Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step. In recent research works, scientists have shown that extremely fast computations and massive parallelism is possible for iterative reconstruction, which makes iterative reconstruction practical for commercialization. == Basic concepts == The reconstruction of an image from the acquired data is an inverse problem. Often, it is not possible to exactly solve the inverse problem directly. In this case, a direct algorithm has to approximate the solution, which might cause visible reconstruction artifacts in the image. Iterative algorithms approach the correct solution using multiple iteration steps, which allows to obtain a better reconstruction at the cost of a higher computation time. There are a large variety of algorithms, but each starts with an assumed image, computes projections from the image, compares the original projection data and updates the image based upon the difference between the calculated and the actual projections. === Algebraic reconstruction === The Algebraic Reconstruction Technique (ART) was the first iterative reconstruction technique used for computed tomography by Hounsfield. === Iterative Sparse Asymptotic Minimum Variance === The iterative sparse asymptotic minimum variance algorithm is an iterative, parameter-free superresolution tomographic reconstruction method inspired by compressed sensing, with applications in synthetic-aperture radar, computed tomography scan, and magnetic resonance imaging (MRI). === Statistical reconstruction === There are typically five components to statistical iterative image reconstruction algorithms, e.g. An object model that expresses the unknown continuous-space function f ( r ) {\displaystyle f(r)} that is to be reconstructed in terms of a finite series with unknown coefficients that must be estimated from the data. A system model that relates the unknown object to the "ideal" measurements that would be recorded in the absence of measurement noise. Often this is a linear model of the form A x + ϵ {\displaystyle \mathbf {A} x+\epsilon } , where ϵ {\displaystyle \epsilon } represents the noise. A statistical model that describes how the noisy measurements vary around their ideal values. Often Gaussian noise or Poisson statistics are assumed. Because Poisson statistics are closer to reality, it is more widely used. A cost function that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of regularization. Sometimes the regularization is based on Markov random fields. An algorithm, usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating the iterations. === Learned Iterative Reconstruction === In learned iterative reconstruction, the updating algorithm is learned from training data using techniques from machine learning such as convolutional neural networks, while still incorporating the image formation model. This typically gives faster and higher quality reconstructions and has been applied to CT and MRI reconstruction. == Advantages == The advantages of the iterative approach include improved insensitivity to noise and capability of reconstructing an optimal image in the case of incomplete data. The method has been applied in emission tomography modalities like SPECT and PET, where there is significant attenuation along ray paths and noise statistics are relatively poor. Statistical, likelihood-based approaches: Statistical, likelihood-based iterative expectation-maximization algorithms are now the preferred method of reconstruction. Such algorithms compute estimates of the likely distribution of annihilation events that led to the measured data, based on statistical principle, often providing better noise profiles and resistance to the streak artifacts common with FBP. Since the density of radioactive tracer is a function in a function space, therefore of extremely high-dimensions, methods which regularize the maximum-likelihood solution turning it towards penalized or maximum a-posteriori methods can have significant advantages for low counts. Examples such as Ulf Grenander's Sieve estimator or Bayes penalty methods, or via I.J. Good's roughness method may yield superior performance to expectation-maximization-based methods which involve a Poisson likelihood function only. As another example, it is considered superior when one does not have a large set of projections available, when the projections are not distributed uniformly in angle, or when the projections are sparse or missing at certain orientations. These scenarios may occur in intraoperative CT, in cardiac CT, or when metal artifacts require the exclusion of some portions of the projection data. In Magnetic Resonance Imaging it can be used to reconstruct images from data acquired with multiple receive coils and with sampling patterns different from the conventional Cartesian grid and allows the use of improved regularization techniques (e.g. total variation) or an extended modeling of physical processes to improve the reconstruction. For example, with iterative algorithms it is possible to reconstruct images from data acquired in a very short time as required for real-time MRI (rt-MRI). In Cryo Electron Tomography, where the limited number of projections are acquired due to the hardware limitations and to avoid the biological specimen damage, it can be used along with compressive sensing techniques or regularization functions (e.g. Huber function) to improve the reconstruction for better interpretation. Here is an example that illustrates the benefits of iterative image reconstruction for cardiac MRI.
