Hyperspectral imaging (HSI) is demonstrating the growing capability for disease diagnosis and surgical cancer resection. That is mainly due to high spectral resolution of HSI when compared with its color (RGB) counterparts. However, increased spectral resolution is often associated with the loss of spatial resolution. That combined with high cost hinders applicability of HSI. Herein, we propose computational approach that attempts to mimic the HSI. It is using an approximate explicit feature map (aEFM) to augment raw and/or stain normalized RGB images of the hematoxylin and eosin stained histopathological specimen. We demonstrate on two public labeled datasets, related to breast cancer and nuclei, the statistically significant improvement of performance of binary (caner vs. non-cancer) segmentation of augmented RGB images in comparison with the results achieved on their RGB counterparts. For the breast cancer, balanced accuracy is increased from 76.56%±9.05% to 80.42%±9.23% and F1 score from 13.34%±6.46% to 17.33%±6.36%. For nuclei, balanced accuracy is increased from 68.68%±9.25% to 79.99%±8.77% and F1 score from 46.92%±15.10% to 63.31%±14.50%. While 0 constrained nonnegative matrix factorization was used for binary segmentation herein, we conjecture that aEFM based augmentation of RGB images can improve performance of more sophisticated segmentation methods such as deep networks.
There is a need for computer-aided diagnosis (CAD) systems to relieve the workload on pathologists. This seems to be especially important for intraoperative diagnosis during surgery, for which diagnostic time is very limited. This paper presents preliminary results of intraoperative pixel-based CAD of colon cancer metastasis in a liver from phase-contrast images of unstained frozen sections. In particular, two deep learning networks: the U-net and the structured autoencoder for deep subspace clustering, were trained on eighteen phase-contrast images belonging to five patients and tested on eight images belonging to three patients. Spectrum angle mapper was also used in comparative performance analysis. The best result achieved by the U-net yielded balanced accuracy of 83.70%±8%, sensitivity of 94.50%±8%, specificity of 72.9%±8% and Dice coefficient of 45.20%±25.4%. However, factors such as absence of tissue fixation and ethanol-induced dehydration, melting of the specimen under the microscope and/or frozen crystals in the specimen cause variations in quality of phase-contrast images of unstained frozen sections. This, in return, affects reproducibility of diagnostic performance.
Development of computer-aided diagnosis (CAD) systems is motivated by reduction of the workload on the pathologist that is increasing steadily. Among approaches upon which CAD-based systems are built, deep learning (DL) methods seem to be well suited for image analysis in digital pathology. However, DL networks include a large number of parameters and that requires a large annotated training dataset. Unfortunately, probably the biggest problem in digital pathology using machine learning methods is a small number of annotated images. That is especially true in intraoperative tissue analysis which coincides with the topic of the present paper: intraoperative CAD-based diagnosis of metastasis of colon cancer in a liver from hematoxylin-eosin (H and E) stained frozen section. To cope with the insufficiency of training images we adopt a transfer learning approach using the Nested UNet architecture. For better diagnostic performance, the trained model predicted pixels multiple times for different striding levels using the sliding window strategy. Threshold optimization using balanced accuracy score showed the validity of such an approach as balanced accuracy has increased significantly. When compared to often used UNet with VGG16 backbone, Nested UNet model with DenseNet201 backbone performs better on our dataset for both balanced accuracy metric and F1 score.
KEYWORDS: Optical coherence tomography, Speckle, Signal to noise ratio, Digital filtering, 3D image processing, Image quality, Image enhancement, 3D image enhancement, Tissues, Image filtering
Suppression of speckle artifact in optical coherence tomography (OCT) is necessary for high quality quantitative assessment of ocular disorders associated with vision loss. However, due to its dual role as a source of noise and as a carrier of information about tissue microstructure, complete suppression of speckle is not desirable. That is what represents challenge in development of methods for speckle suppression. We propose method for additive decomposition of a matrix into low-rank and group sparsity constrained terms. Group sparsity constraint represents novelty in relation to state-of-the-art in low-rank sparse additive matrix decompositions. Group sparsity enforces more noise-related speckle to be absorbed by the sparse term of decomposition. Thus, the low-rank term is expected to enhance the OCT image further. In particular, proposed method uses the elastic net regularizer to induce the grouping effect. Its proximity operator is shrunken version of the soft-thresholding operator. Thus, the group sparsity regularization adds no extra computational complexity in comparison with the ℓ1 norm regularized problem. We derive alternating direction method of multipliers based algorithm for related optimization problem. New method for speckle suppression is automatic and computationally efficient. The method is validated in comparison with state-of-the-art on ten 3D macular-centered OCT images of normal eyes. It yields OCT image with improved contrast-to-noise ratio, signal-to-noise ratio, contrast and edge fidelity (sharpness).
