise and low-light,…
We present a practical methodology for inverse design of compact high-order/multiresonance filters in linear passive 2-port wave-scattering systems, targeting any desired transmission spectrum (such as standard pass/stop-band filters). Our…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
Advances in fluorescence microscopy have reached a plateau in improving depth-to-resolution ratios for imaging scattering tissues, highlighting an urgent need for innovative techniques. We introduce Wavelens, a groundbreaking opaque lens…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…