Universal psychometrics
Universal psychometrics encompasses psychometrics instruments that could measure the psychological properties of any intelligent agent. Up until the early 21st century, psychometrics relied heavily on psychological tests that require the subject to cooperate and answer questions, the most famous example being an intelligence test. Such methods are only applicable to the measurement of human psychological properties. As a result, some researchers have proposed the idea of universal psychometrics - they suggest developing testing methods that allow for the measurement of non-human entities' psychological properties. For example, it has been suggested that the Turing test is a form of universal psychometrics. This test involves having testers (without any foreknowledge) attempt to distinguish a human from a machine by interacting with both (while not being to see either individuals). It is supposed that if the machine is equally intelligent to a human, the testers will not be able to distinguish between the two, i.e., their guesses will not be better than chance. Thus, Turing test could measure the intelligence (a psychological variable) of an AI. Other instruments proposed for universal psychometrics include reinforcement learning and measuring the ability to predict complexity.
Neural cryptography
Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. == Definition == Artificial neural networks are well known for their ability to selectively explore the solution space of a given problem. This feature finds a natural niche of application in the field of cryptanalysis. At the same time, neural networks offer a new approach to attack ciphering algorithms based on the principle that any function could be reproduced by a neural network, which is a powerful proven computational tool that can be used to find the inverse-function of any cryptographic algorithm. The ideas of mutual learning, self learning, and stochastic behavior of neural networks and similar algorithms can be used for different aspects of cryptography, like public-key cryptography, solving the key distribution problem using neural network mutual synchronization, hashing or generation of pseudo-random numbers. Another idea is the ability of a neural network to separate space in non-linear pieces using "bias". It gives different probabilities of activating the neural network or not. This is very useful in the case of Cryptanalysis. Two names are used to design the same domain of research: Neuro-Cryptography and Neural Cryptography. The first work that it is known on this topic can be traced back to 1995 in an IT Master Thesis. == Applications == In 1995, Sebastien Dourlens applied neural networks to cryptanalyze DES by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by Adi Shamir is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time. Hardware application with multi micro-controllers have been proposed due to the easy implementation of multilayer neural networks in hardware. One example of a public-key protocol is given by Khalil Shihab . He describes the decryption scheme and the public key creation that are based on a backpropagation neural network. The encryption scheme and the private key creation process are based on Boolean algebra. This technique has the advantage of small time and memory complexities. A disadvantage is the property of backpropagation algorithms: because of huge training sets, the learning phase of a neural network is very long. Therefore, the use of this protocol is only theoretical so far. == Neural key exchange protocol == The most used protocol for key exchange between two parties A and B in the practice is Diffie–Hellman key exchange protocol. Neural key exchange, which is based on the synchronization of two tree parity machines, should be a secure replacement for this method. Synchronizing these two machines is similar to synchronizing two chaotic oscillators in chaos communications. === Tree parity machine === The tree parity machine is a special type of multi-layer feedforward neural network. It consists of one output neuron, K hidden neurons and K×N input neurons. Inputs to the network take three values: x i j ∈ { − 1 , 0 , + 1 } {\displaystyle x_{ij}\in \left\{-1,0,+1\right\}} The weights between input and hidden neurons take the values: w i j ∈ { − L , . . . , 0 , . . . , + L } {\displaystyle w_{ij}\in \left\{-L,...,0,...,+L\right\}} Output value of each hidden neuron is calculated as a sum of all multiplications of input neurons and these weights: σ i = sgn ( ∑ j = 1 N w i j x i j ) {\displaystyle \sigma _{i}=\operatorname {sgn}(\sum _{j=1}^{N}w_{ij}x_{ij})} Signum is a simple function, which returns −1,0 or 1: sgn ( x ) = { − 1 if x < 0 , 0 if x = 0 , 1 if x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1&{\text{if }}x<0,\\0&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}} If the scalar product is 0, the output of the hidden neuron is mapped to −1 in order to ensure a binary output value. The output of neural network is then computed as the multiplication of all values produced by hidden elements: τ = ∏ i = 1 K σ i {\displaystyle \tau =\prod _{i=1}^{K}\sigma _{i}} Output of the tree parity machine is binary. === Protocol === Each party (A and B) uses its own tree parity machine. Synchronization of the tree parity machines is achieved in these steps Initialize random weight values Execute these steps until the full synchronization is achieved Generate random input vector X Compute the values of the