Course detail

Advanced Methods of Signal Processing

FIT-MZSAcad. year: 2017/2018

Formalised inverse filtering and restoration of signals. Wiener filter, constrained deconvolution and further higher restoration approaches. Kalman filtering, scalar and vector formulation, system modelling based on Kalman filtering. Adaptive filtering and identification, algorithms of adaptive filters, typical applications of adaptive filtering. Multirate systems. Non-linear filtering: polynomial filters, rank filters, homomorphic filtering and deconvolution, non-linear matched filters. Signal processing by neural networks. Time-frequency analysis, wavelet transform and its applications. Concept of multidimensional signal and spectrum, 2D and 3D Fourier transform, discrete unitary multidimensional transforms. Applications in formalised image processing: restoration approaches, tomographic reconstruction from projections, 3D reconstruction from stereo data.

Supervisor

prof. Ing. Jiří Jan, CSc.

Department

Department of Biomedical Engineering (UBMI)

Learning outcomes of the course unit

Understanding of advanced methods of signal processing and analysis, ability to utilise and modify them, and to design and verify a realisation aimed at a particular practical task.

Prerequisites

The course knowledge on the Bachelor´s degree level is requested, namely on digital signal processing.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

  • Jan, J.: Číslicová filtrace, analýza a restaurace signálů, Nakl. VUT Brno 1997, ISBN 80-214-0816-2, 2. vydání, 2001
  • Jan, J.: Digital Signal Filtering, Analysis and Restoration, IEE London, United Kingdom 2000, 407+14 pp., ISBN 0 85296 760 8
  • Gonzales, R.C. , Wintz, P.: Digital Image Processing, 2nd ed., Addison-Wesley Publ. Comp., 1987

  • Madisetti, V.K., Williams, D.B. (ed.): The Digital Signal Processing Handbook, CRC & IEEE Press, USA, 1998, ISBN 0-8493-8572-5
  • Vích, R., Smékal, Z.: Číslicové filtry, Academia Praha 2000, ISBN 80-200-0761-X
  • Mulgrew, B., Grant, P., Thompson, J.: Digital Signal Processing - Concepts & Applications, MacMillan Press Ltd., UK, 1999, ISBN 0-333-74531-0
  • Banks, S., Signal Processing, Image Processing and Pattern Recognition, Prentice Hall Int., UK, Ltd., 1990
  • Jain, A.K.: Fundamentals of Digital Image Processing, Prentice Hall Int. Edit., 1989
  • Jan, J.: Číslicová filtrace, analýza a restaurace signálů, Nakl. VUT Brno 1997, ISBN 80-214-0816-2
  • Gonzales, R.C., Wintz, P.: Digital Image Processing, 2nd ed., Addison-Wesley Publ. Comp., 1987
  • Pratt, W.K.: Digital Image Processing, 2nd ed., J. Wiley & Sons, 1991
  • Rosenfeld, A., Kak, A.C.: Digital Picture Processing, 2nd. edit., Academic Press, 1982
  • Schalkoff, R.J.: Digital Image Processing and Computer Vision, J. Wiley & Sons, 1989

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Obtaining at least 15 points from the computer-labs.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

    Syllabus of lectures:
    1. Formalised inverse filtering and restoration of signals. Wiener filter: classical and discrete formulation
    2. Constrained deconvolution, deconvolution with impulse response optimisation, maximum posterior-probability method
    3. Kalman filtering, scalar and vector formulation, system modelling based on Kalman filtering
    4. Concept of adaptive filtering and identification, algorithms of adaptive filtering
    5. Typical applications of adaptive filtering: system identification and modelling, linear adaptive prediction, adaptive noise and interference suppression
    6. Multirate systems of digital signal processing, multirate filter banks
    7. Non-linear filtering: polynomial filters, rank filters, homomorphic filtering and deconvolution, non-linear matched filters
    8. Signal processing by neural networks: learning neuronal filters and classifiers, restoration by feed-back neuronal networks
    9. Time-frequency analysis, wavelet transform and its applications in processing and compression of signals
    10. Concept of multidimensional signal and spectrum, 2D and 3D Fourier transform. Discrete unitary 2D transforms: cosine, Hadamard and Walsh, Haar and 2D wavelet tr.
    11. Applications of signal-theory-based approaches to formalised image processing: restitution and restoration approaches, formalised image segmentation
    12. Tomographic methods of image reconstruction from 1D projections
    13. Motion analysis and 3D reconstruction from stereo data

