Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: Five Toeplitz-type schemes for the Hadamard finite-part integral operator are presented and the accuracy of schemes for solving integral equations with a hypersingular kernel is shown.
36 citations
20 Aug 2006
TL;DR: A novel method to detect the moving cast shadows in the scene using normalized coefficients of orthogonal transform of image block are proved to be illumination invariant and are used to classify moving shadows and foreground objects.
Abstract: In many image and computer vision applications, shadows interfere with fundamental tasks such as moving objects segmentation and tracking. In this paper, a novel method is proposed to detect the moving cast shadows in the scene. The normalized coefficients of orthogonal transform of image block are proved to be illumination invariant and are used to classify moving shadows and foreground objects. Five kinds of orthogonal transform: DCT, DFT, Haar Transform, SVD and Hadamard Transform, are utilized in our work to detect moving cast shadows. Experimental results show that the proposed method succeeds in detecting moving cast shadows within indoor and outdoor environments.
36 citations
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TL;DR: A novel hybrid quantum-classical algorithm for simulating the dynamics of quantum systems that does not require any classical-quantum feedback loop and by construction bypasses the barren plateau problem.
Abstract: Quantum simulation offers a possibility to explore the exponentially large configuration space of quantum mechanical systems and thus help us study poorly understood topics such as high-temperature superconductivity and drug design. Here, we provide a novel hybrid quantum-classical algorithm for simulating the dynamics of quantum systems. Without loss of generality, the Hamiltonian is assumed to be a linear combination of unitaries and the Ansatz wavefunction is taken as a linear combination of quantum states. The quantum states are fixed, and the combination parameters are variationally adjusted. Unlike existing variational quantum simulation algorithms, our algorithm does not require any classical-quantum feedback loop and by construction bypasses the barren plateau problem. Moreover, our algorithm does not require any complicated measurements, such as the Hadamard test. The entire framework is compatible with existing experimental capabilities and thus can be implemented immediately. We also provide an extension of our algorithm to imaginary time evolution.
35 citations
TL;DR: In this paper, the equivalence classes of Hadamard matrices of order at most 28 have been found by 1994, and the remaining two types of these matrices are expected to be insigniflcant.
Abstract: All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We flnd all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another type. Based on experience with the classiflcation of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insigniflcant.
35 citations
17 May 2019
TL;DR: In this article, the authors introduce the concept of interval (h 1, h 2 ) -convex functions and establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature.
Abstract: We introduce the concept of interval ( h 1 , h 2 ) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples.
35 citations