Multidimensional Processing Research Articles

A sparse and discriminative tensor to vector projection for human gait feature representation

In this paper, we introduce an efficient tensor to vector projection algorithm for human gait feature representation and recognition. The proposed approach is based on the multi-dimensional or tensor signal processing technology, which finds a low-dimensional tensor subspace of original input gait sequence tensors while most of the data variation has been well captured. In order to further enhance the class separability and avoid the potential overfitting, we adopt a discriminative locality preserving projection with sparse regularization to transform the refined tensor data to the final vector feature representation for subsequent recognition. Numerous experiments are carried out to evaluate the effectiveness of the proposed sparse and discriminative tensor to vector projection algorithm, and the proposed method achieves good performance for human gait recognition using the sequences from the University of South Florida (USF) HumanID Database.

Foundations of compositional models: structural properties

The paper is a follow-up of [R.J.: Foundations of compositional model theory. IJGS, 40(2011): 623–678], where basic properties of compositional models, as one of the approaches to multidimensional probability distributions representation and processing, were introduced. In fact, it is an algebraic alternative to graphical models, which does not use graphs to represent conditional independence statements. Here, these statements are encoded in a sequence of distributions to which an operator of composition – the key element of this theory – is applied in order to assemble a multidimensional model from its low-dimensional parts. In this paper, we show a way to read conditional independence relations, and to solve related topics, above all the so-called equivalence problem, i.e. the problem of recognizing whether two different structures induce the same system of conditional independence relations.

Compression of hyperspectral remote sensing images by tensor approach

Abstract Whereas the transform coding algorithms have been proved to be efficient and practical for grey-level and color images compression, they could not directly deal with the hyperspectral images (HSI) by simultaneously considering both the spatial and spectral domains of the data cube. The aim of this paper is to present an HSI compression and reconstruction method based on the multi-dimensional or tensor data processing approach. By representing the observed hyperspectral image cube to a 3-order-tensor, we introduce a tensor decomposition technology to approximately decompose the original tensor data into a core tensor multiplied by a factor matrix along each mode. Thus, the HSI is compressed to the core tensor and could be reconstructed by the multi-linear projection via the factor matrices. Experimental results on particular applications of hyperspectral remote sensing images such as unmixing and detection suggest that the reconstructed data by the proposed approach significantly preserves the HSI׳s data quality in several aspects.

Early-infant diagnostic predictors of the neuro-behavioral development after neonatal care

Multidimensional diagnosis plays a central role in infant developmental care, which leads to the prediction of future disabilities. Information consolidated from objective and subjective, early and late, central and peripheral data may reveal neuro-pathological mechanisms and realize earlier and more precise preventive intervention.In the current study, we retrospectively searched correlating factors to the following neurological and behavioral development of ‘Head Control’ and ‘Roll Over’ using multivariate correlation analysis of different diagnostic domains over age, subject/object information of the patients who were previously admitted in our neonatal intensive care unit (NICU) and could be developmentally followed up in our outpatient clinic. Based on the hematologic and biochemical data, MRI brain anatomy during NICU hospitalization, we characterized all the acquired data distribution from 31 infants with either ‘appeared neurologically normal (ANN, n=21)’ or ‘appeared neurologically abnormal (ANA, n=10)’ pro tempore, with a physician's clinical judgment before discharge. Besides single factor comparisons between ANN and ANA, we examined their development difference by using the multidimensional information processing, principal component analysis (PCA). The diagnostic predictors of neuro-behavioral development were selected by regression analysis with variable selection. It resulted that hematological and brain anatomical factors seemed correlated to both ‘Head Control’ and ‘Roll Over’. This report suggested certain possibility of the cross-domain translational approach between subjective and objective developmental information through multivariate analyses, with candidate markers preliminarily to be evaluated in further studies.