hidden neurons Compute the value of the output neuron Compare the values of both tree parity machines Outputs are the same: one of the suitable learning rules is applied to the weights Outputs are different: go to 2.1 After the full synchronization is achieved (the weights wij of both tree parity machines are same), A and B can use their weights as keys. This method is known as a bidirectional learning. One of the following learning rules can be used for the synchronization: Hebbian learning rule: w i + = g ( w i + σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Anti-Hebbian learning rule: w i + = g ( w i − σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}-\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Random walk: w i + = g ( w i + x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Where: Θ ( a , b ) = 0 {\displaystyle \Theta (a,b)=0} if a ≠ b {\displaystyle a\neq b} otherwise Θ ( a , b ) = 1 {\displaystyle \Theta (a,b)=1} And: g ( x ) {\displaystyle g(x)} is a function that keeps the w i {\displaystyle w_{i}} in the range { − L , − L + 1 , . . . , 0 , . . . , L − 1 , L } {\displaystyle \{-L,-L+1,...,0,...,L-1,L\}} === Attacks and security of this protocol === In every attack it is considered, that the attacker E can eavesdrop messages between the parties A and B, but does not have an opportunity to change them. ==== Brute force ==== To provide a brute force attack, an attacker has to test all possible keys (all possible values of weights wij). By K hidden neurons, K×N input neurons and boundary of weights L, this gives (2L+1)KN possibilities. For example, the configuration K = 3, L = 3 and N = 100 gives us 310253 key possibilities, making the attack impossible with today's computer power. ==== Learning with own tree parity machine ==== One of the basic attacks can be provided by an attacker, who owns the same tree parity machine as the parties A and B. He wants to synchronize his tree parity machine with these two parties. In each step there are three situations possible: Output(A) ≠ Output(B): None of the parties updates its weights. Output(A) = Output(B) = Output(E): All the three parties update weights in their tree parity machines. Output(A) = Output(B) ≠ Output(E): Parties A and B update their tree parity machines, but the attacker can not do that. Because of this situation his learning is slower than the synchronization of parties A and B. It has been proven, that the synchronization of two parties is faster than learning of an attacker. It can be improved by increasing of the synaptic depth L of the neural network. That gives this protocol enough security and an attacker can find out the key only with small probability. ==== Other attacks ==== For conventional cryptographic systems, we can improve the security of the protocol by increasing of the key length. In the case of neural cryptography, we improve it by increasing of the synaptic depth L of the neural networks. Changing this parameter increases the cost of a successful attack exponentially, while the effort for the users grows polynomially. Therefore, breaking the security of neural key exchange belongs to the complexity class NP. Alexander Klimov, Anton Mityaguine, and Adi Shamir say that the original neural synchronization scheme can be broken by at least three different attacks—geometric, probabilistic analysis, and using genetic algorithms. Even though this particular implementation is insecure, the ideas behind chaotic synchronization could potentially lead to a secure implementation. === Permutation parity machine === The permutation parity machine is a binary variant of the tree parity machine. It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons: x i j ∈ { 0 , 1 } {\displaystyle x_{ij}\in \left\{0,1\right\}} The weights between input and hidden neurons are also binary: w i j ∈ { 0 , 1 } {\displaystyle w_{ij}\in \left\{0,1\right\}} Output value of each hidden neuron is calculated as a sum of all exclusive disjunctions (exclusive or) of input neurons and these weights: σ i = θ N ( ∑ j = 1 N w i j ⊕ x i j ) {\displaystyle \sigma _{i}=\theta _{N}(\sum _{j=1}^{N}w_{ij}\oplus x_{ij})} (⊕ means XOR). Th
Multilinear subspace learning
Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality reduction can be performed on a data tensor that contains a collection of observations that have been vectorized, or observations that are treated as matrices and concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D). The mapping from a high-dimensional vector space to a set of lower dimensional vector spaces is a multilinear projection. When observations are retained in the same organizational structure as matrices or higher order tensors, their representations are computed by performing linear projections into the column space, row space and fiber space. Multilinear subspace learning algorithms are higher-order generalizations of linear subspace learning methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA) and canonical correlation analysis (CCA). == Background == Multilinear methods may be causal in nature and perform causal inference, or they may be simple regression methods from which no causal conclusion are drawn. Linear subspace learning algorithms are traditional dimensionality reduction techniques that are well suited for datasets that are the result of varying a single causal factor. Unfortunately, they often become inadequate when dealing with datasets that are the result of multiple causal factors. . Multilinear subspace learning