Increasing the accessible resolution range for computational ghost imaging based on Hadamard matrices (Conference Presentation)

This study proposes two methods of optical watermarking based on multiplexed time-varying signals for computational ghost imaging using the Hadamard matrices. The proposed methods can realize image fusion and dual optical encryption. The time-varying signal is encoded into a specific Hadamard coefficient in advance and hidden in the light source of the transmitting end as a multiplicative factor or loaded at the receiving end as an additive factor. Theory and experiments confirm the feasibility of this scheme. Moreover, the scheme is highly scalable and has potential applications in multispectral single-pixel imaging.

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Some Infinite Series of 2-Weighing and 3-Weighing Matrices from Hadamard Matrices

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/963 ◽

2018 ◽

Vol 9 (12) ◽

pp. 2165-2168

Author(s):

Gopal Prajapati ◽

Mithilesh Kumar Singh

Keyword(s):

Infinite Series ◽

Hadamard Matrices ◽

Weighing Matrices

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Circles on lattices and Hadamard matrices

Information and Control Systems ◽

10.31799/1684-8853-2019-3-2-9 ◽

2019 ◽

pp. 2-9 ◽

Cited By ~ 1

Author(s):

N. A. Balonin ◽

M. B. Sergeev ◽

J. Seberry ◽

O. I. Sinitsyna

Keyword(s):

Hadamard Matrices ◽

Lattice Points ◽

Practical Significance ◽

Upper And Lower Bounds ◽

Problem Size ◽

Orthogonal Matrices ◽

Video Information ◽

Scientific Schools ◽

Gauss Theorem ◽

Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

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Experimental demonstration of spectral domain computational ghost imaging

Scientific Reports ◽

10.1038/s41598-021-87355-z ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Piotr Ryczkowski ◽

Caroline G. Amiot ◽

John M. Dudley ◽

Goëry Genty

Keyword(s):

Signal To Noise Ratio ◽

Michelson Interferometer ◽

Spectral Domain ◽

Proof Of Concept ◽

Ghost Imaging ◽

Spectral Measurements ◽

Spectral Filter ◽

Wavelength Division ◽

Spectral Encoding ◽

Light Effects

AbstractWe demonstrate computational spectral-domain ghost imaging by encoding complementary Fourier patterns directly onto the spectrum of a superluminescent laser diode using a programmable spectral filter. Spectral encoding before the object enables uniform spectral illumination across the beam profile, removing the need for light collection optics and yielding increased signal-to-noise ratio. In addition, the use of complementary Fourier patterns allows reduction of deleterious of parasitic light effects. As a proof-of-concept, we measure the wavelength-dependent transmission of a Michelson interferometer and a wavelength-division multiplexer. Our results open new perspectives for remote broadband spectral measurements.

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Correspondence Fourier-transform ghost imaging

Physical Review A ◽

10.1103/physreva.103.043717 ◽

2021 ◽

Vol 103 (4) ◽

Author(s):

Chenyu Hu ◽

Ruiguo Zhu ◽

Hong Yu ◽

Shensheng Han

Keyword(s):

Fourier Transform ◽

Ghost Imaging

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Hermitian congruence and the existence and completion of generalized Hadamard matrices

Journal of Combinatorial Theory Series A ◽

10.1016/0097-3165(88)90054-4 ◽

1988 ◽

Vol 49 (2) ◽

pp. 233-261 ◽

Cited By ~ 15

Author(s):

Bradley W Brock

Keyword(s):

Hadamard Matrices

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Counterfactual ghost imaging

npj Quantum Information ◽

10.1038/s41534-021-00411-4 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Jonte R. Hance ◽

John Rarity

Keyword(s):

Signal To Noise Ratio ◽

Ghost Imaging ◽

Signal To Noise ◽

Interesting Phenomenon ◽

Order Of Magnitude ◽

Noise Ratio

AbstractWe give a protocol for ghost imaging in a way that is always counterfactual—while imaging an object, no light interacts with that object. This extends the idea of counterfactuality beyond communication, showing how this interesting phenomenon can be leveraged for metrology. Given, in the infinite limit, no photons ever go to the imaged object, it presents a method of imaging even the most light-sensitive of objects without damaging them. Even when not in the infinite limit, it still provides a many-fold improvement in visibility and signal-to-noise ratio over previous protocols, with over an order of magnitude reduction in absorbed intensity.

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Hadamard Matrices with Cocyclic Core

Mathematics ◽

10.3390/math9080857 ◽

2021 ◽

Vol 9 (8) ◽

pp. 857

Author(s):

Víctor Álvarez ◽

José Andrés Armario ◽

María Dolores Frau ◽

Félix Gudiel ◽

María Belén Güemes ◽

...

Keyword(s):

Hadamard Matrices ◽

Combinatorial Designs ◽

Powerful Technique ◽

Uniform Approach ◽

Structured Approach

Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.

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