Applied mathematics


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Applied mathematics

  1. 1. Faculty of applied mathematicsand telecommunications (FAMT)Three Departments:Higher mathematics (HM)Applied mathematics and Informatics (AMI)Radioelectronic equipment (REE)Goal object: Search for jointscientific research partners
  2. 2. Was established in 1963The basis of the team are Vyatka State Universityengineering graduates in the field ofradiotechnics, computers, automatics,telecommunicationsThe academic staff of the department include:4 Doctors of Sciences10 PhD’s2 Postdoctoral students16 Graduate studentsDepartment of radioelectronic equipment (REE)
  3. 3. Department of REE implemented:Four specialities:Communication networks and switching systems;Secure communications;Communication tools with mobile objects;Information security oftelecommunication systems.Two profiles of Bachelors:Information security;Infocommunication technologiesand communication systems.Profile of Masters:Infocommunication technologiesand communication systems.Educational activities:
  4. 4. Three post-graduate academic specialities:Systems, networks and telecommunication equipment;Radiotechnics, including systemsand TV devices;Methods and systems of information security.Information security.Two doctoral academic specialities:System analysis, managementand information processing;Methods and systems of information security.Information security.Doctoral and post-graduate studies
  5. 5. “Application of the theory of nominal Markov’s processesin the problems of digital image processing”Head of the scientific school, Honorary Figure of RussianHigher Education, Head of the REE department,Doctor of Engineering, Proff. Petrov Evgeniy PetrovichScientific schoolResource baseResearch laboratory“Simulation and design of digital signalsand images processing devices”,equipped with modern graphic stations andlicensed software – MatLab и LabView
  6. 6. Research teamTrubin I.S., Dr., Prof. REE dept.Medvedeva E.V., Dr., Assoc. Prof. REE dept.Kharina N.L., PhD, Assoc. Prof. REE dept.Metelev A.P., PhD, Assis. Prof. REE dept.Kolupaev A.V., PhD, Assis. Prof. REE dept.Kurbatova Е.Е., Assis. Prof. REE dept.Kononova V.Yu., Assis. Prof. REE dept.Graduate and Master’s students
  7. 7. Dissertation themes in the last 5 yearsDoctoral:Trubin I.S. Non-linear filtering of digital halftoneimages and video sequences (2008)Medvedevf E.V. Methods for the synthesis of multi-dimensionalmodels and digital image processing algorithms(2012)Candidates:Kharina N.L. The method of simulation of digital halftoneimages based on discrete-valued Markov’s processes(2007)Metelyov A.P. Development and analysis of algorithmsmultidimensional nonlinear adaptive image filtering (2012)Kolupayev A.V., Development and analysis of algorithmsnonlinear filtering of digital halftone images and videoSequences (2009)
  8. 8. Main partners1. Ryazan State Radio Engineering University2. Private company «Znak», Kirov3. FSUE «Research Institute of computer equipment», Kirov4. Ltd «Radiostructure concern «Vega», Moscow5. Moscow State Technical University of Radio Engineeringand Automation6. Ulyanovsk State Technical University7. Vladimir State University8. Nizhny Novgorod State University9. Povolzhskiy State University of Telecommunicationsand Informatics, Samara
  9. 9. ContactsVyatka State University,Radioelectronic equipment Dept.610000, Kirov, Moskovskaya str., 29, VyatSU(8332) 32-26-29e-mail:
  10. 10. Project “Static compression algorithmsand dynamic images”The theoretical basisMulti-dimensional mathematical models of images.The algorithms are based on splitting the digital halftoneimages on bit binary images.The movement of objects is estimated by the senior categoryof digitized image.Achieved results1. The developed compression algorithm exceeds JPEG methodby MSD criteria 1,5…2 times.2. The developed method for estimating motion vectors allows toimprove video compression by 40%.3. The average compression of video is 10 ... 20.
  11. 11. Main publications1. Medvedeva E.V., Petrov E.P. Development of the algorithmof image compression based on statistical relationshipsbetween the picture elements // Information andcommunication technology -2008.- № 1. - p. 94-99.2. Medvedeva E.V., Timofeev B.О. Video compression methodbased on two-dimensional Markov’s chains// T-Comm.Telecommunications and transport, 2011. - № 1.- p. 24-28.3. Medvedeva E.V. Methods for the synthesis ofmulti-dimensional models and digital image processingalgorithms// Dissertation for the degree of Doctortechnical Sciences – 2012. - 265 p.
