Hamiltonian and Q-Inspired Neural Network-Based Machine Learning

Citko, Wiesław; Sienko, Wieslaw

doi:10.1109/access.2020.3043035

Cited by 2 publications

(9 citation statements)

References 30 publications

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“…The transformations

and

, arranged as a realization of the mapping

, have the block structure, as shown in Figure 1 [ 1 ]. The orthogonal transformation

, which makes use of the Hurwitz-Radon matrix family [ 20 ], allows for determining the Haar–Fourier spectra of the system vectors

.…”

Section: Methodsmentioning

confidence: 99%

“…It is worth noting that, as mentioned in the Introduction, the reconstruction of Lena’ s photo was realized by using the structure presented in Figure 7 [ 1 ], as well. For example, one of the distorted images of Lena and the reconstruction is shown in Figure 9 .…”

Section: Methodsmentioning

confidence: 99%

“…However, it is worth noting that on other hand, the system in Figure 13 implements inverse transformation and solves optimization tasks constrained by images stored in memory. Moreover, this system enables the solving of linear Equation (23) by using a random form of training vectors

in Equation (26) [ 1 ] as well.…”

Section: Inpainted Image Recognition and Reconstruction As An Inverse...mentioning

confidence: 99%

“…The machine learning model described in a previous paper [ 1 ] was derived from an extended Hopfield neural network and is based on spectral analysis that uses biorthogonal and orthogonal transformations. It should be emphasized that this system has a universal character that enables the implementation of basic functions of learning systems, such as pattern association, pattern recognition, and inverse modeling.…”

Section: Introductionmentioning

confidence: 99%

“…One of the aforementioned properties of this model is the recognition and reconstruction of image patterns. In [ 1 ], we presented an example where the object of the reconstruction was an incomplete, inpainted image of a subject named Lena. Such examples of reconstruction allow for the development of a system based on the above-mentioned model of machine learning that can recognize people wearing masks.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Citko

Sienko

2022

Sensors

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This paper considers the use of a machine learning system for the reconstruction and recognition of distorted or damaged patterns, in particular, images of faces partially covered with masks. The most up-to-date image reconstruction structures are based on constrained optimization algorithms and suitable regularizers. In contrast with the above-mentioned image processing methods, the machine learning system presented in this paper employs the superposition of system vectors setting up asymptotic centers of attraction. The structure of the system is implemented using Hopfield-type neural network-based biorthogonal transformations. The reconstruction property gives rise to a superposition processor and reversible computations. Moreover, this paper’s distorted image reconstruction sets up associative memories where images stored in memory are retrieved by distorted/inpainted key images.

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“…The transformations

and

, arranged as a realization of the mapping

, have the block structure, as shown in Figure 1 [ 1 ]. The orthogonal transformation

, which makes use of the Hurwitz-Radon matrix family [ 20 ], allows for determining the Haar–Fourier spectra of the system vectors

.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

in Equation (26) [ 1 ] as well.…”

Section: Inpainted Image Recognition and Reconstruction As An Inverse...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Citko

Sienko

2022

Sensors

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Image Recognition and Reconstruction With Machine Learning: An Inverse Problem Approach

Citko,

Sienko

2023

IEEE Access

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Image recognition and reconstruction are common problems in many image processing systems. These problems can be formulated as a solution to the linear inverse problem. This article presents a machine learning system model that can be used in the reconstruction and recognition of vectorized images. The analyzed inverse problem is given by the equations 𝐹(𝒙 𝒊 ) = 𝒚 𝑖 and 𝒙 𝑖 = 𝐹 −1 (𝒚 𝑖 ), 𝑖 = 1, … , 𝑁, where 𝐹(•) is a linear mapping for 𝒙 𝑖 ∈ 𝑋 ⊂ 𝑅 𝑛 , 𝒚 𝑖 ∈ 𝑌 ⊂ 𝑅 𝑚 . Thus, 𝒚 𝑖 can be seen as a projection of image 𝒙 𝑖 , and 𝒙 𝑖 should be reconstructed as a solution to the inverse problem. We consider image reconstruction as an inverse problem using two different schemes. The first one, when 𝒙 𝑖 = 𝐹 −1 (𝒚 𝑖 ), can be seen as an operation with associative memory, and the second one, when 𝒙 𝑖 = 𝐹 −1 (𝒚 𝑖 ), can be implemented by creating random vectors for training sets. Moreover, we point out that the solution to the inverse problem can be generalized to complex-valued images 𝒙 𝑖 and 𝒚 𝑖 . In this paper, we propose a machine learning model based on a spectral processor as an alternative solution to deep learning based on optimization procedures.INDEX TERMS Machine learning systems, image reconstruction and recognition, inverse problem.

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Hamiltonian and Q-Inspired Neural Network-Based Machine Learning

Cited by 2 publications

References 30 publications

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Inpainted Image Reconstruction Using an Extended Hopfield Neural Network Based Machine Learning System

Image Recognition and Reconstruction With Machine Learning: An Inverse Problem Approach

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