Related papers: Polar Separable Transform for Efficient Orthogonal…
Mode sorting is an essential function for optical systems exploiting the orthogonality of photonic orbital angular momentum mode space. The familiar log-polar optical transformation provides an efficient yet simple approach, however with…
Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their…
Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly…
Space situational awareness demands efficient monitoring of terrestrial sites and celestial bodies, necessitating advanced target recognition systems. Current target recognition systems exhibit limited operational speed due to challenges in…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be…
In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO),…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing…
Optical coherence tomography (OCT) is pivotal in corneal imaging for both surgical planning and diagnosis. However, high-speed acquisitions often degrade spatial resolution and increase speckle noise, posing challenges for accurate…
Optical coordinate transformation (OCT) has attracted widespread attention in the field of orbital angular momentum (OAM) (de)multiplexing or manipulation, but the performance of OCT would suffer from its distortion. In this paper, we…
We present a structural resolution to the exact evaluation of the partition function $p_k(n)$, systematically overcoming the limitations of traditional recursive and asymptotic methods. By framing the partition polytope $\mathcal{P}_{n,k}$…
An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
Hybrid Opto-electronic correlators (HOC) overcome many limitations of all-optical correlators (AOC) while maintaining high-speed operation. However, neither the OEC nor the AOC in their conventional configurations can detect targets that…
In the last few years, large improvements in image clustering have been driven by the recent advances in deep learning. However, due to the architectural complexity of deep neural networks, there is no mathematical theory that explains the…
Placing a dataset $A = \{\mathbf{a}_i\}_{i \in [n]} \subset \mathbb{R}^d$ in radial isotropic position, i.e., finding an invertible $\mathbf{R} \in \mathbb{R}^{d \times d}$ such that the unit vectors $\{(\mathbf{R} \mathbf{a}_i)…
The Polar Mellin Transform (PMT) is a well-known technique that converts images into shift, scale and rotation invariant signatures for object detection using opto-electronic correlators. However, this technique cannot be properly applied…
This article presents novel numerical algorithms based on pseudodifferential operators for fast, direct, solution of the Helmholtz equation in 1D, 2D, and 3D inhomogeneous unbounded media. The proposed approach relies on an Operator Fourier…
The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the…