  12. 12. Project “Algorithms for nonlinearimage filtering”The essence of the project:The developed algorithms are aimed at improvingreception quality images corrupted by noise due tothe use of statistical redundancy betweenimage elements within and between framesAchieved results:1. Efficient in terms of computing resources structures andalgorithms for nonlinear filtering device images that preservethe efficiency for the signal/noise ratio up to 12dB.2. The method of multidimensional nonlinear adaptive filtering,which allows to calculate the missing statistics used to improvenoise immunity.
  13. 13. An example of video sequence filteringа) original image b) noisy image ( 212вх дБρ = − )c) filtered 1st shot d) 25th shot
  14. 14. Main Publications1. Petrov E.P., Medvedeva E.V. Nonlinear filtering of statisticallyconnected video sequences based on hidden Markov’s chains// Journal of Communications Technology and Electronics,vol. 55, No. 3, 2010. - pp. 307–315.2. Petrov E.P., Medvedeva E.V., Prozorov D.E., Metelyov A.P.Synthesis of collaborative filtering algorithms of discreteand continuous parameters of multi-dimensional correlatedpulsed signals // Modern electronics successes, № 12, 2012. - p. 5-20.3. Petrov E.P., Kharina N.L., Kharyushin V.F. Mathematicalmodels and algorithms for filtering digital halftoneimages on the basis of complex Markov’s chains // DigitalProcessing of signals», № 3, 2012.- p. 52-57.
  15. 15. Project “Algorithms of image segmentation”Description of the project:1. Isolation circuits based on calculating of the amount ofinformation in the image element with respect to twoneighboring elements.2. Isolation of textural regions based on the calculation ofthe average estimate of the transition probability within thesliding window.Achieved results:1. The gain in speed edge detection of objectsinterest as compared to the known 1,5 ... 6 times.2. Allow to identify regions with different texture statisticalcharacteristics of the images with high accuracy and smallComputing resources.
  16. 16. An example of MRT image segmentationа) original DHI b) contour image c) noisy image ( 2вхρ =-3дБ)d) filtered DHI e) original DHI segmentation f) noisy DHI segmentation
  17. 17. Main Publications1. Medvedeva E.V., Kurbatova Е.Е. A two-stage imagepreprocessing algorithm // Pattern Recognition andImage Analysis, vol. 21, No. 2, 2011. - PP. 297–301.2. Kurbatova Е.Е., Medvedeva Е.V. Method of textureimage segmentation based on Markov’s randomfields // Digital processing of signals, № 3,2012. - p. 76-80.3. Medvedeva Е.V. Kurbatova Е.Е. Segmentation ofdigital halftone images// Certificate № 2011614909– registered in the Registry of the computer programs,FIIP, Moscow, 22.06.2011.
  18. 18. Possible applications of algorithms and devicescompression, filtering and image segmentation1. Compression of video streams in digital TV mobile videotelephony, Internet, video conferencing, multimediacommunication systems, aerial photographs, video surveillanceand other transmitting images systems.2. Improving the quality of images transmitted the channelswith the noise in the image transmission system for differentpurposes.3. Segmentation algorithms can be used in monitoring systems,closed circuit television, video surveillance, medical and otherSystems to highlight objects of interest in the image of minimalcomputer resources and with high precision.
  19. 19. Scientific direction “Self-organizingwireless communication networks”Research team:Prozorov D. Е. – scientific supervisorDr., Prof. REE dept.Chastikov А. V. - Dr., Dean of the FAMTTrubin I. S. - Dr., Prof. REE dept.Lesnikov V. А.- PhD., Assoc. Prof. REE dept.Krayev N. А. - PhD, Assoc. Prof. REE deptМетелев А. П. - PhD, Assis. Prof. REE dept.Naumovich Т. V. - Assis. Prof. REE dept.Graduate and Master’s studentsMaterial base:Computing Cluster Platform 3000 BL460c; performance20 ТFlops, memory 50 terabyte, Xeon 53xx 2.33GHz, OperatingSystem - Linux, Interconnect - Family Infiniband DDR.
