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== EE 596, Wavelets, Spring 2016 ==
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<html>
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'''Course Description:''' The theory and application of wavelet decomposition of signals. Includes subband coding, image compression, multiresolution signal processing, filter banks, and time-frequency tilings.
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<head>
 
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<title>EE 596, Wavelets, Fall 2006</title>
 
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</head>
 
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  <body bgcolor="#ffffff" text="#000000">
 
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<h1>EE 596, Wavelets, Fall 2006</h1>
 
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<h3>Instructor</h3>
 
−
  <a href="http://sipi.usc.edu/%7Eortega"> Antonio Ortega</a> 
 
  
−
<p></p>
+
'''Prerequisites:''' ''EE 483, Introduction to Digital Signal Processing'' and ''EE 441, Applied Linear Algebra for Engineering'', or equivalent courses. Please note that the course will assume some knowledge of standard DSP concepts as well as of some basic linear algebra. If you took these two courses some time ago it would be a good idea to review some of the key material early in the semester.
−
 
 
−
<address> <a href="http://sipi.usc.edu/"> Signal and Image Processing Institute<br>
 
−
  </a> <a href="http://www.usc.edu/dept/imsc/"> Integrated Media Systems
 
−
Center <br>
 
−
  </a> University of Southern California<br>
 
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  3740 McClintock Ave., EEB 436<br>
 
  
−
  Los Angeles, CA 90089-2564 
+
== Instructor ==
−
<p> Tel: (213) 740-2320<br>
+
[http://sipi.usc.edu/~ortega Antonio Ortega]
−
  Fax: (213) 740-4651<br>
 
−
  Email: antonio DOT ortega AT sipi DOT usc DOT edu</a><br>
 
−
  </p>
 
−
  </address>
 
−
     
 
−
<h3>Schedule</h3>
 
  
−
   
+
''[http://sipi.usc.edu Signal and Image Processing Institute]''<br>
−
<ul>
+
''[http://ee.usc.edu/ Department of Electrical Engineering]''<br>
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  <li><b>Lectures</b> Tuesday and Thursday, 11:00-12:20pm, OHE 100C  </li>
+
''[http://www.usc.edu/ University of Southern California]''<br>
−
    <li> <b>Office hours</b> Tuesday and Thursday, 1:30-3pm, EEB 436, and by
+
''3740 McClintock Ave., EEB 436''<br>
−
appointment.  
+
''Los Angeles, CA 90089-2564''<br>
−
  </li>
 
−
    <li> <b>Teaching Assistant</b> Ivy Tseng, hsinyits AT usc Dot edu,
 
−
  </li> TA Office Hours - Mon 10am-noon, Wed 1-3pm, EEB 441.
 
−
    <li> <b>Grader </b> Ozlem Kalinli
 
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- Grader office hours: F 2-4pm, EEB 427.
 
−
  </li>
 
  
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    <li><b>Midterm 1 </b> Oct 10, 2006 (in class) </li>
+
''Tel: (213) 740-2320''<br>
−
    <li><b>Midterm 2 </b> Nov 14, 2006 (in class) </li>
+
''Fax: (213) 740-4651''<br>
−
    <li><b>Final</b> There will be no final exam </li>
+
''Email: antonio DOT ortega AT sipi DOT usc DOT edu''
−
 
 
−
</ul>
 
  
−
 
+
== Schedule ==
−
<h3>Grading</h3>
+
* '''Lectures''' Tuesday and Thursday, 11-12:20pm, KAP 158
−
   
+
* '''Office hours''' Tuesday and Thursday, 1:30-3:00pm, EEB 436, and by appointment.
−
<p> Each midterm will account for 30% of the grade. The remaining 40% will
+
* '''Midterm 1''' Thursday Feb 18, in class (tentative)
−
be based on homeworks and a project. There will be around 4 homeworks and
+
* '''Midterm 2''' Thursday Mar 24, in class (tentative)
−
the project will be due at the end of the semester. </p>
+
* '''Final''' There will be no final exam
−
   
 
−
<p> </p>
 
  
−
<h3>DEN Access</h3>
+
== Grading ==
−
<p> This semester I will use the Blackboard system offered by
+
Each midterm will account for 30% of the grade. 30% will be based on  a project and the remaining 10% will be based on class participation and homeworks. The final project report and project presentations will be due on Monday May 9th (tentative).
−
DEN to post assignments and solutions, as well as grades.
 
