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“Digital
Signal Processing” No. 1-2019 |
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Method of coding of message sources
Bykhovskiy Mark, PhD, Professor at MTUSI, e-mail: bykhmark@gmail.com
Keywords: OFDM Signals, multifrequency broadband signals, reduction of the peak-factor of signals, beam separation in multi-path channels, divesity reception, multipath link channel.
Abstract
The author describes a new method of message sources’ coding. This method allows to eliminate from the messages excessiveness/redundancy resulting from the fact that the simbols constituting these messages are appearing on the source coder (SC) with probabilities which are substantially different from each other. This method is based on the fact that in the SC, the code combinations are formed and they determine the exact spot where the separate sybmols appear in the long sequence of symbols which are to be transmitted through the communication channel. It is shown that the proposed coding method of message sources is optimal (by Shannon) and remains optimal with any changes of statistical characteristics of a message source. There are no technical complications involved in creating of the SC and decoder that use this method. The described method of numbering the sequences with a length of N, in which in k positions are 1s, can be applied for formation of an N-dimensional single ensemble with the permutable modulation (PM) proposed by the American scientis D. Stepian. In a communication system with PM, messages are transmitted by the selection of k orthogonal signals out of N possible signals.
References
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7. Slepian D. Permutation modulation. Proc. IEEE, vol. 53, Mar. 1965
Mathematical model of cognitive permutation decoder
À.À. Gladkikh 1, e-mail: a_gladkikh@mail.ru
A.A. Ovinnikov 2, e-mail: ovinnikov.a.a@tor.rsreu.ru
G.M. Tamrazyan 3, e-mail: tamrazz@bk.ru
The Ulyanovsk State Technical University(UlSTU), Russia, Ulyanovsk 1
The Ryazan State Radio Engineering University named after V.F. Utkin (RSREU), Russia, Ryazan2
Federal research and production center joint stock company “Research and production association “Mars” 3
Keywords: error-correction coding, permutation decoding (PD), cognitive adaptation, cognitive map, a cyclic permutation, lexicographical classification, fast matrix conversion, the soft decision symbols, the energy gain from coding (EGC).
Abstract
The objective basis for the intellectualization of many promising information and technological processes is to improve the management procedures for their implementation in real time. The latter circumstance requires the search for ways to reduce the management cycle, the introduction of the principles of cognitive adaptation and artificial intelligence. Wide application in such systems of radio channels for communication of the managing object with object (objects) of management demands unconditional use for it of means of noise-resistant coding for the purpose of protection of commands of management from influence of various destructive factors. It becomes obvious that the strict requirements for the duration of the control cycle do not allow to use fully to achieve this goal a number of provisions of the theory of error-correcting coding, for example, in the form of turbocoding systems and iterative data transformations. Against this background, there is a problem of effective use of short error-correcting codes with the maximum use of redundancy introduced in such a code and rapid identification of control commands. The solution of such a problem is relevant in the processing of data in the system of high-speed coherent networks in their coordination with the capabilities of processors of end devices. The analysis showed that to the greatest extent the solution of these problems corresponds to the method of PD systematic codes in the modification of its mathematical model using the concept of cognitive data processing.
References
1. MacWilliams F. J. Permutation Decoding of Systematic Codes, Bell System Tech. J., 43, 485 – 505 (1964).
2. Peterson W., Weldon E. error-correcting Codes. Per. with English. – ed. Dobrushin, R. L., and Samoylenko, S. I. – M. : Mir. – 1976. – 594 p.
3. Morelos-Zaragoza R. the Art of error-correcting coding. Methods, algorithms, application. Per. with English. – ed. Afanasyeva V. B. – M. : Technosphere. – 2005. – 320 p.
4. Sklyar B. Digital communication. Theoretical basis and practical application. – M. : Williams. – 2003. – 1104 p.
5. Gladkikh A. A. Fundamentals of the theory of soft decoding of redundant codes in the erasing communication channel. – Ulyanovsk : UlSTU, 2010. – 379 p.
6. Gladkikh A. A. Permutation decoding as a tool to improve the energy efficiency of data exchange systems / Elektrosvyaz . – ¹ 8. – 2017, P. 52-56.
7. Gladkikh A. A., al Tamimi T. F. H. the Concept of cognitive data processing in the system of permutation decoding of non-binary redundant code / Elektrosvyaz. – ¹ 9. – 2018, P. 69-74.
