=Paper= {{Paper |id=Vol-3616/paper9 |storemode=property |title=Inverse Problems in Emerging Technology |pdfUrl=https://ceur-ws.org/Vol-3616/paper9.pdf |volume=Vol-3616 |authors=Sara Bousba,Naila Marir |dblpUrl=https://dblp.org/rec/conf/rif/BousbaM23 }} ==Inverse Problems in Emerging Technology== https://ceur-ws.org/Vol-3616/paper9.pdf 
                                Inverse Problems in Emerging Technology
                                Sara Bousba1 , Naila Marir2
                                1
                                    LaMa Laboratory, Setif University 1, Setif, Algeria
                                2
                                    LIRE Laboratory, Constantine 2-Abdelhamid Mehri University, Constantine, Algeria


                                                                         Abstract
                                                                         Inverse problems are a fundamental tool in many emerging technologies, enabling the recovery of impor-
                                                                         tant information from limited and noisy observations. In this survey, we aim to provide a comprehensive
                                                                         overview of the state of the art in inverse problems within emerging technologies. We focus on several
                                                                         important areas, including artificial intelligence, healthcare, machine learning, wireless communication,
                                                                         and energy modeling. We discuss the challenges and limitations of these inverse problems, as well as
                                                                         the recent advancements in their solution. Additionally, we highlight the significance of these inverse
                                                                         problems in each of these areas, and the potential impact they have on the development of new technolo-
                                                                         gies. This survey provides a comprehensive overview of inverse problems in emerging technologies and
                                                                         serves as a valuable resource for researchers and practitioners in the field.

                                                                         Keywords
                                                                         Inverse problems, Emerging technologies, Machine learning, Modern and emerging systems




                                1. Introduction
                                Mathematical modeling is a powerful tool to solve problems emerging from the development of
                                science and technology. The goal is frequently to gain quantities that can only be indirectly
                                detected through measurements. For instance, a direct scan of the human body’s interior is not
                                conceivable. However, there exist methods that can obtain a scan by measuring the remaining
                                intensity of X-rays that go through the body. Such indirect measurements are the result of
                                processes, which are usually mathematically modeled and depend on the quantities we wish to
                                find. This type of problem is called an inverse problem, involve calculating causal factors from
                                observations [1, 2].
                                   Meanwhile, emerging technologies, such as Artificial Intelligence (AI), Internet of Things
                                (IoT), medical imaging, augmented reality, and energy, are particularly well-suited to the use of
                                inverse problems due to their need for fast and accurate solutions to complex problems. An
                                example of an emerging technology problem that can be posed as an inverse problem is in
                                the field of medical imaging. Medical imaging techniques, such as computed tomography (CT)
                                and magnetic resonance imaging (MRI), allow doctors to visualize the internal structure of the
                                human body. However, these images are often limited by factors such as noise and limited
                                spatial resolution, which can reduce their accuracy and usefulness. One approach to improving
                                the accuracy of these images is to treat the imaging problem as an inverse problem. In this
                                approach, the goal is to estimate the internal structure of the body from the observed images,

                                RIF 2023: The 12th Seminary of Computer Science Research at Feminine, March 9, 2023, Constantine, Algeria
                                $ bousbasara@gmail.com (S. Bousba); naila.marir@univ-constantine2.dz (N. Marir)
                                                                       Β© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
                                    CEUR
                                    Workshop
                                    Proceedings
                                                  http://ceur-ws.org
                                                  ISSN 1613-0073       CEUR Workshop Proceedings (CEUR-WS.org)




CEUR
                  ceur-ws.org
Workshop      ISSN 1613-0073
Proceedings
while taking into account the various limitations and uncertainties associated with the imaging
process.
   The purpose of this survey is to provide an overview of the current state of the field of inverse
problems in emerging technologies. It covers the key concepts and theories in inverse problems,
as well as the various applications and challenges associated with the use of inverse problems in
emerging technologies. This survey aims to provide a comprehensive and accessible resource for
researchers and practitioners interested in the use of inverse problems in emerging technologies.
By highlighting the importance of inverse problems in this field and the potential for continued
growth and innovation, this survey can help to encourage further research and development in
this area.
   The reminder of this paper is organized as follows. Section 2 covers the background behind
the inverse problems. Section 3 discuss the employed research method. Section 4 provides the
finding of our survey. Future directions are given in section 4. Finally, the conclusion to our
work is given to section 5.


