相关论文: Uncertainty Principles for the Offset Linear Canon…
Convolutional Neural Networks (CNNs) are the current de-facto models used for many imaging tasks due to their high learning capacity as well as their architectural qualities. The ubiquitous UNet architecture provides an efficient and…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…
Holographic optical coherence tomography (OCT) is a powerful imaging technique, but its ability to reveal low-reflectivity features is limited. In this study, we performed holographic OCT by incoherently averaging volumes with changing…
Optical coherence tomography (OCT) is an important interferometric diagnostic technique which provides cross-sectional views of the subsurface microstructure of biological tissues. However, the imaging quality of high-speed OCT is limited…
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their…
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the…
Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be non-idealities associated with the photons and the experimental setup which will…
Optical coherence tomography (OCT) is a 3D imaging technique that was introduced in 1991 [Science 254, 1178 (1991); Applied Optics 31, 919 (1992)]. Since 2018 there has been growing interest in a new type of OCT scheme based on the use of…
Optical coherence tomography (OCT) has proven to be a powerful technique for studying tissue morphology in ophthalmology, cardiology, and endomicroscopy. Its performance is limited by the fundamental trade-off between the imaging…
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…
In this paper, we generalize the continuous quaternion shearlet transform on $\mathbb{R}^{2}$ to $\mathbb{R}^{2d}$, called the multivariate two sided continuous quaternion shearlet transform. Using the two sided quaternion Fourier…
The scientific interest in studying high-energy transient phenomena in the Universe has largely grown for the last decade. Now, multiple ground-based survey projects have emerged to continuously monitor the optical (and multi-messenger)…
We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ…
Optical imaging is commonly used for both scientific and technological applications across industry and academia. In image sensing, a measurement, such as of an object's position, is performed by computational analysis of a digitized image.…
Transformers have driven remarkable breakthroughs in natural language processing and computer vision, yet their standard attention mechanism still imposes O(N^2) complexity, hindering scalability to longer sequences. We introduce…
We introduce Observation-aware Conformal Uncertainty Local-Calibration (OCULAR), a conformal prediction-based algorithm that uses perception information to provide uncertainty quantification guarantees for unseen test-time environments.…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \cite{FB} and for the $q$-Fourier-sine transform.
We construct an accurate imaging theory for optical coherence tomography/microscopy (OCT/OCM) without approximations to calculate precise optical resolution and imaging characteristics. Our theory represents a broadband light source using a…