can be applied to observations whose measurements were vectorized and organized into a data tensor for causally aware dimensionality reduction. These methods may also be employed in reducing horizontal and vertical redundancies irrespective of the causal factors when the observations are treated as a "matrix" (ie. a collection of independent column/row observations) and concatenated into a tensor. == Algorithms == === Multilinear principal component analysis === Historically, multilinear principal component analysis has been referred to as "M-mode PCA", a terminology which was coined by Peter Kroonenberg. In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA terminology as a way to better differentiate between multilinear tensor decompositions that computed 2nd order statistics associated with each data tensor mode, and subsequent work on Multilinear Independent Component Analysis that computed higher order statistics for each tensor mode. MPCA is an extension of PCA. === Multilinear independent component analysis === Multilinear independent component analysis is an extension of ICA. === Multilinear linear discriminant analysis === Multilinear extension of LDA TTP-based: Discriminant Analysis with Tensor Representation (DATER) TTP-based: General tensor discriminant analysis (GTDA) TVP-based: Uncorrelated Multilinear Discriminant Analysis (UMLDA) === Multilinear canonical correlation analysis === Multilinear extension of CCA TTP-based: Tensor Canonical Correlation Analysis (TCCA) TVP-based: Multilinear Canonical Correlation Analysis (MCCA) TVP-based: Bayesian Multilinear Canonical Correlation Analysis (BMTF) A TTP is a direct projection of a high-dimensional tensor to a low-dimensional tensor of the same order, using N projection matrices for an Nth-order tensor. It can be performed in N steps with each step performing a tensor-matrix multiplication (product). The N steps are exchangeable. This projection is an extension of the higher-order singular value decomposition (HOSVD) to subspace learning. Hence, its origin is traced back to the Tucker decomposition in 1960s. A TVP is a direct projection of a high-dimensional tensor to a low-dimensional vector, which is also referred to as the rank-one projections. As TVP projects a tensor to a vector, it can be viewed as multiple projections from a tensor to a scalar. Thus, the TVP of a tensor to a P-dimensional vector consists of P projections from the tensor to a scalar. The projection from a tensor to a scalar is an elementary multilinear projection (EMP). In EMP, a tensor is projected to a point through N unit projection vectors. It is the projection of a tensor on a single line (resulting a scalar), with one projection vector in each mode. Thus, the TVP of a tensor object to a vector in a P-dimensional vector space consists of P EMPs. This projection is an extension of the canonical decomposition, also known as the parallel factors (PARAFAC) decomposition. === Typical approach in MSL === There are N sets of parameters to be solved, one in each mode. The solution to one set often depends on the other sets (except when N=1, the linear case). Therefore, the suboptimal iterative procedure in is followed. Initialization of the projections in each mode For each mode, fixing the projection in all the other mode, and solve for the projection in the current mode. Do the mode-wise optimization for a few iterations or until convergence. This is originated from the alternating least square method for multi-way data analysis. == Code == MATLAB Tensor Toolbox by Sandia National Laboratories. The MPCA algorithm written in Matlab (MPCA+LDA included). The UMPCA algorithm written in Matlab (data included). The UMLDA algorithm written in Matlab (data included). == Tensor data sets == 3D gait data (third-order tensors): 128x88x20(21.2M); 64x44x20(9.9M); 32x22x10(3.2M);
Neocognitron
The neocognitron is a hierarchical, multilayered artificial neural network proposed by Kunihiko Fukushima in 1979. It has been used for Japanese handwritten character recognition and other pattern recognition tasks, and served as the inspiration for convolutional neural networks. Previously in 1969, he published a similar architecture, but with hand-designed kernels inspired by convolutions in mammalian vision. In 1975 he improved it to the Cognitron, and in 1979 he improved it to the neocognitron, which learns all convolutional kernels by unsupervised learning (in his terminology, "self-organized by 'learning without a teacher'"). The neocognitron was inspired by the model proposed by Hubel & Wiesel in 1959. They found two types of cells in the visual primary cortex called simple cell and complex cell, and also proposed a cascading model of these two types of cells for use in pattern recognition tasks. The neocognitron is a natural extension of these cascading models. The neocognitron consists of multiple types of cells, the most important of which are called S-cells and C-cells. The local features are extracted by S-cells, and these features' deformation, such as local shifts, are tolerated by C-cells. Local features in the input are integrated gradually and classified in the higher layers. The idea of local feature integration is found in several other models, such as the Convolutional Neural Network model, the SIFT method, and the HoG method. There are various kinds of neocognitron. For example, some types of neocognitron can detect multiple patterns in the same input by using backward signals to achieve selective attention.
SwissCovid
SwissCovid is a COVID-19 contact tracing app used for digital contact tracing in Switzerland. Use of the app is voluntary and based on a decentralized approach using Bluetooth Low Energy and Decentralized Privacy-Preserving Proximity Tracing (dp3t). == Development == The app was developed in collaboration with the FOPH by Federal Office for Information Technology, Systems and Communications FOITT, École polytechnique fédérale de Lausanne (EPFL) and the Swiss Federal Institute of Technology in Zurich (ETH) as well as other experts. == Non-interoperability with applications in European countries == There is an agreement between EU countries to make applications compatible. However, there is no legal basis for the SwissCovid application to be part of this portal even though technically speaking it is ready, according to Sang-Ill Kim, head of the digital transformation department of the Federal Office of Public Health. == Criticism == === Not full open source and dependence on Google and Apple === In June 2020, researchers Serge Vaudenay and Martin Vuagnoux published a critical analysis of the application, noting that it relies heavily on Google and Apple's exposure notification system, which is integrated into their respective Android and iOS operating systems. Since Google and Apple have not released the full source code of this system, this would call into question the truly open source nature of the application. The researchers note that the dp3t collective, which includes the developers of the application, has asked Google and Apple to release their code. Moreover, they criticize the official description of the application and its functionalities, as well as the adequacy of the legal basis for its effective operation. === Cyber attacks === Professor Serge Vaudenay and Martin Vuagnoux identify also various security vulnerabilities in the application. The system would thus allow a third party to trace the movements of a phone using the application by means of Bluetooth sensors scattered along its path, for example in a building. Another possible attack would be to copy identifiers from the phones of people who may be ill (for example, in a hospital), and to reproduce those identifiers in order to receive notification of exposure to COVID-19 and illegitimately benefit from quarantine (thus entitling them to paid leave, a postponed examination, or other benefits). The system would also allow a third party to use a phone using the application by means of Bluetooth sensors scattered along the way. Paul-Olivier Dehaye of Personaldata.io and professor Joel Reardon of the University of Calgary published in June 2020 several examples of AEM (Associated Encrypted Metadata) replay and manipulation attacks via software development kits (SDKs) found in benign third-party mobile applications downloaded by the general public and having the phone's Bluetooth access permissions and in September 2020 a paper indicating that "Bluetooth-based proximity tracing apps are fundamentally insecure with respect to an attacker leveraging a malevolent app or SDK". === Costs === According to a publication by the federal administration, "the costs of developing the software for the mobile phone application, the GR back-end and the code management system as well as the costs for access management for the cantonal doctors' services are estimated at a one-off amount of 1.65 million francs. However, the Zurich-based company Ubique, responsible for the development of the application, was finally awarded the mandate to develop the application for an amount of 1.8 million francs. Through the Botnar Foundation based in Basel, École polytechnique fédérale de Lausanne received 3.5 million Swiss francs for the development of the application
Multiple discriminant analysis
Multiple Discriminant Analysis (MDA) is a multivariate dimensionality reduction technique. It has been used to predict signals as diverse as neural memory traces and corporate failure. MDA is not directly used to perform classification. It merely supports classification by yielding a compressed signal amenable to classification. The method described in Duda et al. (2001) §3.8.3 projects the multivariate signal down to an M−1 dimensional space where M is the number of categories. MDA is useful because most classifiers are strongly affected by the curse of dimensionality. In other words, when signals are represented in very-high-dimensional spaces, the classifier's performance is catastrophically impaired by the overfitting problem. This problem is reduced by compressing the signal down to a lower-dimensional space as MDA does. MDA has been used to reveal neural codes.