−
Please register with DEN and create your DEN profile
 
−
as soon as possible by following
 
−
the instructions on the
 
−
<a href="http://den.usc.edu">  DEN Webpage</a>.  
 
  
−
</p>
+
== Lectures ==
 +
*Lecture 1 (1/12/16)
 +
** Introduction, goals, historical perspective
 +
*Lecture 2 (1/14/16)
 +
** Uncertainty principle
 +
** Practical time frequency localization example
 +
*Lecture 3 (1/19/16)
 +
** Signal spaces
 +
** Piecewise constant signals and Haar Wavelets
 +
** Bases
 +
*Lecture 4 (1/21/16)
 +
** Norms, Spaces, subspaces, orthogonal complements,
 +
*Lecture 5 (9/11/12)
 +
** View lecture 4-5 from 2010
 +
**  successive approximation
 +
*Lecture 6 (9/13/12)
 +
** Haar Wavelet construction, discrete time Haar construction example
 +
*Lecture 7 (9/18/12)
 +
** View lecture 6-7 from 2010
 +
** Bi-orthogonal bases, overcomplete representations
 +
*Lecture 8 (9/20/12)
 +
**View Lecture 8-9 from 2010
 +
* No Lecture on 9/25/12
 +
*Lecture 9 (9/27/12)
 +
**View Lecture 10 from 2010
 +
**Criteria to select a representation in an overcomplete set
 +
**Why is sparsity useful?
 +
**Least squares solution, brute force search
 +
*Lecture 10 (10/2/12)
 +
**Matching pursuits and Orthogonal Matching Pursuits
 +
**Why does l1 promote sparsity?
 +
**Basis pursuit
 +
*Lecture 11 (10/4/12)
 +
**Compressed sensing
 +
** Discussion of compressed sensing requirements and applications
 +
*Lecture 12 (10/9/12)
 +
** View Lectures 11-12 from 2010
 +
** Multirate signal processing
 +
** Modulation domain representation of filterbanks
 +
*Lecture 13 (10/11/12)
 +
** Time domain representation, polyphase domain representation
 +
*Lecture 14 (10/16/12)
 +
** Polyphase domain representation, QMF solutions
 +
*Lecture 15 (10/18/12)
 +
** Review session -- Problems
 +
*Midterm #1 (10/23/12)
 +
*Lecture 16 (10/25/12)
 +
** View lectures 13-15, 2010
 +
** Orthogonal filterbank solutions
 +
*Lecture 17 (10/30/12)
 +
** View Lecture 16-17, 2010
 +
** Adaptive bases
 +
** Wavelet packets
 +
** Examples
 +
*Lecture 18 (11/1/12)
 +
** Bi-orthogonal conditions and solutions
 +
*Lecture 19 (11/6/12)
 +
** View lectures 18-20, 2010
 +
** Lifting
 +
*Lecture 20 (11/8/12)
 +
** Multichannel transforms
 +
** Multidimensional transforms
  
−
<h3>Prerequisites</h3>
+
== Texbooks ==
−
   
+
'''Required:'''
−
<p> <i> EE 483, Introduction to Digital Signal Processing</i>, or equivalent
+
* Martin Vetterli and Jelena Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995. This textbook is now available electronically at http://www.waveletsandsubbandcoding.org
−
course. Please note that the course will assume some knowledge of standard
+
* Martin Vetterli , Jelena Kovacevic and Vivek K. Goyal, Foundations of Signal Processing, Cambridge University Press, 2014, available electronically at http://www.waveletsandsubbandcoding.org
−
DSP concepts as well as of some basic linear algebra. If you took these
+
* Jelena Kovacevic, Vivek K. Goyal and Martin Vetterli, Fourier and Wavelet Signal Processing, Cambridge University Press, to be published, available electronically at http://www.waveletsandsubbandcoding.org
−
two  courses some time ago it would be a good idea to review some of the
+
* Matlab Wavelet Toolbox, This toolbox is available on the student computer accounts.
−
key material early in the semester. <br>
 