2. Background
2.1. what is an inverse problems
Inverse problems involve the recovery of information about an unknown system or process
from observations or measurements of its outputs. A problem is called inverse if the solution
of the first part is required to formulate the second part. In other words, it is the technique of
discovering causes from the information of their effects. This process is illustrated in Figure 1.




Figure 1: An illustration of forward and inverse problem.


  Differentiation of data is a common example of an inverse problem. Given a set of data points
that represent a function, the goal of the differentiation problem is to recover the derivative of
the function from the data.

    β€’ Direct problem: let π‘₯ : [0.1] β†’ R be a continuous function, compute
                                            ∫︁ 𝑑
                                    𝑦(𝑑) :=      π‘₯(𝑠)d𝑠, 𝑑 ∈ [0, 1].
                                              0

    β€’ Inverse Problem: Given a differentiable function 𝑦 : [0.1] β†’ R, determine π‘₯ := 𝑦 β€²
   In practice, the differentiation of data is an important problem that arises in many fields. Ac-
curately differentiating data is crucial for understanding the underlying dynamics and behavior
of signals and systems, and for making informed decisions and predictions based on the data.

2.2. Well-Ill posed problems
The three conditions for a problem to be well-posed in the sense of Hadamard [3] are 1)Existence
of a solution, 2)Uniqueness of solution and 3) Stability or continuity.
   Mathematically, we formulate the notion of well-posedness [4] as follow:
   Let 𝑋 and π‘Œ be nomed spaces, 𝐾 : 𝑋 β†’ π‘Œ a linear or nonlinear mapping. The equation
𝐾π‘₯ = 𝑦 is called well-posed if the following holds:
   1. Existence of solution: For every 𝑦 ∈ π‘Œ there is at least one π‘₯ ∈ 𝑋 such that 𝐾π‘₯ = 𝑦.
   2. Uniqueness of a solution: For every 𝑦 ∈ π‘Œ there is at most one π‘₯ ∈ 𝑋 with 𝐾π‘₯ = 𝑦.
   3. Continuous dependence of the solution on the data: The solution π‘₯ depends continuously
      on 𝑦. That is, for every sequence (π‘₯𝑛 ) βŠ‚ 𝑋 with 𝐾π‘₯𝑛 β†’ 𝐾π‘₯ (𝑛 β†’ ∞), it follows that
      π‘₯𝑛 β†’ π‘₯ (𝑛 β†’ ∞).
These three conditions are important because they ensure that the problem is well-defined and
that the solution is both predictable and stable. In many practical applications, it is essential to
have a well-posed problem in order to make accurate predictions and ensure the stability of
the solution. If any of the three condition are not satisfied, the problem is called improperly-
posed or ill-posed.This ill-posed fundamental property makes inverse problems difficult and
mathematically challenging. Ill-posed problems can pose significant difficulties when trying to
solve them numerically, as small errors can result in arbitrarily large variations in the solution.
To mitigate these difficulties, various regularization techniques can be used to stabilize the
solution of an ill-posed problem. The idea behind regularization is to add additional information
or constraints to the problem, in order to make it well-posed and to obtain a stable solution.
This additional information is usually encoded as a penalty term in the objective function that
is being minimized.
   There are several types of regularization methods, including: 1) Tikhonov Regularization, 2)
Morozov’s discrepancy principle and Bayesian Regularization.
   Each of these regularization methods has its own strengths and weaknesses, and the choice
of method depends on the specific problem and the available data. In some cases, it may
be beneficial to use a combination of regularization methods, or to adapt the regularization
parameters based on the data.


