Lecture Notes

Here you will find the lecture notes, and references to additional material to study.
Most of these notes are a summary of the points discussed in the class.
So they are not meant to be a substitute for the lectures themselves, or the textbook.

SUGGESTIONS:
(1) print the lecture notes each week,
(2) bring them with you at each lecture, and
(3) complete them by adding your own notes!



  • WEEK 1 - INTRODUCTION

    PDF


    • + Textbook (3rd Ed. 2008) chapters 1.1, 1.2, 1.4, 2.4 (except 2.4.4), 2.6.1, 2.6.2, 2.6.3

  • WEEK 1 - IMAGE ENHANCEMENT I: Transform Functions, and Histogram Equalisation

    PDF


    • + One of the Exams in 2008/2009: 1(a), 1(b)
    + Problems A3a, A3b, A3c
    + Studio Exercises 1 (from Introduction), 1
    + Textbook (3rd Ed. 2008) chapters 3.1, 3.2, 3.3 (except 3.3.4)
    + Textbook (3rd Ed. 2008) figures 3.5, 3.8, 3.9, 3.10, 3.16, 3.20, 3.21

  • WEEK 1 - IMAGE ENHANCEMENT II: Image Smoothing and Sharpening

    PDF


    • + Overheads: what do the different types of correlation mean ?
    + Problems A4a, A4d
    + Studio Exercise 1, followed by IMPORTANT discussion! Summary
    + Studio Exercise 4
    + Textbook (3rd Ed. 2008) chapters 3.4, 3.5, 3.6
    + Textbook (3rd Ed. 2008) figure 3.34

  • WEEK 1 - IMAGE ENHANCEMENT III: Edge Detection and Noise Reduction

    PDF


    • + Problems A4b, A4c
    + Studio Exercise 2
    + Studio Exercise 3, followed by IMPORTANT discussion! Summary
    + Textbook (3rd Ed. 2008) chapters 3.6, 5.3.2, 10.2.5
    + Textbook (3rd Ed. 2008) figures 3.35, 10.16, 10.18, 10.20

  • WEEK 2 - Do it yourself: CONTINUOUS 2D FOURIER TRANSFORM

    Textbook (3rd Ed. 2008) chapters 4.1, 4.2, 4.5.2

  • WEEK 2 - DISCRETE 2D FOURIER TRANSFORM

    PDF (credits: Magnus, Daria, Eskil, Alessandro)


    • + Problems B4a, B4b
    + Studio Exercises 1, 2, 3
    + Textbook (3rd Ed. 2008) chapters 4.3, 4.4, 4.5, 4.6
    + Textbook (3rd Ed. 2008) figures 4.6, 4.7, 4.8, 4.9, 4.10, 4.15, 4.16, 4.17

  • WEEK 2 - IMAGE ENHANCEMENT IV: Fourier Domain Methods

    PDF (credits: Magnus, Daria, Eskil, Alessandro)


    • + Studio Exercises 1, 2, 3, 4
    + Textbook (3rd Ed. 2008) chapters 4.7, 4.8, 4.9 (except 4.9.6)
    + Textbook (3rd Ed. 2008) figures 4.29, 4.31, 4.40, 4.43, 4.44, 4.46, 4.47, 4.52, 4.53
    + Textbook (3rd Ed. 2008) tables 4.4, 4.5

    Remember: A summary of the steps for filtering in the frequency domain is given in chapter 4.7.3 and figure 4.36 of the textbook.

  • WEEK 3 - IMAGE COMPRESSION I: General Compressor/Decompressor, Coding Theorem, Huffman Coding and Multi-Pixel Coding

    PDF


    • + One of the Exams in 2008/2009: 3(b)
    + Problem E1
    + Studio Exercise 1
    + Textbook (3rd Ed. 2008) chapters 8.1 (except 8.1.7), 8.2.1

  • WEEK 3 - IMAGE COMPRESSION II: Run Length Coding, Predictive Coding and Digital Pulse Code Modulation

    PDF


    • + Problems (E2a) E2b, E2c (E2d)
    + Studio Exercises 1, 2
    + Textbook (3rd Ed. 2008) chapters 8.2.5, 8.2.9
    + Textbook (3rd Ed. 2008) figures 8.34, 8.35

  • WEEK 3 - IMAGE COMPRESSION III: Cosine Transform; Block Coding, Zonal Mask and Threshold Mask

    PDF


    • + Problems (D1a) (D1b)
    + Studio Exercise 3 (from Introduction)
    + Textbook (3rd Ed. 2008) chapter 8.2.8
    + Textbook (3rd Ed. 2008) figures 8.9, 8.27, 8.28

  • WEEK 3 - IMAGE COMPRESSION IV: JPEG

    From Wikipedia

    More technical paper


    • + Studio Exercise 1

  • WEEK 4 - WAVELETS AND WAVELET APPLICATIONS I: The Fundamental Property of Wavelets, Fast Wavelet Transform

    Romeo et al. (2003)
    • : Study only Figs 1 and 2. These figures are discussed in Sects 2.1 and 2.2 of Romeo et al. (2004).