Automatic modulation classification of phase shift keyed signals using spectrum analysis structures of the range of even degrees
A.L. Zavadskiy, P.A. Kazak, S.M. Kadantsev, e-mail: kazak-pavel.89@yandex.ru
Interspecies Center of Training and Combat Use of Electronic Warfare Troops, Russia, Tambov
Keywords: phase-shift keyed signal, PSK, fast Fourier transform, power conversion, dispersion, δ-function, harmonics.
Abstract
The article introduces phased-shift keyed signals modulation type recognition algorithm in terms of lack of priory data on signal parameters. The algorithm is based on signal power conversion and received spectrum analysis with presence of pronounced harmonics.
Automatic modulation recognition is an important task on identification of different kinds of signals. In most cases, the process of signal detection and parameter recognition is held in terms of lacking priory data on functioning device capabilities. In such terms automatic signal recognition of radio source allows us to classify: transmitting device type, connection type and connection system in general. In the meantime, there are lots of ways and algorithms of digital signal identification, each appropriate for solving different tasks.
Special attention is paid to works devoted to modern PSK modulation recognition methods. Algorithms highlighted in the works do not count features of shift-keyed phase signals. Proposed algorithm allows to automatically classify signal modulation type with unknown parameters (amplitude, signal spectrum band, instant phase, rate etc…) in terms of receiving signal with PSK modulation type.
Algorithm of PSK signal modulation recognition based on even degrees structure analysis, software module in math modeling space (MATLAB), practical research on noise resilience of proposed algorithm,, in which probability of correct classification is achieved with SNR > 6dB for QPSK and with SNR>7dB with DQPSK and OQPSK, and SNR>16dB for 8PSK and D8PSK signals. BPSK modulation signals are classified correctly in the SNR range >0dB.
References
1. Azzouz E.E. and Nandi A.K. Automatic Modulation Recognition of Communication Signals, Kluwer Academic Publishers, 1996, p. 233.
2. Chunlei Zhang, Hui Wu, Huanyu Ning. A Novel Digital Signal Modulation Mode Recognition Algorithm. School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, China. // Sensors & Transducers, Vol. 178, Issue 9, September 2014, pp. 194 – 198.
3. D. Le Guen, A, Mansour. Automatic Recognition Algorithm for Digital Modulated Signals / Procedings of the IASTED International Conference SIGNAL PROCESSING, PATTERN RECOGNITION & APPLICATIONS June 25-28, 2002, Crete, Greece, pp. 32-37.
4. Erem Erdem. Digital Modulation Recognition / A Thesis Submitted to the Graduate School of Natural and Applied Sciences of Middle East Technical University, Desember 2009. – 161 p.
5. Ivan A. Hashim, Jafar W. Abdul Sadah, Thamir R. Saeed & Jawad K. Ali. Recognition of QAM Signaks with Low SNR Using a Combined Threshold Algorithm. // IETE Journal of Research – January 2015. P.9.
6. Pedzisz M., Mansour A. Automatic modulation recognition of MPSK signals using constellation rotation and its 4th order cumulant // Digital Signal Processing 15 (2005), pp. 295-304.
7. Prakasam P., Madheswaran. Modulation Identification Algorithm for Adaptive Demodulator in Software Defined Radios Using Wavelet Transform.// International Journal of Information and Communication Engineering 5:1, 2009, 74-81
8. Young A.F. Classification of Digital Modulation Types in Multipath Environments, Master’s Thesis, NAVAL POSGRADUATE SCHOOL, June 2008. P. 83.
9. Baskakov S.I., Radiotehnicheskie tsepi I signaly: uchebnik dlya vuzov po spetsial’nosti “Radiotehnika” (Radio technical chains and signals: Manual for Radio technical faculties of Universities) // Fourth edition, M. Vysshaya shkola, 2003 462 p.
10. Harisov V.N., Perov A.I., Boldina V.A Global’naya sputnikovaya radionavigatsionnaya sistema GLONASS (Global sattelite radionavigation system GLONASS) // M. IPRZR 1998 – P. 400
11. Lyons R., Tsifrovaya obrabotka signalov (Signal digital processing) // Seconds edition, translation OOO “Binom-Press”, 2006, 656 p.