Hyperspectral imaging (HSI) is being shown as an emerging modality with a great potential in disease diagnosis and surgical cancer resection. Herein, we evaluate feasibility of the HSI to discriminate and diagnose colon cancer metastasis in a liver from five hematoxylin and eosin stained histopathological specimens. They were collected from the same patient during intraoperative frozen section analysis. Cancer and non-cancer spectra along with corresponding spatial maps were estimated from hyperspectral images by means of spectral unmixing. It was found that maximal angle between cancer spectra is 1.02 degrees less than minimal angle between cancer vs. non-cancer spectra. Thus, spectrum angle mapper was used for pixel-based diagnosis of cancer yielding sensitivity between 81.23% and 97.12%, specificity between 85.85% and 97.3%, and accuracy between 86.85% and 96.92%.
Algorithms for subspace clustering (SC) are effective in terms of the accuracy but exhibit high
computational complexity. We propose algorithm for SC of (highly) similar data points drawn from
union of linear one-dimensional subspaces that are possibly dependent in the input data space. The
algorithm finds a dictionary that represents data in reproducible kernel Hilbert space (RKHS).
Afterwards, data are projected into RKHS by using empirical kernel map (EKM). Due to
dimensionality expansion effect of the EKM one-dimensional subspaces become independent in
RKHS. Segmentation into subspaces is realized by applying the max operator on projected data
which yields the computational complexity of the algorithm that is linear in number of data points.
We prove that for noise free data proposed approach yields exact clustering into subspaces. We also
prove that EKM-based projection yields less correlated data points. Due to nonlinear projection, the
proposed method can adopt to linearly nonseparable data points. We demonstrate accuracy and
computational efficiency of the proposed algorithm on synthetic dataset as well as on segmentation
of the image of unstained specimen in histopathology.
KEYWORDS: Optical coherence tomography, Speckle, Signal to noise ratio, Digital filtering, 3D image processing, Tissues, Image enhancement, Detection and tracking algorithms, Biomedical optics, 3D image enhancement
Speckle artifacts can strongly hamper quantitative analysis of optical coherence tomography (OCT), which is necessary to provide assessment of ocular disorders associated with vision loss. Here, we introduce a method for speckle reduction, which leverages from low-rank + sparsity decomposition (LRpSD) of the logarithm of intensity OCT images. In particular, we combine nonconvex regularization-based low-rank approximation of an original OCT image with a sparsity term that incorporates the speckle. State-of-the-art methods for LRpSD require a priori knowledge of a rank and approximate it with nuclear norm, which is not an accurate rank indicator. As opposed to that, the proposed method provides more accurate approximation of a rank through the use of nonconvex regularization that induces sparse approximation of singular values. Furthermore, a rank value is not required to be known a priori. This, in turn, yields an automatic and computationally more efficient method for speckle reduction, which yields the OCT image with improved contrast-to-noise ratio, contrast and edge fidelity. The source code will be available at www.mipav.net/English/research/research.html.
Recently, novel data-driven offset-sparsity decomposition (OSD) method was proposed by us to increase colorimetric difference between tissue-structures present in the color microscopic image of stained specimen in histopathology. The OSD method performs additive decomposition of vectorized spectral images into image-adapted offset term and sparse term. Thereby, the sparse term represents an enhanced image. The method was tested on images of the histological slides of human liver stained with hematoxylin and eosin, anti-CD34 monoclonal antibody and Sudan III. Herein, we present further results related to increase of colorimetric difference between tissue structures present in the images of human liver specimens with pancreatic carcinoma metastasis stained with Gomori, CK7, CDX2 and LCA, and with colon carcinoma metastasis stained with Gomori, CK20 and PAN CK. Obtained relative increase of colorimetric difference is in the range [19.36%, 103.94%].