Journal of Real-Time Image Processing: second issue of volume 9

The editorial board of JRTIP met in Brussels in April 2014 where they were attending the SPIE Conference on RealTime Image and Video Processing. The editorial board will have its next meeting in San Francisco in February 2015 where the same conference will take place as part of the SPIE Electronic Imaging Symposium. In the recently held editorial meeting (see Fig. 1), various items related to the status of the journal were discussed; a summary of these items is provided below. To address the backlog of printed versions of the accepted manuscripts that appear on Online First, we are pleased to state that the number of printed pages per issue will be increased to 200 pages per issue starting in 2015 for a total page count of 800 pages annually. It is hoped that the backlog situation is eased as a result of this page count increase. We will revisit this issue in 2015 to see whether further actions would be needed to resolve this issue. The journal performance numbers that have become available for the year 2013 clearly reflect the elevated recognition level of JRTIP. In 2013, similar to 2012, the acceptance rate of manuscripts submitted to JRTIP has remained at about 25 %. This is an indication that our review process is conducted in such a way that only quality papers are published in JRTIP. It is worth noting that the usage factor (UF) of JRTIP, which is the ratio of the number of paper downloads over the number of papers for a 2-year period, has increased by about 75 % from 2011 to 2012. With the substantial increase in the number of downloads to 34,000? in 2013 from 25,500? in 2012, it is expected that the 2013 UF would increase significantly. We would like to particularly thank the Associate Editors and the Springer Editorial Office for the major roles they have played in increasing these numerical indicators while maintaining the quality of published papers. Here, it is worth pointing out that the third issue in 2014 will be allocated to two special issues that are scheduled to appear together. These special issues are named ‘‘Algorithms and Architectures for Real-time Multi-Dimensional Image Processing’’ and ‘‘Convergence of Real-Time 3D Imaging and Optical Communications’’. This regular issue of JRTIP includes six papers. The first paper by Juliet et al. presents a compound image segmentation algorithm based on the mixed raster content (MRC) model (foreground/mask/background). After segmenting a compound image into different classes, each class is transformed to the MRC model according to its properties. The foreground and the background layers are compressed using JPEG 2000 while the mask layer is compressed using JBIG2. It is shown that this MRC compression achieves a higher subjective quality and coding efficiency than the state-of-the-art compression algorithms, such as JPEG, JPEG 2000 and H.264/AVC-I. The second paper by Bartovsky et al. introduces an additional, intra-operator level of parallelism for dilation/ erosion operations. Realized in a dedicated hardware, for rectangular structuring elements with programmable size, the implementation allows obtaining real-time performances for these operators that were previously unachievable. Low latency and memory requirements are the other main attributes of this parallelism. The third paper by Gaceb et al. describes a document classification approach based on physical layout features N. Kehtarnavaz (&) University of Texas at Dallas, Richardson, USA e-mail: kehtar@utdallas.edu

Application of Multidimensional Data Model in the Traffic Accident Data Warehouse

The traffic administrative department would record real-time information of accidents and update the corresponding database when dealing with daily traffic routines. It is of great significance to study and analyze these data. In this paper, we propose a Multi-dimensional Data Warehouse Model (M-DWM) combined with the concept of Data Warehouse and multi-dimensional data processing theory. The model can greatly improve the efficiency for statistical analysis and data mining.

Single Photon Avalanche Diode Imaging Systems for Biomedical Applications

Ever since the discovery of the photon by Einstein and Planck, scientists have continually strived to achieve single photon imaging; considered the holy grail of photosensing, since it represents the ultimate detection and precision limit of electromagnetic radiation. With the invention of the photomultiplier tube (PMT) in the 1930s, single-photon detection became feasible. Since then, PMTs have been developed to meet a wide range of application needs. For the most demanding time-resolved measurements, micro-channel plate (MCP) PMTs have been used. However, PMT devices are inherently limited due to their large size, high-cost, fragility, high operating voltages, and magnetic field susceptibility. On the other hand, Geiger-mode APDs realized in CMOS technology do not suffer from these limitations, and in recent years, their performance has significantly improved so they are now comparable to PMTs. As such, single photon imagers based on CMOS single-photon avalanche detectors (SPAD) have been realized for applications where speed, cost, miniaturization and power consumption are critical [1].The main components of a high-speed single photon imaging system is the SPAD, which converts a single photon to an electrical pulse, the SPAD front-end circuit, which shapes the pulse and controls the SPAD, and the time-to-digital converter (TDC), which converts the time interval between the detected photon and a reference pulse, or the time between two detected photons, into a digital code. Deep sub-micron (DSM) CMOS technology lends itself very well to the realization of such a system; all the components can be integrated together with very high reliability at a very low cost, digital processing can be readily applied to the detected photons, and dense arrays can be realized for multi-dimensional processing. Over the last decade, CMOS single-photon imaging systems have been applied in the fields of biomedical research, astronomy, nuclear physics, ranging and communications [2], [3], [4].This work describes the design of the main components of a high-speed single photon imaging system for biomedical applications, implemented in a standard, commercial CMOS 0.13 μm technology from IBM. A passively-quenched SPAD pixel was characterized in terms of its noise, temporal resolution, efficiency, and temperature performance. By fabricating the SPAD in a DSM technology, we were able to take advantage of the inherent speed, lower parasitic capacitance, and increased integration density afforded by the CMOS process. Indeed, a dead-time down to 20 ns was achievable with the SPAD front-end circuit, since the total capacitance of the 9.6 x 8.5 μm2 SPAD remained below 100 fF. Also, a new dual-interpolating tapped-delay-line TDC prototype chip was designed and evaluated for a future integration with an SPAD in a multichannel fluorescent lifetime imaging / positron emission tomography (FLIM/PET) system. The design goals were to achieve simultaneously a high-resolution, high throughput, good linearity, wide measurement range, small size and low power. The 8-bit TDC chip measures time intervals with a 156 ns least-significant bit (LSB) between a common STOP pulse from a laser and a START pulse generated by an SPAD, as in a typical time-correlated single-photon counting (TCSPC) acquisition chain shown in figure 1. In this presentation, details of the key design issues and the results from extensive testing will be provided and discussed.