12. Loginov A.A., Morozov O.A., Hmelev S.L. Opredelenie tipa modulyatsii fazomanipulirovannyh signalov na osnove stepennyh preobrazovaniy v analize spektra (Phase shift-keyed modulation recognition based on power conversion and spectrum analysis) // Izvestiya vuzov. Radiofizika. Tom LV, ¹10-11, 2012
13. Makarov K.S. Metody raspoznovaniya modulyatsii. (Modulation recognition methods) // Tsifrovaya obrabotka signalov ¹1, 2014. pp. 29-35
14. Nagornyuk O.A., Pavlyuk V.V. Algoritm avtomatichnogo vyavleniya ta klassifikatsii signaliv z tsifrovimy vidami modulyatsii (Digital signal modulation type automatic recognition and classification algorithm) // Visnik ZDTU ¹4 (59) pp.1-10
15. Nevdyaev L.M. Mobil’naya svyaz’ tret’ego pokoleniya (Third generation mobile network) // Seriya izdaniy “Svyaz’I biznes”, M. MCTNI – Mezhdunarodniy centr nauchnoy i tehnicheskoy informatsii, OOO Mobil’nye kommunikatsii, 2000 – P. 208.
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17. Solonina A.I., Ulakovich D.A., Arbuzov S.M., Solovyeva E.B. Osnovy tsifrovoy obrabotki signalov. Kurs lekciy (Signal digital processing basis) // 2 edition – SPb.: BHV-Peterburg, 2005. – P. 768
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21. Stogov A.A. Tereshonok M.V., Chirov D.S., Kuz’min G.V. Raspoznovanie vidov modulyatsii radiosignalov s ispol’zovaniem momentov vysokogo poryadka (Radio signal modulation type recognition using high order moments) // T-Comm: Telekommunikatsiya i transport, ¹ 1, 2012, pp. 56-59
Minimization of influence of the parasitic frequency the modulations, caused the echo signals, in frequency short-range finders with the spectral method of estimation difference frequency
V. M. Davydochkin 1, e-mail: skb@kontakt-1.ru
S. V. Davydochkina 2, e-mail: dav-sv@yandex.ru
V. V. Ezerskiy 3, e-mail: ezerski@yandex.ru
The Open Company enterprise " KONTAKT -1", Russin, Ryazan 1
The institute of FSIN of Russia academy on department of mathematics and information technologies of management , Russia, Ryazan 2
The Ryazan State Radio Engineering University named after V.F. Utkin (RSREU), Russia, Ryazan3
Keywords: the frequency waveguide level gage, measurement error, dispersion of speed, draft on wave guide walls.
Abstract
The waveguide level gage for measurement of level of liquid on the basis of a frequency range finder is considered. Influence of dispersion in a wave guide and uncontrollable increase of rainfall on wave guide walls is investigated. Theoretically and numerical modeling it is shown that these factors lead to unacceptably big error of measurement of distance.
It is noted that dependence of rated differential frequencies on rated time within the range of frequency modulation strongly changes at change of equivalent dielectric permeability, diameter of a wave guide and size of range of reorganization of frequency at frequency modulation. It is offered to estimate the current value of equivalent permeability, by comparison of such dependence with the reference dependence calculated at in advance preset value of reference dielectric permeability. The variation of reference dielectric permeability allows to pick up its such value at which both schedules coincide.
Practical realization of the offered method is possible with use of digital processing of signals. At the same time the initial massif of counting of a signal of differential frequency breaks into a number of podmassiv, in each of which also its comparison with the same number of the reference values received at a preset value of reference dielectric permeability is made calculations of average differential frequency. The variation of value of reference dielectric permeability allows to find its such value at which there is minimum a sum of modules of differences of the received values of rated frequencies.
It is offered limit simplification of this method when all massif of initial counting breaks into two podmassiv and on the average rated frequencies found for them assessment of equivalent dielectric permeability is calculated. For such calculation analytical expression is received. This expression is a basis for adaptation of the waveguide level gage to the changing value of equivalent dielectric permeability. The procedure of adaptation is iterative.
The received value of dielectric permeability is used at final assessment of distance from the level gage to liquid level. For such assessment expressions for the modified integrally discrete transformation of Fourier, considering dispersive properties of a wave guide and size of equivalent permeability are received.