3. Research method
This study aims to investigate the inverse problems in emerging technologies to identify
innovative techniques that can help to address the challenges of existing methods. These
advancements can help to improve the accuracy and reliability of systems and applications.
This research employs a systematic review methodology known as mapping study or scoping
[5], which is based on the following steps: A. Specifying research questions. B. Search strategy.
C. Identification of primary studies. D. Data extraction. E. Threat to validity.
3.1. Research questions
The prime question that leads the investigation of inverse problems in emerging technologies is
"How can we find the unknown inputs or parameters that produce a given output or observation
in modern emerging systems?" This question is at the heart of our work, and drives the search
for new and improved solutions and techniques. To pipeline this systematic mapping review
this key question was split into two research questions:
   1. What are the different emerging technologies that uses inverse problem solutions?
   2. How this technologies defined their problems as an inverse problem?
The motivation behind understanding the different emerging technologies that use inverse
problem solutions is to keep up-to-date with the latest developments and advancements in these
fields. By having a clear understanding of the different technologies that use inverse problems,
one can have a better appreciation of the diverse applications of this mathematical concept. This
knowledge can be useful for researchers and engineers who are developing new algorithms and
systems that use inverse problems. Overall, the motivation behind understanding the different
emerging technologies that use inverse problem solutions is to stay informed and to have a
deeper understanding of this important mathematical concept and its many applications.

3.2. Search strategy
The time frame covered by this study is from 2009 to 2022 inclusive. Additionally, the publications
were re-searched using IEEEXplore, ACM Digital Library, Science Direct, and Google Scholar
as the repositories.


4. Finding and discussions
In this section, we will try to answer the research questions posted in section 3.
   1. What are the different emerging technologies that uses inverse problem solutions?
   There are several emerging technologies that use inverse problem solutions, including:
   Artificial Intelligence:
   The importance of inverse problems in artificial intelligence is due to their ability to provide
valuable insights and solutions to complex problems. By combining mathematical models and
machine learning algorithms, AI systems can extract information from data, find hidden patterns
and relationships, and make predictions and decisions in real-time [6, 7]. In [8], the authors
presented an original contribution to the intersection of inverse problems and deep learning and
proposed a new strategy for handling the regularization task in inverse problems. The approach
taken in the paper is to leverage the inherent structure and information within the image data
itself, rather than relying on external data or prior knowledge. The results showed that the deep
neural network was capable of restoring images with high accuracy, even when the degradation
was severe. The authors conclude that the Deep Image Prior is a powerful tool for solving
inverse problems in computer vision, and can be applied to a wide range of image processing
tasks such as denoising, super-resolution, and inpainting. They also suggest that the approach
can be extended to other inverse problems in other fields, such as audio and speech processing.
The authors in [9], provides a review of the use of inverse problems in artificial intelligence,
in which they discuss the different types of inverse problems and their applications in various
areas such as image processing, pattern recognition, and computer vision. The authors highlight
the importance of inverse problems in artificial intelligence and how they can be used to address
some of the challenging problems in the field. They provide examples of how inverse problems
have been used in various applications such as image restoration, image recognition, and object
detection. They also discuss some of the limitations and challenges of using inverse problems
in artificial intelligence and suggest future directions for research.
   Health care:
   In the field of healthcare, mathematical inverse problems have been used to address a variety of
problems, such as image analysis and interpretation, disease diagnosis, and treatment planning
[10, 11, 12, 13]. For example, medical imaging techniques such as magnetic resonance imaging
(MRI) and computed tomography (CT) use inverse problems to reconstruct images of internal
organs and tissues based on measurements taken from the body. Additionally, inverse problems
have been used in the analysis of biological signals, such as electroencephalography (EEG) and
electrocardiography (ECG), to identify and diagnose diseases.
   One example of a research paper in this area is [14]. This paper provides an overview of
inverse problems in medical imaging and the various techniques used to address these problems,
including MRI, CT, and ultrasound. The author also discusses the challenges and limitations of
using inverse problems in medical imaging and the future directions for research in this area.
   Overall, the use of mathematical inverse problems in healthcare has shown promise in the
analysis and interpretation of medical data and has the potential to improve patient outcomes
by providing more accurate and efficient diagnoses and treatments.
   Cybersecurity:
   The inverse problem in cybersecurity refers to the process of determining the cause of a
security breach or vulnerability by analyzing its effects and symptoms. Anomaly and misuse de-
tection in cybersecurity can be considered as an inverse problem, as it requires the identification
of unusual and malicious behavior in a complex network system. To tackle these challenges,
researchers are exploring a range of solutions, including machine learning algorithms, artificial
intelligence, and data analytics, to develop more accurate and effective methods for detecting
anomalies and misuses in cybersecurity. The inverse machine learning algorithm described in
[15] appears to be a novel approach for addressing the problem of cyber anomaly detection. The
authors model an anomaly detection system using an inverse model approach, which involves
mapping observed network activity data to the underlying causes of anomalous behavior.
   Energy:
   The use of inverse problems in energy systems is becoming increasingly important as we look
for more efficient and sustainable energy solutions. One example of the use of inverse problems
in energy systems is in the field of renewable energy sources such as wind and solar power
[16]. The goal of these systems is to maximize the energy output while minimizing the costs
associated with energy production. However, this is a complex task, as the energy output of
these systems is influenced by a variety of factors, including weather patterns, energy demand,
and technological limitations. To tackle this challenge, researchers are using inverse problems to
model and optimize the energy output of these systems. Another area where inverse problems
are being used in energy systems is in the development of smart energy grids [16]. Smart energy
grids are designed to help optimize the distribution and use of energy in a more efficient and
sustainable manner. To achieve this goal, researchers are using inverse problems to model and
optimize the energy demand patterns, energy distribution networks, and other aspects of smart
energy grids.
   2. How this technologies defined their problems as an inverse problem?
   There are several examples of emerging technologies that have defined their problems as
inverse problems:
   Intrusion detection systems:
   One common approach to intrusion detection is to treat the problem as an inverse problem.
In this context, the inverse problem is to determine the underlying behavior patterns of the
network or system, and to identify deviations from these patterns that may indicate an intrusion
[17, 18, 15]. For example, one could consider a network traffic monitoring system, where the
goal is to detect malicious activity by analyzing the incoming and outgoing traffic. This can be
posed as an inverse problem, where the goal is to infer the presence of an intrusion based on
observed network traffic patterns. The inverse problem is to reconstruct the network behavior
patterns, taking into account the normal traffic patterns and any anomalies that might indicate
an intrusion. The inverse problem can be formalized as a mathematical optimization problem,
where the goal is to find the most likely intrusion scenario that fits the observed data. The
solution to this inverse problem can then be used to identify and respond to potential intrusions
in real-time.
   Internet of Things (IoT) systems: Internet of Things (IoT) systems can encounter various
problems that can be defined as inverse problems such as sensor calibration, localization [19],
wireless channel estimation and fault detection and diagnosis [20]. One of the key challenges
in IoT systems is the calibration of sensors, which is often necessary to obtain accurate and
reliable measurements. The problem of sensor calibration can be defined as an inverse problem,
where the goal is to estimate the parameters of the sensor model from the observed data.
Another common problem in IoT systems is the localization of devices, which is the process
of determining the physical location of a device based on its measurements. The problem of
localization can be defined as an inverse problem, where the goal is to estimate the location of
a device from the observed measurements and a model of the environment. These are some
examples of how IoT problems can be defined as inverse problems, and the solutions to these
inverse problems can help to improve the performance and reliability of IoT systems.
   Overall, the use of inverse problems in modern emerging technologies provides a powerful
tool for solving a wide range of problems where limited information is available. By formulating
the problem as an inverse problem, the unknowns can be found through mathematical modeling
and numerical algorithms, leading to improved solutions and better outcomes.