Improvement of multi-dimensional processing efficiency by layout optimization of multi-axis machine tools

The article considers the issues of optimizing the layout of multi-axis machine tools for multi-dimensional processing using various criteria. Optimization of layouts is implemented using CAD/CAM/CAE/PDM systems, SolidWorks and MS Excel.

Special issue on algorithms and architectures for real-time multi-dimensional image processing

This special issue collects eight contributions, selected among many submitted papers after a multi-cycle review process, which are representative of the recent advances on real-time multi-dimensional image processing algorithms and architectures. The published works come from both academia and industry R&D sites in Europe, North America, Asia and Africa. These works show that more and more applications involve multi-dimensional image processing (multi- and hyperspectral imaging, multi-camera vision, multi-frame imaging, etc.), such as remote sensing, surveillance, computer vision and image/video enhancement for avionic and automotive.

Implementation of JDL Model for Multidimensional Measurements Processing in the Environment of Intelligent GIS

The paper describes the JDL model oriented on solving tasks of multidimensional measurements processing in various subject domains. The results of the processing are represented in a form that is interpretable by both computers and common users and can be used for solving a wide range of applied tasks. The proposed model is implemented in an agile systems for multidimensional measurements processing based on intelligent GIS technologies. The systems are efficiently used for solving a number of complicated tasks of measurements of dynamic objects parameters processing and analyses.