  20. 20. Todays decision of the organization of communicationin areas where there are no cellular communications,is the deployment of Self-Organizing Ad Hoc Networks.To solve this problem are encouraged to develophierarchical Ad Hoc network, effective routing algorithm anda set of protocols for its functioning.Performance measures Ad Hoc network is expected to improvethrough the use of cognitive radio technology. One of theUrgent tasks cognitive radio is spectrum analysis of radiofrequency bands.Problem description
  21. 21. Achieved results1. Patent research were conducted2. Criteria of evaluation of routing mobile algorithms Ad-Hoc Networkswere developed3. Architecture of the network protocol and algorithm of hierarchicalrouting were developed4. Algorithms for clustering network nodes and interacluster andgeographic routing were developed5. Experimental studies of software routing protocols models wereconducted6. Systematic analysis of the detection algorithms of employmentSpectrum section were performed7. The structure of the spectral perception was developed8. Model specification of spectral perception was developed9. Two algorithms of spectral perception were simulated
  22. 22. Main Publications1. Romanov S.ВV, Zholobov А.N., Prozorov D.Е. Simulators ofwireless MANET-networks // Info-communication technologies,2012. №3. - p. 28-33.2. Romanov S.V. Prozorov D.Е., Trubin I.S. The analysis of thehierarchical routing protocol of MANET-networks // Perspectivesciences, 2012. - №4. - p. 86-89.3. Prozorov D.Е., Metelyov А.P., Chistyakov А.V., Romanov S.V.Protocols of self-organizing mobile networks geo routing // T-Comm,2012. №5. - p.16-19.4. Zholobov А.N., Lesnikov А.V. , Romanov S.V. Principles of clustersin ad-hoc networks formation // Scientific Review,2012. - №4. - p. 264-273.5. Lesnikov V.А., Romanov S.V., Chastikov А.V., Dubovtsev D.V.Protocol stack of cognitive Ad-Hoc networks // Scientific Review,2013 (accepted for publication).
  23. 23. Possible fields of applicationApps:in law enforcement agencies, in emergencies, at public events,in the absence of cellular communication.The practical implementation is possible in the form of:1. Cross-platform application that implements thecommunications protocol of self-organizing distributed mobilecommunication network.2. Scale-model of the spectral components of the subsystemof cognitive perceptions of self-organizing wireless network.
  24. 24. Contacts6100000, Kirov, Moskovskaya, 29Radioelectronic equipment Dept.(8332) 35-72-59Prozorov E. Dmitriye-mail: V. Аlexandere-mail: alchast@mail.ruLesnikov A. Vladislave-mail:
  25. 25. Scientific direction "Synthesis, Analysis and Design ofrecursive digital filters with finite capacity"Research Team:Chastikov А.V. – Dr., Dean of the FAMTLesnikov V.А. – PhD, Assoc. Prof. REE dept.Naumovich Т.V. – Assis. Prof. REE dept.Project description:In the development of devices DSP packages(MatLab, etc.) algorithms for recursive digital filters withcritical features are working insufficiently. To overcomethe lack of a theory of designing digital filters based onconsideration of the number-theoretic and algebraicaspects of functional and structural synthesis ofrecursive digital filters.
  26. 26. Recursive digital filters could significantly reduce the needFor computational resources compared with non-recursive.Problem of synthesis and design of non-recursive digitalfilters are well developed and implemented in the design ofDSP devices. Design of recursive digital filters with finitecapacity is associated with considerable difficulties,especially when the characteristics of designed digital filtersimposed "hard" requirements for bandwidth, frequency, etc.The reason - a poorly understood nature of recursive digitalfilters. Therefore, the study and consideration of theoreticaland numerical aspects of the synthesis of functional andalgebraic aspects of the structural synthesis of digital filtersis important. The project aims to develop the algorithms ofsynthesis, analysis and design of recursive digital filters withfinite capacity of satisfying the specified performancerequirements, complexity and accuracy.Annotation
  27. 27. Capacity:RFFR grant 10-07-00528-а «Number-theoretic and algebraicaspects of the structural synthesis of linear digital signalprocessing systems», 2010-12.An application for a grant 13-01-00974 «The solution of thefundamental problems of synthesis, analysis and automateddesign of recursive digital filters with finite precision»,2013-15.Achieved results:1. A new paradigm, based on the separation and mutualisolation of functional and structural stages of the synthesisof recursive digital filters.2. An algebraic-numerical nature of the problem for assuringstated accuracy of the characteristics was educed.3. The technique of generating structures of digital filterswith the ultimate word length was developed.
  28. 28. Achieved results1. A new paradigm, based on the separation and mutualisolation of functional and structural stages of the synthesisof recursive digital filters was offered.2. An algebraic-numerical nature of the problem to ensurethe specified accuracy was spotted.3. The technique of generating structures of digital filters withfinite word length was developed.Possible fields of applicationApplication software that implements the algorithmsdeveloped:- system design of recursive digital filters- toolbox for Matlab system- toolbox for NI LabView system- toolbox for development system PLIS of Xilinx, Alteracorporations.