Assessment of sensitivity of the offered method to an error of assessment of frequency and influence of noise is executed.
References
1. Jdankin V.K. Izmerenie urovnia posredstvom napravlennogo electromagnitnogo izluchenia (Measurement of level by means of the directed electromagnetic radiation) // Sovremennie tehnologii avtomatizacii (Modern technologies of automation). 2004, No. 4, pp. 6–14.
2. Davydochkin V.M. Preobrazovanie Fourie v zadache izmerenia rasstoiania chastotnim dalnomerom v prostranstve s dispersiei (Fourier's transformation in a problem of measurement of distance a frequency range finder in space with dispersion) // Cifrovaja obrabotka signalov (Digital signal processing), 2015, no.1, pp. 66 – 70.
3. Spravochnik po volnovodam. Pod redakciei prof. Ja. N. Felda (Reference book on wave guides. Under edition of the prof. Ja. N. Feld. Translation from English). M “Sovetskoe radio” («Soviet radio»), 1952, 432 p.
4. Davydochkin V.M., Davydochkina S.V. Vesovie funkcii dla cifrovogo adapnivnogo garmonicheskogo analiza signalov c mnogomodovim spectrom (Weight functions for the digital adaptive harmonious analysis of signals with a multimode range) // Radiotehnika, 2009. No. 9. pp. 11 – 22.
5. Davydochkin V.M., Davydochkina S.V., Ezerski V.V. Snigenie metodicheskoi i shumovoi pogreinostei v zadache ocenki chastoti otrezka garmonicheskogo signala (Decrease in methodical and noise errors in a problem of assessment of frequency of a piece of a harmonious signal) // Radiotehnika, 2015, no. 11, pp. 66 – 71.
6. Davydochkin V.M., Ezerski V.V. Vlianie pomeh na pogreshnost radiolokacionnih urovnemerov s chastotnoi moduliaciei (Influence of hindrances on an error of radar level gages with frequency modulation) // Uspehi sovremennoj radiojelektroniki, M.: Radiotehnika. 2014, no.10, pp. 30 – 37.
Synthesis of group multi-frequency signals detectors
D.I.Popov, e-mail: adop@mail.ru
The Ryazan State Radio Engineering University named after V.F. Utkin (RSREU), Russia, Ryazan
Keywords: adaptation, detection algorithms, group processing, multifrequency signal, clutter, rejection filter.
Abstract
The problem of synthesizing adaptive detectors of group multi-frequency signals of moving targets against a background of clutter with an a priori uncertainty of the clutter parameters is considered. A statistical description of group multi-frequency signals and clutter is given.
Based on the calculation of the likelihood ratio and the subsequent statistical averaging of the optimal processing algorithm, principles for constructing systems for the adaptive detection of group multi-frequency signals are proposed, and algorithms for group and sliding signal processing with clutter are presented.
Due to the difference in Doppler phase shifts in the processed groups, the signal from a moving target falls into different Doppler channels of each of the coherent accumulators, which excludes the combination of output values of the accumulators. Overcoming the a priori uncertainty of the Doppler phase shifts of the signal is achieved by averaging the processing algorithm according to these parameters.
The resulting algorithm determines the structure of the detection system, invariant to the Doppler phase shifts of the groups of the reflected multi-frequency signal. In this case, the inter-period processing of each group of samples is combined, i.e., the group of samples and the subsequent incoherent summation of the results of matrix filtering fall into adaptive coherent matrix filtering. Processing is completed by summing the results of separate processing of groups of samples.
A block diagram of the system for adaptive detection of a group multifrequency signal against a background of clutter is proposed. In the system, the clutter rejection is performed separately for each group of coherent pulses with a known arrival time corresponding to the tuning of the carrier frequency of the transmitter. Carrier frequency tuning in combination with adaptive group processing of incoming samples allows to significantly increase the detection efficiency of group multifrequency signals at high detection probabilities.
References
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5. Popov D.I. Adaptive notch filter with complex weight // Vestnik Kontserna PVO «Almaz – Antej». 2015. no 2 (14). pp. 21-26. (in Russian).
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8. Popov D.I. Adaptivnije regektornjie filtrij kaskadnogo tipa // Cifrovaya obrabotka signalov. 2016. no. 2. pp. 53-56. (in Russian).