Multidimensional Signal Processing and Applications

In our daily lives and almost unconsciously, we deal with multidimensional data. From color images converted to the luminance and chrominance format to magnetic resonance images commonly acquired for health purposes, from different fashions to write an alphabet to array processing signals underlying any telecommunication system, we deal with multidimensional data. In this special issue, we tried to show the variety of the topics which are currently investigated with multidimensional signal processing tools. The mathematical tools presented in this issue are as diverse as adaptive detectors, wavelet processing, principal component analysis, and improved classical image processing tools such as histogram equalization. In the array processing paradigm, a two-dimensional matrix containing the data depends on the polarization properties of the sources, their number, and the number of sensors in the receiving antenna. Hence the interest of a multidimensional representation, including a polarization variable with two or three possible values, and a real and a complex part for the source amplitudes. In the image processing paradigm, data are as various as magnetic resonance or color images, whose representation can be transferred from the RGB (red green blue) format to other spaces emphasizing for instance the luminance or the chrominance. It is shown how magnetic resonance brain images are classified with support vector machine. To avoid problems related to high dimensionality, which is current in big data processing, adequate features are extracted from the data by discrete wavelet transform and principal component analysis. Color spaces, which are useful for skin detection, for instance, are also further investigated: whatever the representation space is, a color image is a third order tensor, in other words, a three-dimensional data. It is shown how to detect image splicing with the help of merged features in the chrominance space: the relationships between pixels in a neighborhood are studied with a Markov process and the extraction of DCT features from the chrominance channel. Then, with the help of new color spaces, it is shown how evolved versions of neural networks called extreme learning machines can fuse multiple information such as color and local spatial information from face images. The “multi” aspect can also appear in the image processing paradigm when multiple images are obtained from several parameters. In images provided by synthetic aperture radar exploited for flood detection, contrast enhancement is achieved by an adjustable histogram equalization technique. For such an application where the visual aspect of the results are much important much, a color image, that is, a multidimensional signal, can be built from several two-dimensional result images, to get an informative map, where the color informs on the nature of the imaged scene, flooded or not, for instance. Starting from images, a set of multidimensional data is extracted from Serbian texts: the Serbian alphabet, made of 30 letters, can be expressed in a Latin or in a Cyrillic fashion. All letters can be classified into four sets. By studying the frequencies of occurrence of each type of letter in a text, one can deduce that this text is written in the Latin or the Cyrillic fashion. In this application, matrices describing the cooccurrence in the distribution of the four types of letters are built out of any text, to make use of the classical texture features. Adapting the texture features to such a text recognition application, introducing a parameter which is the writing fashion, is a brand new idea. The “multi” aspect can also relate to multiresolution. Histogram of oriented gradients and hue descriptors can be merged to combine information related to the shape of an object and its color. By computing the merged data at several resolution levels, an innovative multidimensional descriptor is obtained. An application considered in this special issue is aircraft characterization and detection of images. In a nutshell, the “multi” representation attracts the interest of researchers from very diverse application fields. Hopefully, this special issue will contribute in diffusing the models and tools of multidimensional signal processing to various application fields. Salah Bourennane Julien Marot Caroline Fossati Ahmed Bouridane Klaus Spinnler

Special issue on multidimensional signal processing applications

This special issue onmultidimensional signal processing applications covers a broad range of methodologies and algorithms for spatially extended configurations of sensors and emitters for various purposes and applications. The spectrum of the typical wavelengths for these applications ranges from very short ones in electron transmission microsopy to visibile light, up to radio frequencies and further to sound waves in the audio range suitable for human perception. In spite of the diversity of the underlying physical principles there are similarities in the arising problems. Consequently also some of the approaches to the processing of the resulting sensor or emitter signals are shared between these applications. One common problem is the detection of drift and translation between images acquired by electron transmission microsopy and conventional cameras. Also the detection of motion in video sequences falls into this category. Another set of problems is concerned with the detection of the direction of a source of either electromagnetic or sound waves using suitable receiver arrays. But the situation may also be turned around by forming directed wave fronts from loudspeaker arrays to produce sound fields with certain spatial requirements. This set of seven papers shows thatmodernmultidimensional signal processing overcomes the traditional separation of image processing and audio processing. The presented methods and algorithms prescind from plain processing of available sensor or emitter signals. Instead the focus lies on physical processes andmathematical foundations underlying all applications. The paper A comparison between minimum variance control and other online compensation methods for specimen drift in transmission electron microscopy by A. Tejada and A.J. den Dekker presents an online method to reduce image blurring by specimen drift dur-

Hierarchy Based on Neighborhood Template about k-Neighborhood Template A-Type Three-Dimensional Bounded Cellular Acceptor

Recently, due to the advance in dynamic image processing, computer animation, augmented reality (AR), and so forth, it has become increasingly apparent that the study of four-dimensional pattern processing (three-dimensional pattern processing with time axis) should be very important. Thus, the study of four-dimensional automata as the computational model of four-dimensional pattern processing has been meaningful. From this point of view, we first introduced a four-dimensional automaton in 2002. In the multi-dimensional pattern processing, designers often use a strategy whereby features are extracted by projecting high-dimensional space on low-dimensional space. In this paper, from this viewpoint, we introduce a new computational model, k-neighborhood template A-type three-dimensional bounded cellular acceptor (abbreviated as A -3BCA(k)) on four-dimensional input tapes, and discuss hierarchy based on neighborhood template about A-3BCA(k).