    Syllabus of computer exercises:
    1. Simulation of discrete Wiener filter and evaluation of efficiency in stationary case
    2. Simulation of a 3rd order Kalman filter and comparison with the above Wiener filter in stationary environment
    3. Simulation of adaptive filters of RLS and LMS type as applied to a system modelling. Comparison of both results in stationary and slowly varying environment
    4. Wavelet transform: application to analysis and denoising of a signal, verification of compression ability
    5. Restoration of blurred and noisy image by pseudoinversion and by 2D classical Wiener filter - comparison of results
    6. 2D image reconstruction from tomographic data (1D projections) via frequency domain - evaluation of artefacts
    7. Learning 2D neuronal filter: applied for texture analysis. Comparison with feature-oriented classification

Aims

Becoming familiar with advanced methods of digital signal processing and their application in practice. Design and testing of systems for advanced signal processing, aiming at optimum and adaptive noise reduction, identification and modelling of systems, reconstruction and restoration, analysis and classification of signals and images.

Specification of controlled education, way of implementation and compensation for absences

Active participation in the computer-lab tutorials is checked, the minimum participation is 4 out of 7 tutorials, can not be substituted.

Classification of course in study plans

  • Programme IT-MGR-2 Master's

    branch MBI , any year of study, summer semester, 6 credits, elective
    branch MPV , any year of study, summer semester, 6 credits, elective
    branch MGM , any year of study, summer semester, 6 credits, elective
    branch MSK , any year of study, summer semester, 6 credits, elective
    branch MIS , any year of study, summer semester, 6 credits, elective
    branch MBS , any year of study, summer semester, 6 credits, elective
    branch MIN , any year of study, summer semester, 6 credits, elective
    branch MMM , any year of study, summer semester, 6 credits, elective

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. Ing. Jiří Jan, CSc.

Syllabus


  1. Formalised inverse filtering and restoration of signals. Wiener filter: classical and discrete formulation
  2. Constrained deconvolution, deconvolution with impulse response optimisation, maximum posterior-probability method
  3. Kalman filtering, scalar and vector formulation, system modelling based on Kalman filtering
  4. Concept of adaptive filtering and identification, algorithms of adaptive filtering
  5. Typical applications of adaptive filtering: system identification and modelling, linear adaptive prediction, adaptive noise and interference suppression
  6. Multirate systems of digital signal processing, multirate filter banks
  7. Non-linear filtering: polynomial filters, rank filters, homomorphic filtering and deconvolution, non-linear matched filters
  8. Signal processing by neural networks: learning neuronal filters and classifiers, restoration by feed-back neuronal networks
  9. Time-frequency analysis, wavelet transform and its applications in processing and compression of signals
  10. Concept of multidimensional signal and spectrum, 2D and 3D Fourier transform. Discrete unitary 2D transforms: cosine, Hadamard and Walsh, Haar and 2D wavelet tr.
  11. Applications of signal-theory-based approaches to formalised image processing: restitution and restoration approaches, formalised image segmentation
  12. Tomographic methods of image reconstruction from 1D projections
  13. Motion analysis and 3D reconstruction from stereo data

Exercise in computer lab

26 hours, optionally

Teacher / Lecturer

prof. Ing. Jiří Jan, CSc.

Syllabus


  1. Simulation of discrete Wiener filter and evaluation of efficiency in stationary case
  2. Simulation of a 3rd order Kalman filter and comparison with the above Wiener filter in stationary environment
  3. Simulation of adaptive filters of RLS and LMS type as applied to a system modelling. Comparison of both results in stationary and slowly varying environment
  4. Wavelet transform: application to analysis and denoising of a signal, verification of compression ability
  5. Restoration of blurred and noisy image by pseudoinversion and by 2D classical Wiener filter - comparison of results
  6. 2D image reconstruction from tomographic data (1D projections) via frequency domain - evaluation of artefacts
  7. Learning 2D neuronal filter: applied for texture analysis. Comparison with feature-oriented classification