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arXiv:quant-ph/0401016 · Applied Optics

Quantum-implementable selective reconstruction of high-resolution images

Mitja Peruš, Horst Bischof, H. John Caulfield, Chu Kiong Loo

Published Nov 20, 2004• 37 citations
arXivHTMLPDF

Abstract

This paper, written for interdisciplinary audience, presents computational image reconstruction implementable by quantum optics. The input-triggered selection of a high-resolution image among many stored ones, and its reconstruction if the input is occluded or noisy, has been successfully simulated. The original algorithm, based on the Hopfield associative neural net, was transformed in order to enable its quantum-wave implementation based on holography. The main limitations of the classical Hopfield net are much reduced with the simulated new quantum-optical implementation.

DOI
10.1364/ao.43.006134

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This paper, written for interdisciplinary audience, presents computational image reconstruction implementable by quantum optics. The input-triggered selection of a high-resolution image among many stored ones, and its reconstruction if the input is occluded or noisy, has been successfully simulated. The original algorithm, based on the Hopfield associative neural net, was transformed in order to enable its quantum-wave implementation based on holography. The main limitations of the classical Hopfield net are much reduced with the simulated new quantum-optical implementation.
A quantum associative memory, much more natural than those of “quantum computers”, is presented. Neural-net-like processing with real-valued variables is transformed into processing with quantum waves. Successful computer simulations of image storage and retrieval are reported. Our Hopfield-like algorithm allows quantum implementation with holographic procedure using present-day quantum-optics techniques. This brings many advantages over classical Hopfield neural nets and quantum computers with logic gates.
A holographic experimental procedure assuming use of quantum states of light is simulated. It uses merely interference-based image storage and nonunitary image retrieval realized by wave function collapse. Successful results of computational view-invariant recognition of object images are presented. As in neural net theory, recognition is selective reconstruction of an image from a database of many concrete images (simultaneously stored in an associative memory) after presentation of a different version of that image. That is, in the first step, we store many high-resolution images of objects into quantum memory (a hologram). In the second step, we present a “nonlearned” noisy image version. We thereby trigger memory-influenced reorganization of the state of the system so that it finally encodes those corrected object images that correspond to the newly presented version. The holographic procedure seems to be implementable with present-day quantum optics.
It is computationally demonstrated how quantum associative networks, implemented using quantum holography, could be harnessed for object recognition. These simulated quantum nets alone execute efficient image recognition, i.e., reconstruction of an image selected from associative memory (hologram). However, optically implementable neural-net preprocessing of object-images is needed for appearance-based viewpoint-invariant recognition of objects. We present computer simulation results of two methods: Moore-Penrose orthogonalization and encoding of object-images with Gabor wavelets. A computer-supported quantum Gabor-wavelet holography is proposed. © 2005 Optical Society of America
Abstract Quantum computing is a new mode that follows the laws of quantum mechanics. It performs computational tasks based on the control of quantum units. From the view of computable problems, quantum computers can only solve the problems that traditional computers can solve, but considering the efficiency of computation, due to the existence of quantum superposition, some known quantum algorithms are exponentially faster than traditional general-purpose computers. In this article, we combine quantum computing with a classical neural network to design a quantum Hopfield network. Each neuron is initialized to a specified state and evolved into a steady state. The output result is one of patterns in a training set. We also present an application of this protocol in image recognition. The simulation results show that this network works in the quantum environment and the output images are correct, therefore the feasibility of this protocol is verified.
This paper investigates a novel image reconstruction algorithm leveraging the unique properties of high-order quantum entanglement. Traditional image reconstruction methods often struggle with high-resolution imagery, suffering from computational limitations and susceptibility to noise. We propose a new approach that utilizes quantum entanglement to accelerate the reconstruction process, enhancing image fidelity and robustness. The core of the algorithm centers around a quantum state representation and a carefully crafted entanglement protocol. The proposed method offers a significant advancement in image reconstruction, particularly for complex scenes and high-resolution images, potentially overcoming the limitations of classical approaches.
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.