    Romeo et al. (2004) : Study Sects 2.1 and 2.2, and Fig. 6.

    + Introduction to the Matlab Wavelet Toolbox

    HOMEWORK - TO DO BEFORE NEXT LECTURE: (1) Which matlab command implements the Fast Wavelet Transform? (2) Choose your signal s(t) and sample it. (3) Choose a wavelet and take the full FWT, so that the approximation consists of a single data point. Look at the structure of the transformed signal. (4) Where are the finest detail coefficients? What does such a component mean? .......... (5) Where are the coarsest detail coefficients? What does such a component mean? (6) Where are the approximation coefficients? What does such a component mean? (7) Reconstruct the signal through Inverse FWT after setting to zero the finest detail, then the finest but one detail, and so on until you only have the approximation. Plot the results. What you have done in this homework is SMOOTHING via FWT. Do you think that smoothing is a good method of noise reduction? Or, can we do better? Think about this point as a prelude to the lecture on data de-noising!

  • WEEK 4 - WAVELETS AND WAVELET APPLICATIONS II: Data Pre-Compression

    Romeo et al. (2004)
    • : Study Sect. 3.1 + Sects 2.3 and 2.4.

    + Special Notes for a very important topic: Wavelet Properties !!
    + Introduction to the Matlab Wavelet Toolbox

    Remember: if you want to use the Graphic User Interface of the Matlab Wavelet Toolbox for pre-compressing your data correctly, then you must type dwtmode('zpd') after opening the wavemenu !

  • WEEKS 4 & 5 - WAVELETS AND WAVELET APPLICATIONS III: Data De-Noising

    Romeo et al. (2004)
    • : Study Sect. 3.2 + Sects 2.3 and 2.4. Details are given in Sect. 4 (4.1, 4.2, 4.3, 4.4, 4.5, 4.6).

    + Special Notes for a very important type of noise: Poissonian noise !!
    + Textbook (3rd Ed. 2008) figures 5.2, 5.3, 5.4, 5.4 (continued)
    + Introduction to the Matlab Wavelet Toolbox

    Remember: if you want to use the Matlab Wavelet Toolbox for de-noising your data correctly, in the case of Gaussian additive white noise, then you must [1] zero-pad the data by yourself, [2] type dwtmode('per'), [3] FWT using the function wavedec (for 1D data) or wavedec2 (for 2D data), [4] threshold the wavelet coefficients by yourself, [5] IFWT using the function waverec (for 1D data) or waverec2 (for 2D data), [6] remove the padding.

    Enjoy the colours of noise ... and their music :-)

  • WEEKS 4 & 5 - WAVELETS AND WAVELET APPLICATIONS I-III: (Even) More Exercises and Problems

    Discussion of the HOMEWORK

    + One of the Exams in 2009/2010: 2(d) ..... smoothing
    + One of the Exams in 2009/2010: 2(e) ..... sharpening, high-boosting
    + One of the Exams in 2011/2012: 2(c) ..... detection of "breakdown" points
    + One of the Exams in 2010/2011: 2(a) ..... pre-compression
    + One of the Exams in 2010/2011: 1(d) ..... de-noising
    + One of the Exams in 2010/2011: 1(e) ..... de-noising
    + One of the Exams in 2011/2012: 1(e) ..... de-noising

  • WEEK 6 - IMAGE RESTORATION I: Linear Space-Invariant Distortions, Point Spread Function, Inverse and Pseudoinverse Filters

    PDF


    • + Problems F1c, F5a
    + Textbook (3rd Ed. 2008) chapters 5.1, 5.5, 5.6, 5.7
    + Textbook (3rd Ed. 2008) figures 5.24, 5.25, 5.27

  • WEEK 6 - IMAGE RESTORATION II: Wiener Filter

    PDF


    • + Studio Exercises 1, 2, 3, all followed by IMPORTANT discussion!
    + Textbook (3rd Ed. 2008) chapter 5.8
    + Textbook (3rd Ed. 2008) figures 5.28, 5.29

  • WEEKS 6 & 7 - IMAGE RESTORATION III: Image Reconstruction from Projections

    PDF


    • + Studio Exercise 1
    + Textbook (3rd Ed. 2008) chapter 5.11 (except 5.11.6)
    + Textbook (3rd Ed. 2008) figures 5.32, 5.33, 5.34, 5.36, 5.37, 5.38, 5.39, 5.40, 5.41, 5.42, 5.43, 5.44