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The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
Finding strong gravitational lenses in astronomical images allows us to assess cosmological theories and understand the large-scale structure of the universe. Previous works on lens detection do not quantify uncertainties in lens parameter…
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is…
It is demonstrated that non-constant kernel solution, that can fit the spatial variations of the kernel can be obtained with minimum computing time. The CPU cost required with this new extension of the image subtraction method is almost the…
Strong scattering medium brings great difficulties to optical imaging, which is also a problem in medical imaging and many other fields. Optical memory effect makes it possible to image through strong random scattering medium. However, this…
We propose a numerical interferometry method for identification of optical multiply-scattering systems when only intensity can be measured. Our method simplifies the calibration of optical transmission matrices from a quadratic to a linear…
In this paper we propose and analyse a Gedankenexperiment involving three non-linear crystals and two objects inserted in the idler beams. We show that, besides the behaviour that can be extrapolated from previous experiments involving two…
In order to efficiently image a non-absorbing sample (a phase object), dedicated phase contrast optics are required. Typically, these optics are designed with the assumption that the sample is weakly scattering, implying a linear relation…
Single borehole radar detection suffers from azimuthal ambiguity, while borehole optical tests only provide information about the borehole wall. These limitations prevent either detection method from revealing the complete spatial patterns…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
Extreme amodal detection is the task of inferring the 2D location of objects that are not fully visible in the input image but are visible within an expanded field-of-view. This differs from amodal detection, where the object is partially…
Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity.…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…
Fabric defect detection confronts two fundamental challenges. First, conventional non-maximum suppression disrupts gradient flow, which hinders genuine end-to-end learning. Second, acquiring pixel-level annotations at industrial scale is…
Weak gravitational lensing, the correlated distortion of background galaxy shapes by foreground structures, is a powerful probe of the matter distribution in our universe and allows accurate constraints on the cosmological model. In recent…
We consider the inverse scattering problem for inhomogeneous media of compact support governed by the fractional s-Helmholtz equation, with $0<s<1$, in dimensions $d=1,2,3$. In particular, we study the determination of the support of the…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
Many optical measurement techniques, such as light scattering from wavelength-scale particles or detecting motion from a surface with an optical lever, encode information in a complex radiation pattern. Extracting all available information…