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11. Gul'shin V. A. Mnogochastotnye signaly i metody ih formirovanija i obrabotki. Vestnik Koncerna PVO «Almaz – Antej». 2013, no. 1 (9), pp. 34–40 (in Russian).
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19. Popov D.I. Measurements of Characteristics of Clutter // Measurement Techniques. May 2017. Vol. 60. No 2. – P. 190-195.
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Algorithm of the terrain contour matching using a small radar with a high resolution synthetic aperture antenna
K.S. Ivannikov 1, e-mail: ivannikov_ks@radar-mms.com
I.F. Kupryashkin 2, e-mail: ifk_78@mail.ru
L.B. Ryazantsev 2, e-mail: kernel386@mail.ru
JSC "Radar mms", Saint Petersburg 1
Air Force Academy, Russia, Voronezh 2
Keywords: FMCW SAR, radar image, terrain contour matching.
Abstract
Today one of the most effective unmanned aerial vehicles (UAVs) countermeasures is jamming the receivers of satellite navigation signals. Using jamming transmitters, which are rather simple in design and application, it will be able to essentially avoid a chance of autonomous UAV flights within the specified areas.
Among the existing UAV autonomous navigation problem solutions the particular interest are those that are based on the comparison of the altitude profile estimating with using the radio altimeter with a digital terrain map wrote down in the UAV onboard memory. First of all, the interest is due to the possibility of obtaining high-precision estimates of the UAV's own coordinates in a wide range of flight heights, regardless of the natural surface illumination state and weather conditions at the correction sector.
As a rule the UAVs’ radio altimeters antennas are characterized by small sizes and wide pattern as a consequence because of their weight and size restrictions. This results in terrain contour matching (with the sufficient sector length to compare it with a digital map of the area) is time consuming – tens of seconds or more.
At the same time, broadband signal using combined with the methods of synthetic aperture can quite improve the resolution of radio altimeters and use them as terrain contour matching equipment with detail, providing a significant increase in the accuracy and efficiency of determining the UAV's own coordinates by comparing the measured altitude estimates with a digital map of the terrain.
The article reveals the algorithm of detail terrain contour matching for airborne broadband radio altimeters. It shows the results of experimental test of the algorithm with data obtained using a small-sized C-band radar. Also it was found, that in addition to the terrain contour estimation, the problem of classification the probed surface can be solved. It makes it possible to determine the UAV’s own coordinates using data not only the surface heights at the correction sector, but also semantic information included with the structure of digital terrain maps.
References
1. Naumov A.I., Kichigin E.K., Safonov I.A., Moh A. M. Bortovoj kompleks vysokotochnoj navigacii s korrelyacionno-ekstremal'noj navigacionnoj sistemoj i cifrovoj kartoj rel'efa mestnosti // Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta, 2019. Tom 9, vypusk 6-1, S. 51-55.
2. Likhachev V.P., Ryazantsev L.B. Assessment of Range and Radial Velocity of Objects of a Broadband Radar Station Under Conditions of Range Cell Migration // Measurement Techniques. February 2018, Volume 60, Issue 11, pp 1158–1162.
3. Ryazancev L.B., Kupryashkin I.F., Lihachev V.P., Gnezdilov M.V. Algoritm formirovaniya radiolokacionnyh izobrazhenij s submetrovym razresheniem v malogabaritnyh RLS s sintezirovannoj aperturoj // Cifrovaya obrabotka signalov. 2018. ¹2. S. 53-58.
4. Aviacionnye sistemy radiovideniya. Monografiya / Pod red. G.S. Kondratenkova. M.: «Radiotekhnika», 2015. 648 s.
5. Ryazancev L.B., Kupryashkin I.F., Lihachev V.P. Metodika obosnovaniya trebovanij k analogo-cifrovomu preobrazovaniyu v RLS s sintezirovannoj aperturoj nepreryvnogo izlucheniya // Cifrovaya obrabotka signalov. 2017. ¹2. S. 49-52.
6. Phalippou L., Demeestere F. Optimal re-tracking of SAR altimeter echoes over open ocean: Theory versus results for SIRAL2 data // https://www.aviso.altimetry.fr/fileadmin/documents/OSTST/2011/oral/01_Wednesday/Splinter%201%20IP/02%20OSTST-2011-Phalippou-Demeestere.pdf.