We propose an offset-sparsity decomposition method for the enhancement of a color microscopic image of a stained specimen. The method decomposes vectorized spectral images into offset terms and sparse terms. A sparse term represents an enhanced image, and an offset term represents a “shadow.” The related optimization problem is solved by computational improvement of the accelerated proximal gradient method used initially to solve the related rank-sparsity decomposition problem. Removal of an image-adapted color offset yields an enhanced image with improved colorimetric differences among the histological structures. This is verified by a no-reference colorfulness measure estimated from 35 specimens of the human liver, 1 specimen of the mouse liver stained with hematoxylin and eosin, 6 specimens of the mouse liver stained with Sudan III, and 3 specimens of the human liver stained with the anti-CD34 monoclonal antibody. The colorimetric difference improves on average by 43.86% with a 99% confidence interval (CI) of [35.35%, 51.62%]. Furthermore, according to the mean opinion score, estimated on the basis of the evaluations of five pathologists, images enhanced by the proposed method exhibit an average quality improvement of 16.60% with a 99% CI of [10.46%, 22.73%].
A method is proposed for unsupervised 3D (volume) segmentation of registered multichannel
medical images. To this end, multichannel image is treated as 4D tensor represented by a
multilinear mixture model, i.e. the image is modeled as weighted linear combination of 3D
intensity distributions of organs (tissues) present in the image. Interpretation of this model suggests
that 3D segmentation of organs (tissues) can be implemented through sparseness constrained
factorization of the nonnegative matrix obtained by mode-4 unfolding of the 4D image tensor.
Sparseness constraint implies that only one organ (tissue) is dominantly present at each pixel or
voxel element. The method is preliminary validated, in term of Dice's coefficient, on extraction of
brain tumor from synthetic multispectral magnetic resonance image obtained from the TumorSim
database.
A methodology is proposed for contrast enhanced unsupervised segmentation of a liver from a twodimensional
multi-phase CT image. The multi-phase CT image is represented by a linear mixture model,
whereupon each single-phase CT image is modeled as a linear mixture of spatial distributions of the organs
present in the image. The methodology exploits concentration and spatial diversities between organs present
in the image and consists of nonlinear dimensionality expansion followed by matrix factorization that relies
on sparseness between spatial distributions of organs. Dimensionality expansion increases concentration
diversity (contrast) between organs. The methodology is demonstrated on an experimental three-phase CT
image of a liver of two patients.
Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting
tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral
responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or
PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the
number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the
spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image
tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image
preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based
decomposition methods (such as non-negative matrix factorization and independent component analysis) are
used. Superior performance of the tensor-based image decomposition over matrix factorization-based
decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as
well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).
Independent component analysis (ICA) has been widely used for hyperspectral image classification in an
unsupervised fashion. It is assumed that classes are statistically mutual independent. In practice, this assumption may
not be true. In this paper, we apply dependent component analysis (DCA) to unsupervised classification, which does
not require the class independency. The basic idea of our DCA approaches is to find a transform that can improve the
class independency but leave the basis mixing matrix unchanged; thus, an original ICA method can be employed to the
transformed data where classes are less statistically dependent. Linear transforms that possess such a required
invariance property and generate less dependent sources include: high-pass filtering, innovation, and wavelet
transforms. These three transforms correspond to three different DCA algorithms, which will be investigated in this
paper. Preliminary results show that the DCA algorithms can slightly improve the classification accuracy.
Method for robust demarcation of the basal cell carcinoma (BCC) is presented employing novel dependent component
analysis (DCA)-based approach to unsupervised segmentation of the red-green-blue (RGB) fluorescent image of the
BCC. It exploits spectral diversity between the BCC and the surrounding tissue. DCA represents an extension of the
independent component analysis (ICA) and is necessary to account for statistical dependence induced by spectral
similarity between the BCC and surrounding tissue. Robustness to intensity fluctuation is due to the scale invariance
property of DCA algorithms. By comparative performance analysis with state-of-the-art image segmentation methods
such as active contours (level set), K-means clustering, non-negative matrix factorization and ICA we experimentally
demonstrate good performance of DCA-based BCC demarcation in demanding scenario where intensity of the
fluorescent image has been varied almost two-orders of magnitude.
We investigate the application of independent-component analysis (ICA) to remotely sensed hyperspectral image classification. We focus on the performance of two well-known and frequently used ICA algorithms: joint approximate diagonalization of eigenmatrices (JADE) and FastICA; but the proposed method is applicable to other ICA algorithms. The major advantage of using ICA is its ability to classify objects with unknown spectral signatures in an unknown image scene, i.e., unsupervised classification. However, ICA suffers from computational expensiveness, which limits its application to high-dimensional data analysis. In order to make it applicable or reduce the computation time in hyperspectral image classification, a data-preprocessing procedure is employed to reduce the data dimensionality. Instead of using principal-component analysis (PCA), a noise-adjusted principal-components (NAPC) transform is employed for this purpose, which can reorganize the original data with respect to the signal-to-noise ratio, a more appropriate image-ranking criterion than variance in PCA. The experimental results demonstrate that the major principal components from the NAPC transform can better maintain the object information in the original data than those from PCA. As a result, an ICA algorithm can provide better object classification.
KEYWORDS: Independent component analysis, Principal component analysis, Hyperspectral imaging, Image classification, Remote sensing, Signal to noise ratio, Data modeling, Image processing, Signal processing, Dimension reduction
In this paper, we investigate the application of independent component analysis (ICA) to remotely sensed hyperspectral image classification. We focus on the performance of Joint Approximate Diagonalization of Eigenmatrices (JADE) algorithm, although the proposed method is applicable to other popular ICA algorithms. The major advantage of using ICA is its capability of classifying objects with unknown spectral signatures in an unknown image scene, i.e., unsupervised classification. However, ICA suffers from computational expensiveness, which limits its application to high dimensional data analysis. In order to make it applicable to hyperspectral image classification, a data preprocessing procedure is employed to reduce the data dimensionality. Noise adjusted principal component analysis (NAPCA) is used for this purpose, which can reorganize the original data information in terms of signal-to-noise ratio, a more appropriate criterion than variance when dealing with images. The preliminary results demonstrate that the selected major components from NAPCA can better represent the object information in the original data than those from ordinary principal component analysis (PCA). As a result, better classification using ICA is expected.
The novel approach to the image sharpening problem is proposed in this paper. It is based on the application of the independent component analysis (ICA) algorithm on the image sequence with the appropriate time displacement between the image frames. The novelty is in the data representation required by the ICA algorithms where each selected image frame has been used as a sensor implying that underlying sources are temporally independent. The proposed concept enables blurring effects contributed by atmospheric turbulence to be extracted as separate physical sources. It has been ensured through images registration technique that motion of the video recorder is compensated. Encouraging preliminary results were obtained when ICA algorithm has been applied on the experimental data (video sequence) with the known ground truth. It has been verified that extracted spatial turbulence patterns are highly impulsive with Gaussian exponent between 0.5 and 0.6 where Laplacian distribution is characterized with Gaussian exponent 1.
Harold Szu, James Buss, Joseph Garcia, Nancy Breaux, Ivica Kopriva, Nicholas Karangelen, M. Hsu, Ting Lee, Jeff Willey, Gary Shield, Steve Brown, R. Robbins, John Hobday
We review various image processing algorithms for micro-UAV EO/IR sub-pixel jitter restoration. Since the micro-UAV, Silver Fox, cannot afford isolation coupling mounting from the turbulent aerodynamics of the airframe, we explore smart real-time software to mitigate the sub-pixel jitter effect. We define jitter to be sub-pixel or small-amplitude vibrations up to one pixel, as opposed to motion blur over several pixels for which there already exists real time correction algorithms used on other platforms. We divide the set of jitter correction algorithms into several categories: They are real time, pseudo-real time, or non-real-time, but they are all standalone, i.e. without relying on a library storage or flight data basis on-board the UAV. The top of the list is demonstrated and reported here using real-world data and a truly unsupervised, real-time algorithm.
We proposed the physics approach to solve a physical inverse problem, namely to choose the unique equilibrium solution (at the minimum free energy: H= E - ToS, including the Wiener, l.m.s E, and ICA, Max S, as special cases). The "unsupervised classification" presumes that required information must be learned and derived directly and solely from the data alone, in consistence with the classical Duda-Hart ATR definition of the "unlabelled data". Such truly unsupervised methodology is presented for space-variant imaging processing for a single pixel in the real world case of remote sensing, early tumor detections and SARS. The indeterminacy of the multiple solutions of the inverse problem is regulated or selected by means of the absolute minimum of isothermal free energy as the ground truth of local equilibrium condition at the single-pixel foot print.