5. Future Directions
Inverse problems have been a topic of research for many years and have been used in various
emerging technologies. As these technologies continue to evolve, the future directions of inverse
problems are expected to focus on several key areas. Some of these directions include:
   Machine Learning and deep learning approaches: In machine and deep learning, the
future direction is expected to focus on developing more efficient and scalable inverse problems
solutions that can handle large datasets, as well as new machine learning models that can be
integrated with existing inverse problem algorithms. This integration is likely to lead to the
development of new hybrid approaches that can address even more challenging problems, such
as non-linear inverse problems and multi-modal inverse problems. In addition, we can expect to
see more applications of inverse problems in machine learning, particularly in natural language
processing.
   Real-time and big data applications: The increasing demand for real-time and big data
applications in emerging technology is driving research efforts to develop methods that can
efficiently solve inverse problems in these contexts. In real-time applications, inverse problems
can be used to process large amounts of data in real-time and provide quick, accurate results. Big
data applications, on the other hand, can benefit from the use of inverse problems by leveraging
the scalability and efficiency of inverse problem algorithms. Inverse problems can be used to
process large amounts of data and extract meaningful insights, even when the data is noisy or
incomplete. In both real-time and big data applications, the use of inverse problems can help
to improve the accuracy of results and reduce the amount of time and resources required to
process large amounts of data.
   Internet of Things (IoT): Inverse problems can be used to process and analyze the massive
amounts of data generated by IoT devices, helping to uncover insights and make informed
decisions. Energy: Inverse problems can be used to improve the efficiency and accuracy of
energy systems, such as wind and solar power, by allowing engineers to better understand and
model the underlying dynamics of these systems.