  29. 29. Main publications1. Lesnikov V.A., Naumovich T.V., Chastikov A.V.,Armishev S.V. A new paradigm in design of IIR digitalfilters – Proceedings of IEEE East-West Design & TestSymposium (EWDTS’09), Moscow, 2009. - PP. 115-118.2. Lesnikov V.A., Naumovich T.V., Chastikov A.V.Implementation of New Paradigm in Design of IIR DigitalFilters //Proceedings of IEEE East-West Design & TestSymposium (EWDTS-2010). - St- Petersburg, 2010.- PP. 156-159.3. Lesnikov V. А., Naumovich Т.V., Reshetnikov S.М.,Chastikov А.V. Relationship-theoretic nature of the polesof the topological structure of the matrix and the recursivedigital filter // Perspectives of Science, 2011. - №11 (26). –p.112-115.
  30. 30. The result of the digital filter blockdiagram generationz-1231−z41341c β= 1231c β=1121cβ==1k,2xk,3xk,4xk,1xk,2yk,3yk,4yk,1y32 11c p=2143pc==d2d2c11154c α= 1253c α=5212c == α5111c == ε5k,5x k,5y21142bgc===N4z2p2d2p3d2N3z2p1d2p3d2
  31. 31. Digital filters poles distribution-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 2=-2.5b2=-2 b2=-1b 2=0b2=1b2 =20,25 0,5 0,75 10,250,50,751Re zImz-1 -0.75 -0.5 -0.25 0.25 0.5 0.75 zIm z
  32. 32. 3-rd order recursive digital filter body stability-3-2-1012-3-2-1012-1-0,5 00,5 1-1-0,500,51
  33. 33. Algebraic aspects of the structural synthesisof recursive digital filtersz-1z-1( )12T z−( )10T z−=z-1( )13T z−0[ ]( )1 10T z−( )11T z−c41234c311 c21c32c435c42c54c51c53c526c65c64c63c62c61
  34. 34. Synthesis of recursive digital filter withoutmultiplying blocks+ z-15 1+4z-1+2+3xk+yk60.Передача разрядов отсчетов сосдвигом на два разряда в сторонумладших разрядов0.25П е р е д а ч а и н в е р т и р о в а н н ы хразрядов отсчета со сдвигом на дваразряда в сторону младших разрядов
  35. 35. Applied mathematics andInformatics DepartmentThe department was established in 2002.The basis of the group are graduates from leadinguniversities in the country:St.Petersburg, Novosibirsk, Perm, Nizhny Novgorod
  36. 36. Educational activitiesTwo Bachelor directions– 010400 «Applied Mathematics and Informatics»– 036000 «Intelligent systems in the humanitarian field»One Magistrates direction– 010400 «Applied Mathematics and Informatics»Two postgraduate directions– 05.13.01 «System analysis, management and informationprocessing»– 05.13.18 «Mathematical modeling, numerical methodsand software»
  37. 37. Scientific direction "Mathematical Modeling"Research Team:Inomistov V.Yu., Head AMI dept.Pushkaryov I.А., Assoc. Prof. AMI dept.Chuprakov P.G., Assoc. Prof. AMI dept.Belits А.B., lecturer AMI dept.Byzov V.А., graduate student AMI dept.Material baseResearch laboratory "Mathematical Modeling",equipped with modern graphic stations andsoftware licenses - MatLab
  38. 38. Project “Mathematical models ofnano-objects interaction”Capacity:- Analytical Review-monograph “Mathematical Methodsand Models in nanobiotechnology” (2008)- FSP “Development of intelligent nanolevel objects controlsystem” (2012-13)- application for programs registration- articles publication in leading scientific journals of RussiaExpected results:1. High-precision, low requirements for compute-intensivehybrid model of object interaction nanolevel combiningtechniques of molecular dynamics and discrete algebraicStructures2. Software that implements the model
  39. 39. Possible applications1. In theory - a new model of the interactionof nano-objects2. In medicine - in nanorobots modeling3. In technique - modeling the interaction ofnano-objects in nanotechnology4. In the educational process – studentsresearch work
  40. 40. ContactsVyatka State University,Applied Mathematics and Informatics Department610000, Kirov, Moskovskaya, 29, VyatSU(8332) 35-81-28e-mail: