Quantum Image Processing -- Challenges and Future Research Issues

arXiv:2008.12983 · quant-ph · Submitted 2020-08-29 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum Image Processing -- Challenges and Future Research Issues".

Mira: The gist: This review article provides an overview of progress in Quantum Image processing while also simulating further interest to pursue more advanced research in it.

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper today called Quantum Image Processing -- Challenges and Future Research Issues. Mira, what do you think about the title itself?

Mira: I think it’s pretty straightforward, it sets the stage for a deep dive into how we move from classical image processing to something quantum.

Kai: Exactly. It tells us this isn't just some quick fix; they're looking at the real challenges and what comes next in this area.

Lev: From my side, I’m curious if they’re talking about things that are actually feasible right now on current hardware setups or if it's purely theoretical stuff.

Mira: Well, based on what I see in the introduction of this paper, they start by setting up the basics of quantum computing and qubits before jumping into image stuff.

Kai: Right, so we're getting the fundamentals first—the physics behind how these quantum bits actually work before we even touch an image.

Lev: That sounds like a necessary foundation if you want to assess the real engineering hurdles later on, since those are where things usually get messy for actual hardware.

Mira: It seems they want to establish that groundwork so we understand the context of why this research matters in the first place.

The paper's summary: Kai: So, what’s the core idea here, fundamentally? This paper reviews different methods for storing and retrieving 2D image data using quantum systems <ref:2008.12983#pg1>.

Mira: They are looking at things like Quantum Normalized Amplitude Based Image Processing or QNAIMP, and Quantum Entangled Image Processing or QEIP.

Kai: Right, so instead of a regular pixel value, they’re trying to represent the visual information through quantum states and then figure out how to pull that information back out.

Lev: When they talk about representation—like the QNAIMP where you have a matrix of row and column vectors—that implies we're mapping classical pixels onto this quantum structure first.

Mira: Precisely, and then they show the math for that, like defining the normalized amplitude image matrix M N alpha p,q as the square root of AMPp,q divided by the square root of a sum over all AMPp,q >

Kai: And then they propose representing those amplitudes with multiple qubits using something like M N Z> equals the sum over alpha eta p,q times Lpq.

Lev: That representation sounds complicated to run; if you have to store visual information in a three-dimensional set of qubit lattices, that’s a massive resource requirement for any current machine we have <ref:2008.12983#pg1>.

Mira: The goal of this approach is to store the visual information in Z where Z is a three-dimensional set of qubit lattices and each layer Q k in Z will be used to store a copy of the image.

The paper's improvements: Kai: Moving past just defining the methods, what are the actual suggested improvements or directions they point toward for this research area?

Mira: They suggest several areas for future work, and one big thing is exploring quantum operations that affect multiple images together.

Kai: They specifically mention things like image matching and image searching on a set of images within FRQI states as future scopes to investigate.

Lev: If they're talking about complex operations affecting multiple images at once, you immediately have to think about how that scales up the error correction overhead significantly.

Mira: And another point is the issue of quantum noise reduction from medical images, which they flag as a big problem right now in that application.

Kai: They also touch on using a more flexible representation called Flexible Representation of Quantum Images or FRQI to encode color and position information deterministically through the state Q> equals C>m P>2n <ref:2008.12983#pg1>.

Lev: Deterministic encoding is good for control, but it means we need a very precise way to prepare those multi-qudit states you mentioned earlier, which brings us back to the preparation challenge.

Conclusion: Kai: So wrapping up this paper on Quantum Image Processing -- Challenges and Future Research Issues, what’s the main thing we should take away about where this field stands right now?

Mira: The main point is that while there are different quantum methods to represent and retrieve images, there's a lot of work still needed to figure out which approach offers the real advantage over classical systems.

Kai: It’s clear they are mapping out a path for smooth, effective, and fast Quantum Image Processing technologies that can actually give us full use of quantum computing potential.

Lev: From an engineering standpoint, it sounds like the immediate hurdle is reducing those resource requirements and managing the error rates when you try to implement these complex representations.

Mira: Right, so it’s a survey showing the landscape but still pointing toward very specific, hard problems that need solving before we see widespread results in this area.

Sanjay Chakraborty, Sudhindu Bikash Mandal, Soharab Hossain Shaikh

A.K.Choudhury School of Information Technology, University of Calcutta · BML Munjal University

quant-ph

Submitted: 2020-08-29

Updated: 2020-08-29

Journal ref: International Journal of Information Technology, 14(1), 2018

DOI: 10.1007/s41870-018-0227-8

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 68/100

The gist: The gist: This review article provides an overview of progress in Quantum Image processing while also simulating further interest to pursue more advanced research in it.

Key concepts

Qubit: A qubit is the basic unit of quantum information, analogous to a classical bit but capable of being in a superposition of both states |0> and |1>. This allows quantum systems to hold more complex information simultaneously, which is crucial for advanced image representation.
Quantum Normalized Amplitude Based Image Processing (QNAIMP): QNAIMP represents an image using a matrix where pixel locations are defined by row and column numbers. It calculates a normalized amplitude matrix that stores all pixel locations sharing the same amplitude values across the entire image, providing a structured way to encode visual data into quantum states.
Quantum Entangled Image Processing (QEIP): QEIP utilizes quantum entanglement to store binary images. By encoding an array of qubits, specific vertices corresponding to a square shape can be stored as |1> states. Retrieving the image involves applying Grover’s search algorithm to find these specific entangled locations.
Quantum Image Compression (QIC): QIC aims to reduce the quantum resources needed for image preparation. This is achieved by applying minimization strategies to transformed Boolean minterm forms, effectively finding more efficient ways to store visual information within the limited space of quantum bits.

Terminology

Quantum Physics — 1× in this paper · explained in 12 episodes

Summary

The gist: This review article provides an overview of progress in Quantum Image processing while also simulating further interest to pursue more advanced research in it.

Introduction and Motivation

Quantum computing is an emerging technology that aims to improve overall performance of computation by exploiting the laws of quantum physics, such as information encoding, processing, and communication [1] (Page 1). This concept helps build much smaller embedded electronic devices to perform computation more quickly, effectively and efficiently [6] (Page 1). Quantum computing is part of futuristic computing but experiments have been carried out where quantum computational operations were executed on a very small number of quantum bits [6] (Page 1). Among all these fields, quantum computing has an important impact on image processing field [2] (Page 2). Researchers are working on optimizing various image processing algorithms in terms of their quickness, efficiency and accuracy in the quantum image processing field [2] (Page 2). The major questions to be described throughout this paper include what is the advantage of using quantum computing approach in image processing? (Page 2).

Qubit Fundamentals

The basis of classical computing is bits whereas the basis of quantum computing is qubits [1.2]. A qubit represents some sort of atomic structure like, hydrogen atom [1.2]. It is confined to be 0> and 1> states which represents ground and excited states respectively [7] (Page 2). The general state of an electron can be represented by the superposition (S>) of the above two qubits states, S> = a0> + b1> (1) where a and b belongs to a complex vector space and a squared + b squared = 1, which represents square of the length of the vectors, sometimes called “Unit Vector” [7] (Page 2). Qubit measurements can be based on standard basis states or arbitrary basis states [1.2]. Measurement on standard basis states involves a state S> which makes an angle θ with 0> state (X-axis), where S>= cosθ 0> + sinθ 1> = (2) (Page 3). This results in the state projecting either onto ground state or excited state with probabilities cos 2θ and sin 2θ respectively [3] (Page 3). Measurement based on arbitrary basis states allows measurement with respect to u> and u'> basis, where u> is measured with probability cos 2θ and u'> is measured with probability sin 2θ [1.2].

Quantum Image Representation Techniques

Different methods of image storage, representation and retrieval in a quantum system are discussed [1] (Page 3). Quantum Normalized Amplitude Based Image Processing (QNAIMP) represents an image by two-dimensional matrix of row and column vectors, where the pixel location is specified by a row and a column number (like, f(x,y), where f represents the amplitude value of the pixel and (x,y) represents the pixel’s positions) [5] (Page 4). The two-dimensional location of a pixel can be identified by Lpq = I>p <Jq (4) (Page 5). The normalized amplitude image matrix is defined as M N α p,q = √AMPp,q / √ ∑ ∑ AMPp,q (5) (Page 5). This approach stores all the pixel locations having the same amplitude values for all the amplitudes present in the image [4] (Page 6).

Quantum Entanglement and Retrieval

Quantum Entangled Image Processing (QEIP) uses quantum entanglement to store binary images [5] (Page 7). An array of n qubits is stored in a memory register, where Sinitial> = 0>i(x,y) (10) i=1 (Page 7). A square shape can be stored by choosing each vertex of the square and its corresponding qubit to 1> [10] (Page 7). The appropriate vertex positions may then be retrieved by applying Grover’s quantum search algorithm to the array [5] (Page 7).

Quantum Image Operations and Compression

Image negative can be achieved by quantum NOT gate, defined such that X0> = 1> and X1> = 0>, which acts linearly: state a0>+b1> is transformed in a corresponding state b0>+a1> [7] (Page 8). Quantum image binarization and quantum image histogram analysis are presented through quantum circuit representation [13] (Page 8). Quantum image compression (QIC) aims to reduce the quantum resources used to prepare quantum images by applying minimization strategy on transformed Boolean minterm form [40] (Page 12).

Applications and Future Research Issues

Applications of quantum natural computing into image processing include quantum noise restoration, image compression based on quantum neural network approach, image and video processing applications on quantum computers, automatic object extraction using quantum computing [2.3] (Page 12). Quantum noise can be reduced by using certain special transforms like Anscombe Transform and Wiener Filter [16] (Page 12). A novel enhanced FRQI based image representation model is used for classification of images [42] (Page 13). Future research scopes include investigating quantum operations having impacts on multiple images such as image matching, image searching on a set of images in FRQI states [3]. Quantum noise reduction from medical images is a big issue now days [2.3] (Page 15). Image processing can be exploited in a multivalued quantum system with more benefits than a binary valued quantum system [14] (Page 14). The relationship between radiation energy values and probabilities of projection measurement on qubits is quantified, which makes the representation model more flexible and clear [16] (Page 16). The number of qubits increases with the image dimension while storing an image [15] (Page 15). A watermarking authentication scheme for quantum images is proposed based on the quantum cosine transform (QCT) and as an application of FRQI image representation model [34] (Page 13).

Conclusion

This article provides a brief survey of the current status of research in the quantum image processing paradigm [4]. It discusses the different benefits of using quantum image processing over classical image processing [2] (Page 17). The overall layout and structure of this paper is influenced by the contents of the papers [25] (Page 17). All these efforts are needed for the realization of smooth, effective, fastest and secure QIMP technologies which help mankind to take full advantage of the immense potential of quantum computing and quantum information processing.

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How it works

**- In the QNAIMP approach, an image is represented by two-dimensional matrix of row and column vectors, where each pixel location is specified by a row and a column number (like, f(x,y), where f represents the amplitude value of the pixel and (x,y) represents the pixel’s positions) [5] (Page 4). The two-dimensional location of a pixel can be identified by Lpq = I>p <Jq (4) (Page 5). This approach stores all the pixel locations having the same amplitude values for all the amplitudes present in the image [4] (Page 6). The normalized amplitude image matrix is defined as M N α p,q = √AMPp,q / √ ∑ ∑ AMPp,q (5) (Page 5). The next task is to represent these amplitudes also by multiple qubits quantum states [5] (Page 6). The proposed quantum image representation mathematically is M N Z> = ∑ ∑ α η p,q × Lpq (7) where Z> is a two-dimensional gray scale quantum image or one of the color channels of the quantum color image [5] (Page 6). The goal is to store visual information in Z where Z is a 3-dimensional set of qubit lattices and each layer Q k ∈ Z will be used to store a copy of the image [5] (Page 6).

Improvements for AI systems

The improved AI system can perform image processing by processing images by means of a quantum computer, specifically optimizing the various image processing algorithms in terms of their quickness, efficiency and accuracy.
The system can handle image storage and retrieval using methods like the Quantum Normalized Amplitude Based Image Processing (QNAIMP), where an image is represented as a sum of pixel locations weighted by normalized amplitudes: "Z> = ∑ αηp,q × Lpq" (Equation 7).
The system can implement Image negative using quantum gates, specifically the transformation s = T(r) = L –1 – r, which is analogous to the classical NOT gate but acts linearly on superposition states.
The AI can perform advanced image segmentation by utilizing a multiobjective quantum inspired evolutionary algorithm for the establishment of the non-dominated solutions set (Reference [30]), allowing it to achieve automatic object extraction using quantum computing.
The system can enhance image noise reduction by employing an approximate non-linear neural filter (NF) trained via backpropagation, and subsequently applying transforms like the Anscombe Transform and Wiener Filter to reduce quantum noise from medical images (Reference [15], [16]).
The system can perform content-based image retrieval by deriving a contour based shape representation method using shape signature where the feature vector is derived from centroidal distances, allowing for matching shapes based on distance histograms.
The system can utilize a Flexible Representation of Quantum Images (FRQI) model to encode color and position information deterministically through the state "Q> = C>m P>2n, which allows for more complex image processing operations" compared to simpler qubit-based models.

Abstract

Image processing on quantum platform is a hot topic for researchers now a day. Inspired from the idea of quantum physics, researchers are trying to shift their focus from classical image processing towards quantum image processing.This paper starts with a brief review of the principles which underlie quantum computing, and also deals with some of the basics of qubits and quantum computing.Then this paper starts to deal with some different methods of image storage, representation and retrieval in a quantum system.This paper also describes the advantages of using those methods in quantum systems compare to classical systems. In the next section, a short discussion on some of the important aspects, comparison among them and applications of quantum image processing is presented. A few other hot topics and open problems in quantum image processing are mentioned in this paper. This review article will provide the readership an overview of progress witnessed in the area of Quantum Image processing while also simulating further interest to pursue more advanced research in it.