A Novel Non-canonical Forkhead-associated (FHA) Domain-binding Interface Mediates the Interaction between Rad53 and Dbf4 Proteins

Forkhead-associated (FHA) and BRCA1 C-terminal (BRCT) domains are overrepresented in DNA damage and replication stress response proteins. They function primarily as phosphoepitope recognition modules but can also mediate non-canonical interactions. The latter are rare, and only a few have been studied at a molecular level. We have identified a crucial non-canonical interaction between the N-terminal FHA1 domain of the checkpoint effector kinase Rad53 and the BRCT domain of the regulatory subunit of the Dbf4-dependent kinase that is critical to suppress late origin firing and to stabilize stalled forks during replication stress. The Rad53-Dbf4 interaction is phosphorylation-independent and involves a novel non-canonical interface on the FHA1 domain. Mutations within this surface result in hypersensitivity to genotoxic stress. Importantly, this surface is not conserved in the FHA2 domain of Rad53, suggesting that the FHA domains of Rad53 gain specificity by engaging additional interaction interfaces beyond their phosphoepitope-binding site. In general, our results point to FHA domains functioning as complex logic gates rather than mere phosphoepitope-targeting modules.

Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state

Multi-dimensional color image processing has two difficulties: One is that a large number of bits are needed to store multi-dimensional color images, such as, a three-dimensional color image of $$1024 \times 1024 \times 1024$$1024?1024?1024 needs $$1024 \times 1024 \times 1024 \times 24$$1024?1024?1024?24?bits. The other one is that the efficiency or accuracy of image segmentation is not high enough for some images to be used in content-based image search. In order to solve the above problems, this paper proposes a new representation for multi-dimensional color image, called a $$(n\,+\,1)$$(n+1)-qubit normal arbitrary quantum superposition state (NAQSS), where $$n$$n qubits represent colors and coordinates of $${2^n}$$2n pixels (e.g., represent a three-dimensional color image of $$1024 \times 1024 \times 1024$$1024?1024?1024 only using 30?qubits), and the remaining 1?qubit represents an image segmentation information to improve the accuracy of image segmentation. And then we design a general quantum circuit to create the NAQSS state in order to store a multi-dimensional color image in a quantum system and propose a quantum circuit simplification algorithm to reduce the number of the quantum gates of the general quantum circuit. Finally, different strategies to retrieve a whole image or the target sub-image of an image from a quantum system are studied, including Monte Carlo sampling and improved Grover's algorithm which can search out a coordinate of a target sub-image only running in $$O(\sqrt{N/r} )$$O(N/r) where $$N$$N and $$r$$r are the numbers of pixels of an image and a target sub-image, respectively.

Multidimensional gray-wavelet processing in interferometric fiber-optic gyroscopes

A multidimensional signal processing method for a single interferometric fiber-optic gyroscope (IFOG) is proposed, to the best of our knowledge, for the first time. The proposed method, based on a novel IFOG structure with quadrature demodulation, combines a multidimensional gray model (GM) and a wavelet compression technique for noise suppression and sensitivity enhancement. In the IFOG, two series of measured rotation rates are obtained simultaneously: an in-phase component and a quadrature component. Together with the traditionally measured rate, the three measured rates are processed by the combined gray-wavelet method. Simulations show that the intensity noise and non-reciprocal phase fluctuations are effectively suppressed by this method. Experimental comparisons with a one-dimensional GM(1, 1) model show that the proposed three-dimensional method achieves much better denoising performance. This advantage is validated by the Allan variance analysis: in a low-SNR (signal-to-noise ratio) experiment, our method reduces the angle random walk (ARW) and the bias instability (BI) from 1 × 10−2 deg h−1/2 and 3 × 10−2 deg h−1 to 1 × 10−3 deg h−1/2 and 3 × 10−3 deg h−1, respectively; in a high-SNR experiment, our method reduces the ARW and the BI from 9 × 10−4 deg h−1/2 and 5 × 10−3 deg h−1 to 4 × 10−4 deg h−1/2 and 3 × 10−3 deg h−1, respectively. Further, our method increases the dimension of the state-of-the-art IFOG technique from one to three, thus obtaining higher IFOG sensitivity and stability by exploiting the increase in available information.