−
  </p>
 
−
   
 
−
<h3>Recommended preparation</h3>
 
−
   
 
−
<p> <i>MATH 599, Introduction to Wavelets,</i> and <i>EE 569, Introduction
 
−
to Digital Image Processing</i>. None of these courses is required. </p>
 
  
−
     
+
'''Recommended:'''
−
<h3>Texbooks </h3>
+
* Gilbert Strang and Truong Q. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1995
−
    <li>     
+
* Stephane Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd Ed., Academic Press - Elsevier, 2009
−
  <h4>Required</h4>
+
* P. P. Vaidyanathan, Multirate Systems and Filter Banks , Prentice Hall, 1993
−
       
 
−
  <ul>
 
−
    <li><a href="http://lcavwww.epfl.ch/%7Evetterli/">Martin Vetterli</a>
 
−
and <a href="http://www.andrew.cmu.edu/user/jelenak/"> Jelena Kovacevic</a>,
 
−
  <a href="http://www.andrew.cmu.edu/user/jelenak/Book/index.html"> <i>Wavelets and Subband
 
−
Coding</i></a>, Prentice Hall, 1995.  </li>
 
  
−
      <li> <a href="http://www.mathworks.com/wavelet.html">      Matlab
+
== Material Covered (Subject to Change) ==
−
Wavelet  Toolbox</a>, This toolbox is available on the student
+
* '''Weeks 1 and 2''' Introduction and Motivation. Signal representation using bases. Hilbert spaces. Orthogonal, bi-orthogonal basis and overcomplete expansions. Example: representing finite energy continuous signals using Haar basis. Example of construction of Haar basis
−
  computer
+
* '''Week 3''' Bases for discrete signals. Finite and infinite dimensional spaces.
−
accounts. <br>
+
* '''Week 4''' Overcomplete expansions. Searching for the best representation. Matching pursuits and variations. Compressed sensing.
−
  </li>
+
* '''Weeks 5 and 6''' Multirate signal processing. Filterbanks and discrete wavelet transforms. Time domain, frequency domain and polyphase domain representations.
−
     
+
* '''Week 7 and 8''' 2-Channel orthogonal filterbanks. Iterated filterbanks. Bi-orthogonal filterbanks. Lifting factorizations. Multichannel filterbanks. Modulated filterbanks.
−
  </ul>
+
* '''Weeks 9 and 10''' Multidimensional wavelets. Edgelets, bandlets, ridgelets and other extensions. Lifting for video representation.
−
  </li>
+
* '''Week 11''' Continuous time wavelets. Series expansions of continuous signals. Haar, Sinc, Meyer, Daubechies and Spline wavelets. Mallat algorithm.
−
  <li>     
+
* '''Weeks 12, 13, 14 and 15''' Applications. Compression. Classification. Graphics. Class Projects.
−
  <h4>Recommended</h4>
 
−
       
 
−
  <ul>
 
  
−
  <li> <a href="http://www-math.mit.edu/%7Egs/">Gilbert Strang</a> and <a
+
== Projects ==
−
href="http://www.engr.wisc.edu/ece/faculty/nguyen_truong.html">Truong Q.
+
* Project requirements:
−
Nguyen</a>,    <a
+
** Projects should be done individually.
−
href="http://saigon.ece.wisc.edu/%7Ewaveweb/Tutorials/book.html"><i>Wavelets
+
** Each project must involve using the wavelet transform as a tool. A signal is analyzed/classified, etc by computing its wavelet transform and then the required task (e.g. denoising/classification) is performed in the transform domain.
−
and Filter Banks</i></a>, Wellesley-Cambridge Press, 1995 </li>
+
** The Matlab toolbox or C libraries can be used for the project. C libraries are available at [http://www.geoffdavis.net/dartmouth/wavelet/wavelet.html Dartmouth] and [http://math.rutgers.edu/%7Eojanen/wavekit/ Rutgers].
−
      <li><a href="http://www.systems.caltech.edu/EE/Faculty/PPV.html">P.
+
** Whichever method is used, the source code will have to be made available along with the project report (only for the routines that you write, which could call those available in matlab or C.)
−
P. Vaidyanathan</a>, <a
+
*Reporting requirements: a final report and a class presentation.
−
href="http://www.prenhall.com/013/605717/60571-7.html">    <i>Multirate
+
* [http://sipi.usc.edu/~ortega/Projects596.html Project descriptions and references]
−
Systems and Filter Banks</i>    ,</a> Prentice Hall, 1993<br>
+
* Test data for the projects
 +
* [http://sipi.usc.edu/~ortega/ee596_wavelet_toolbox.html Software packages]
  