The application of independent component analysis (ICA) to remotely sensed image classification has been studied recently. It is particularly useful for classifying objects with unknown spectral signatures in an unknown image scene, i.e., unsupervised classification. Since the weight matrix in ICA is a square matrix for the purpose of mathematical tractability, the number of objects that can be classified is equal to the data dimensionality, i.e., the number of spectral bands. When the number of spectral bands is very small (e.g., 3-band CIR photograph and 6-band Landsat image), it is impossible to classify all the different objects present in an image scene with the original data. In order to solve this problem, we present a data dimensionality expansion technique to generate artificial bands. Its basic idea is to use nonlinear functions to capture the second and high order correlations between original bands, which can provide additional information for detecting and classifying more objects. The results from such nonlinear band generation approach are compared with a linear band generation method using cubic spline interpolation of pixel spectral signatures. The experiments demonstrate that nonlinear band generation approach can significantly improve unsupervised classification accuracy, while linear band generation method cannot since no new information can be provided.
Nonlinear distortions are always introduced to biomedical signals during the acquisition stage, which consequently fail the traditional linear independent component analysis (ICA) methods for further signal processing. This paper investigates the non-linearity system function in the pre-amplifier and A/D converter of the biomedical instruments. A polynomial general model structure with adjustable parameters to approximate the nonlinear relation is proposed for medical instruments. Model parameters are validated using a typical electrocardiograph (ECG) acquisition system with sinusoids of varying frequency and amplitude. Thus the inverse nonlinear transform is applied to acquired data to cancel the nonlinear distortions. The ICA method is then applied to the originally linear mixed data, non-rectified data and also rectified data and the results are favorably compared in the designed experiment using both clinical ECGs and the simulated data from cardiac simulators.
A Cauchy Machine has been applied to solve nonlinear space-variant blind imaging problem with positivity constraints on the pixel-by-pixel basis. Nonlinearity parameters, de-mixing matrix and source vector are found at the minimum of the thermodynamics free energy H=U-T0S, where U is estimation error energy, T0 is temperature and S is the entropy. Free energy represents dynamic balance of an open information system with constraints defined by data vector. Solution was found through Lagrange Constraint Neural Network algorithm for computing the unknown source vector, exhaustive search to find unknown nonlinearity parameters and Cauchy Machine for seeking de-mixing matrix at the global minimum of H for each pixel. We demonstrate the algorithm capability to recover images from the synthetic noise free nonlinear mixture of two images. Capability of the Cauchy Machine to find the global minimum of the golf hole type of landscape has hitherto never been demonstrated in higher dimensions with a much less computation complexity than an exhaustive search algorithm.
KEYWORDS: Data modeling, Sensors, Signal to noise ratio, Transformers, Binary data, Interference (communication), Data communications, Receivers, Signal attenuation, Broadband telecommunications
Powerline communication has become interesting as a new choice of communication media by using OFDM in the Europe Internet application and using TDMA in power meters' reading in Japan mimicking the function of phone-line DSL. However, this raw copper media without hefty infrastructure investment such as the telephone twisted pair DSL has many challenges, because it was designed to transmit an electrical current that had isolated power grid with transformers, it has nothing that is suitable to convey data but it is everywhere in the last mile of connecting households. To make everything worse, the powerline is also easily interfered by unpredictable impulsive noise, background colored noise, and fatal attenuation of signal. Our goal is to take the US city grid power-line as a supplement to the concept of a single-user & multiple- sensor-broadcasting applications for security. To successfully communicate through the power-line for the household/stadium/subway/traffic-lights security application, e.g. separated video feds find themselves the single owner PC through the common household/stadium/subway/traffic-lights power-line, we develop and test an appropriate sparse coding, compression, and error correction to succeed the task with a limited bandwidth technique. In this paper we did not apply out human sensory preserving compression code, but to concentrate on sparse coding BSS with the less-bandwidth- demanding audio signals. In this paper, we describe a detail model of the power-line topologies based on realistic powerline data, and quantify the error rates of transmitted data on the powerline in the cases when noise is presented in the channel.