6. Conclusion
In conclusion, the use of inverse problems in emerging technologies is growing as more re-
searchers and practitioners explore the potential applications of this field. Inverse problems
are becoming increasingly relevant in areas such as artificial intelligence, internet of things,
medical imaging, augmented reality, and energy, where they are being used to address problems
such as model inversion, data analysis, and image and signal processing.
   The future direction of the use of inverse problems in emerging technologies is likely to
be driven by the need for fast and accurate solutions to complex problems in a wide range
of applications. As new technologies emerge and existing ones continue to evolve, the use
of inverse problems solutions is likely to play an increasingly important role in shaping the
future of many industries and fields. Therefore, this survey highlights the importance of inverse
problems in emerging technologies and the potential for continued growth and innovation in
this field. By providing a comprehensive overview of the current state of the field, this survey
can serve as a useful resource for researchers and practitioners interested in the use of inverse
problems in emerging technologies.
References
 [1] A. Tarantola, Inverse Problems: An Introduction, Springer Science and Business Media,
     2005.
 [2] U. Gunther, Inverse problems: seeing the unseen, Bull. Math. Sci. 4 (2014) 209–279.
 [3] J. Hadamard, Lectures on Cauchy’s Problems in Linear Partial Differential Equations, Yale
     University Press, New Haven, 1923.
 [4] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Springer,
     2011.
 [5] M. A. M Saleemi, M. Rehman, Services classification, trends, and analysis: A systematic
     mapping study, IEEE Access 5 (2017) 26104–26123.
 [6] C. A. M. R. G. B. A. G. D. G Ongie, A Jalal, R. Willett, Inverse identification of temperature
     dependent volumetric heat capacity by neural networks, Int. J. Thermophys. 34 (2013)
     284–305.
 [7] H. R. R Samuel, S Santiago, G. M. Antonio, Untrained graph neural networks for denoising,
     IEEE Trans. Signal Process. 70 (2022) 5708 – 5723.
 [8] V. A. U Dmitry, L. Victor, Deep image prior, In IEEE CVPR (2020) 9446–9454.
 [9] Y. Kim, Inverse problems in artificial intelligence: a review 42 (2014) 223–246.
[10] A. V. Goncharsky, S. Y. Romanov, Iterative methods for solving coefficient inverse problems
     of wave tomography in models with attenuation, Inverse Prb 33 (2017) 025003.
[11] A. V. Goncharsky, S. Y. Romanov, Inverse problems of ultrasound tomography in models
     with attenuation, Phys Med Biol 59 (2014) 1979–2004.
[12] A. V. Goncharsky, S. Y. Romanov, Supercomputer technologies in inverse problems of
     ultrasound tomography, Inverse Prb 29 (2013) 075004.
[13] L. X. Y Song, L Shen, S. Ermon, Solving inverse problems in medical imaging with
     score-based generative models, International Conference on Learning Representations
     (2022).
[14] K. H. Jin, Inverse Problems in Medical Imaging, Springer, New York, 2019.
[15] A. Sever, A machine learning algorithm based on inverse problems for cyber anomaly
     detection, Curr. j. appl. sci. technol. 28 (2018) 1–14.
[16] H. A. L. Thi, O. Nguyen, Smart energy grid: An overview of challenges and recent advances,
     Renewable Sustainable Energy Rev. 80 (2017) 1267–1279.
[17] M. A. A. Guezzaz, Y. Asimi, A. Asimi, Mathematical validation of proposed machine
     learning classifier for heterogeneous traffic and anomaly detection, Big Data Mining and
     Analytics 4 (2021) 18–24.
[18] N. Y. W Zhong, C. Ai, Applying big data based deep learning system to intrusion detection,
     Big Data Mining and Analytics 3 (2020) 181–195.
[19] IEEE (Ed.), Sensor networks and inverse scattering, 2006.
[20] Z. J. W. F. R. Y. Y Chi, Y Dong, V. C. M. Leung, Knowledge-based fault diagnosis in industrial
     internet of things: A survey, IoT-J 9 (2022) 12886–12900.