Electronically scanned RF-to-bits beam aperture arrays using 2-D IIR spatially bandpass digital filters

A beamforming system based on two-dimensional (2-D) spatially bandpass infinite impulse response (IIR) plane wave filtering is presented in a multi-dimensional signal processing perspective and the implementation details are discussed. Real-time implementation of such beamforming systems requires modeling of computational electromagnetics for the antennas, radio frequency (RF) analog design aspects for low-noise amplifiers (LNAs), mixed-signal aspects for signal quantization and sampling and finally, digital architectures for the spatially bandpass plane wave filters proposed in Joshi et al. (IEEE Trans Very Large Scale Integr Syst 20(12):2241---2254, 2012). Multi-dimensional spatio-temporal spectral properties of down-converted RF plane wave signals are reviewed and derivation of the spatially bandpass filter transfer function is presented. An example of a wideband antipodal Vivaldi antenna is simulated at 1 GHz. Potential RF receiver chains are identified including a design of a tunable combline microstrip bandpass filter with tuning range 0.8---1.1 GHz. The 1st-order sensitivity analysis of the beam filter 2-D $$\mathbf z $$ z -domain transfer function shows that for a 12-bits of fixed-point precision, the maximum percentage error in the 2-D magnitude frequency response due to quantization is as low as $$0.3\,\%$$ 0.3 % . Monte-Carlo simulations are used to study the effect of quantization on the bit error rate (BER) performance of the beamforming system. 5-bit analog to digital converter (ADC) precision with 8-bit internal arithmetic precision provides a gain of approximately 16 dB for a BER of $$10^{-3}$$ 10 - 3 with respect to the no beamforming case. ASIC Synthesis results of the beam filter in 45 nm CMOS verifies a real time operating frequency of 429 MHz.

Structure and Activity of the Peptidyl-Prolyl Isomerase Domain from the Histone Chaperone Fpr4 toward Histone H3 Proline Isomerization

The FK506-binding protein (FKBP) family of peptidyl-prolyl isomerases (PPIases) is characterized by a common catalytic domain that binds to the inhibitors FK506 and rapamycin. As one of four FKBPs within the yeast Saccharomyces cerevisiae, Fpr4 has been described as a histone chaperone, and is in addition implicated in epigenetic function in part due to its mediation of cis-trans conversion of proline residues within histone tails. To better understand the molecular details of this activity, we have determined the solution structure of the Fpr4 C-terminal PPIase domain by using NMR spectroscopy. This canonical FKBP domain actively increases the rate of isomerization of three decapeptides derived from the N terminus of yeast histone H3, whereas maintaining intrinsic cis and trans populations. Observation of the uncatalyzed and Fpr4-catalyzed isomerization rates at equilibrium demonstrate Pro(16) and Pro(30) of histone H3 as the major proline targets of Fpr4, with little activity shown against Pro(38). This alternate ranking of the three target prolines, as compared with affinity determination or the classical chymotrypsin-based fluorescent assay, reveals the mechanistic importance of substrate residues C-terminal to the peptidyl-prolyl bond.

Ubiquitin Interacts with the Tollip C2 and CUE Domains and Inhibits Binding of Tollip to Phosphoinositides

A large number of cellular signaling processes are directed through internalization, via endocytosis, of polyubiquitinated cargo proteins. Tollip is an adaptor protein that facilitates endosomal cargo sorting for lysosomal degradation. Tollip preferentially binds phosphatidylinositol 3-phosphate (PtdIns(3)P) via its C2 domain, an association that may be required for endosomal membrane targeting. Here, we show that Tollip binds ubiquitin through its C2 and CUE domains and that its association with the C2 domain inhibits PtdIns(3)P binding. NMR analysis demonstrates that the C2 and CUE domains bind to overlapping sites on ubiquitin, suggesting that two ubiquitin molecules associate with Tollip simultaneously. Hydrodynamic studies reveal that ubiquitin forms heterodimers with the CUE domain, indicating that the association disrupts the dimeric state of the CUE domain. We propose that, in the absence of polyubiquitinated cargo, the dual binding of ubiquitin partitions Tollip into membrane-bound and membrane-free states, a function that contributes to the engagement of Tollip in both membrane trafficking and cytosolic pathways.

A Blind Source Separation Method Applied to Simultaneous Kinetic Multicomponent Determination

A multi-dimensional data processing method, independent component analysis-based principal component regression (ICA-PCR) was developed for simultaneous kinetic determination of Cu (II), Fe (III) and Ni (II). Independent component analysis is a newly developed signal processing technique aiming at solving related blind source separation (BSS) problem. One program, PICAPCR, was designed to perform relative calculations. Experimental results showed the ICA-PCR method to be successful for simultaneous multicomponent kinetic determination even where there was severe overlap of spectra.