Since in remote sensing each pixel could have its own unique radiation source s including man-made objects associated with different spectral reflectance matrix A, we could not average over neighborhood pixels. Instead, we solve pixel-by-pixel independent classes analysis (ica) without pixel average by Lagrange Constraint of the data measurement model and Gibbs' equal a priori probability assumption based on Shannon's Entropy H(s) with probability normalization condition for an arbitrary number of M classes that is bounded by the spectral data components N. We formulate the Fast Lagrangian method to maximize the Shannon entropy with the equality constraints in order to achieve O(N) numerical complexity contrary to the O(N2) numerical complexity associated with the solution of the inverse problem required in the classical Lagrangian formulation. Trivial equal probability solution with uniformly distributed class vector s is avoided by introducing additional set of the inequality constraints. The unknown spectral reflectance matrix A is estimated blindly in non-parameterized form minimizing an LMS energy function. We apply the Riemannian metric to the gradient learning for reproducing the biological Hebbian rule in terms of a full rank vector outer product formula and demonstrate faster convergence than standard Euclidean gradient. Since the proposed Fast Lagrangian method has O(N) numerical complexity we have achieved a real time hyperspectral remote sensing capability as platform moves, samples and processes. A FPGA firmware implementation for massive pixel parallel algorithm has been fired for patent.
Noisy incoherent objects, which are too close to be remotely separated by optically imaging beyond the Rayleigh diffraction limit, might be resolved by employing the Artificial Neural Network (ANN) smart pixel post processing and its mathematical framework, Independent Component Analysis (ICA). It is shown that ICA ANN approach to superresolution based on information maximization principle could be seen as a part of the general approach called space-bandwidth (SW) product adaptation method. Our success is perhaps due to the Blind Source Separation (BSS) Smart-Pixel Detectors (SPD) behind the imaging lens (inverse adaptation), while the Rayleigh diffraction limit remains valid for a single instance of the deterministic imaging systems' realization. The blindness is due to the unknown objects, and the unpredictable propagation effect on the net imaging point spread function. Such a software/firmware enhancement of imaging system may have a profound implication to the designs of the new (third) generation imaging systems as well as other non-optical imaging systems.
Reticle systems are considered to be the classical approach for estimating the position of a target in a considered field of view and are widely used in IR seekers. Due to the simplicity and low cost, since only a few detectors are used, reticle seekers are still in use and are subject of further research. However, the major disadvantage of the reticle trackers has been proven to be sensitivity on the IR countermeasures. To resolve this problem modification of optical trackers is analyzed here for a wide class of reticles that are producing frequency or amplitude modulated signals either by nutation or by spinning. When Independent Component Analysis (ICA) algorithms are applied on the outputs of appropriately modified trackers the reticle type dependent transmission functions, also called the source signals in the context of the ICA theory, can be recovered on the basis of the output signals only. Position of each optical source is obtained by applying appropriate demodulation method on the recovered source signals. The three conditions necessary for the ICA theory to work (statistical independence and non-Gaussianity of the source signals and nonsingularity of the mixing matrix) are shown to be fulfilled in principle for any kind of the reticle geometry. In relation to some IR counter-countermeasures algorithms which are based on heuristic and sometimes unrealistic assumptions (target performs no maneuvering) the approach exposed here has been proven to be theoretically consistent without any special constraints imposed on the optical sources.
Reticle systems are considered to be the classical approach for estimating the position of a target in a considered field of view an are widely used in IR seekers. Due to the simplicity and low cost, since only a few detectors are used, reticle seekers are still in use and are subject of further research. However, the major disadvantage of reticle trackers has been proven to be sensitivity on the IR countermeasures such as flares and jammers. When redesigned adequately they produce output signals that are linear convolutive combinations of the reticle transmission functions that are considered as the source signals in the context of the Independent Component Analysis (ICA) theory. Each function corresponds with single optical source position. That enables ICA neural network to be applied on the optical tracker output signals giving on its outputs recovered reticle transmission functions. Position of each optical source is obtained by applying appropriate demodulation method on the recovered source signals. The three conditions necessary for the ICA theory to work are shown to be fulfilled in principle for any kind of the reticle geometry.
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