7. Constant False Alarm Rate (CFAR) Detection // https://www.mathworks.com/help/phased/examples/constant-false-alarm-rate-cfar-detection.html.
On accuracy of trigonometric interpolation
S.V. Porshnev, Ural Federal University, Russia, Yekaterinburg, e-mail: sergey_porshnev@mail.ru
D.V. Kusaykin, Ural Technical Institute of Communication and Computer Science, Russia, Yekaterinburg, e-mail: kusaykin@mail.ru
Keywords: trigonometric interpolation, signal reconstruction, interpolation error, trigonometric polynomial, Fourier series, mean square error reconstruction.
Abstract
Today trigonometric interpolation based on Fourier transform is extensively used in digital signal processing for numerous tasks, from discrete-time signal reconstruction to oversampling. At the same time, the literature review shows that the vast majority of digital signal processing books processing books doesn’t report the facts that the theory of trigonometric interpolation is built for periodic functions explicitly and that these functions must satisfy the Dirichlet condition. Only in this case the interpolating trigonometric polynomial will converge to the interpolated piecewise monotone signal in a finite time interval. If these conditions are not satisfied, formally the coeffi-cients and values of the interpolating polynomial can also be calculated. However, there will be an additional component of the trigonometric interpolation error, which needs to be considered in prac-tical application. Note that real discrete-time signals do not satisfy this condition in most cases.
The analysis of trigonometric interpolation errors in case when Dirichlet conditions are not satisfied was produced. Formulas for estimating of the mean square error of trigonometric interpo-lation are obtained. The mean square error of trigonometric interpolation for finite-lengrth periodic discrete-time signal is calculated. The results are obtained for case when interpolation time interval contains non-integer number of the signal periods. It is proved that, contrary to popular opinion, tri-gonometric interpolation error is not equal to zero even if the number of samples tends to infinity, but it tends to some value which depends on the parameter, one that is a product of signal duration and frequency of the recovered signal. Analytical expressions for estimation of the lower bound on mean square error for periodic finite-length discrete-time signal in case of different signal duration and signal frequency are obtained.
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The comparison of multispectral image fusion quality metrics and fuzzy image quality improvement algorithms for video surveillance systems
Kirillov S.N., e-mail: kirillov.lab@mail.ru
Pokrovskij P.S., e-mail: paulps@list.ruu
Skonnikov P.N., e-mail: skonnikovpn@yandex.ru
Baukov A.A. ., e-mail: baukov.andrej@yandex.ru
The Ryazan State Radio Engineering University named after V.F. Utkin (RSREU), Russia, Ryazan
Keywords: enhanced vision, multispectral images, image quality metrics, CLAHE.
Abstract
In complex weather conditions, as well as at night, multispectral improved vision systems are used. During digital signal processing in such systems, two tasks are solved: improving the image quality at individual channels and multispectral image fusion.
The solution of the first problem is aimed at eliminating the effects of static interference (such as fog, smoke, smog, etc.), leading to a decrease in the range of visibility in video images and wor-sening the distinguishability of objects. In such conditions, to improve the quality of video images, it is advisable to increase the contrast. A modified CLAHE algorithm is proposed, the use of which leads to an improvement in processed images quality indexes in comparison with known algorithms: the quality of edges increases by 2 times, the standard error is reduced by 12 ... 16%, the improvement of the SSIM, PSNR, and Fast-FMI indices is 16 ... 18%, 5 ... 7% and 6 ... 18%, re-spectively, in comparison with known methods.
During fusion, images coming from video cameras of different ranges are combined into a single frame containing information about all objects that are distinguishable in the image of at least one channel. This allows video surveillance at any time of the day and further improve visibility under the influence of interfering factors. When choosing the appropriate algorithm, it is advisable to use an objective quality index of multispectral image fusion, the values of which are most iden-tical to the results of a subjective quality assessment. For comparison with the results of subjective assessments, the most widely used objective assessments of multispectral image fusion quality were selected. From the analysis of the calculated values of accuracy, monotony and inconsistency of the considered quality indicators, it follows that when choosing the algorithm for combining multispec-tral images for video surveillance tasks, it is advisable to use a spatial feature and a modified index of structural similarity. For these quality indicators, the accuracy value is not more than 0.68, and monotonicity is not more than 0.5. Moreover, the level of inconsistency with the subjective assess-ment does not exceed 6%.
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