−
      </li>
+
Demos on the web
−
     
+
* [http://jelena.ece.cmu.edu/bimagic.html Jelena Kovacevic's webpage] contains numerous pointers to books, projects, demos, applets, etc.
−
  </ul>
+
* [http://bigwww.epfl.ch/demo/fractsplines/demoprep.html Biomedical Group at EPFL - Fractional Splines Demo]
−
         
+
* [http://www.surveillance-video.com/wavelet-feb-2010.html Wavelet Resources]
−
  <h3>Some useful pointers</h3>
 
−
       
 
−
  <ul>
 
−
    <li> General links                   
 
−
      <ul>
 
−
  <a href="http://www.mathsoft.com/wavelets.html">Wavelet page at Mathsoft</a>
 
−
<li> <a href="http://www.amara.com/current/wavelet.html"> Amara's Wavelet
 
−
Page</a> </li>
 
  
−
          <li> <a href="http://www.math.wustl.edu/wavelet/"> Washington Univ.
+
== Sample Project Topics - Organized by Areas ==
−
  Wavlet NetCare </a>      </li>
+
* Coding
−
             
+
** Implementation of a Pyramidal Image Coder
−
      </ul>
+
** Compression of finite-length discrete-time signals using flexible adaptive wavelet packets<
−
    </li>
+
** Wavelet Descriptors for Planar Curves
−
      <li> Tutorials                   
+
** Sinusoidal Modeling of Audio Signals Using Frame-Based Perceptually Weighted Matching Pursuits
−
      <ul>
+
** Low Complexity Motion Estimation Algorithm for Long-term Memory Motion Compensation Using Hierarchical Motion Estimation
−
  <li> <a href="http://www.amara.com/IEEEwave/IEEEwavelet.html">An Introduction
+
** Global/Local Motion Compensation for 3D Video Coding Based on Lifting Techniques
−
to Wavelets </a> </li>
 
  
−
          <li> <a
+
* Classification/Recognition
−
href="http://engineering.rowan.edu/~polikar/WAVELETS/WTtutorial.html">
+
** Shift Invariant Texture Classification by Using Wavelet Frame
−
The Wavelet tutorial by Robi Polikar</a>      </li>
+
** Texture Feature Extraction with Non-Separable Wavelet Transforms
−
             
+
** Comparison of Two Wavelet-Based Image Watermarking Techniques
−
      </ul>
+
** Application of Wavelet Transform in Analysis of Fractal Signals
−
    </li>
+
** Human-Face Detection and Location in Color Images Using Wavelet Decomposition
−
      <li> Software                   
+
** Music/Speech Classifier using Wavelets
−
      <ul>
+
** Wavelet Decomposition for the Analysis of Heart Rate Variability
−
  <li> <a href="http://www-dsp.rice.edu/software/RWT/">Rice Wavelet Toolbox
+
** Wavelet-based fMRI dynamic activation detection
−
for Matlab</a> </li>
+
** Wavelet analysis of evoked potentials
 +
** Detection of Microcalcifications in Mammograms using Wavelet Transforms
 +
** Wavelet-based Tone Classification for Thai
 +
 
 +
* Denoising
 +
** Comparison of Denoising via Block Wiener Filtering in Wavelet Domain with Existing Ad-hoc Linear and Non-linear Denoising Techniques
 +
** Wavelet-domain filtering of data with Poisson noise
 +
** Contrast Enhancement and De-noising using Wavelets
 +
** Wavelet Denoising Applied to Time Delay Estimation
 +
** Comparison of image denoising using Wavelet Shrinkage vs. MMSE using an exponential decay autocorrelation model
 +
** Threshold Denoising Effects on Covariance Matrices
 +
** Comparing Performance of Different Wavelet De-noising algorithms with Basic Noise Removal Techniques
 +
** Information Driven Denosing of MEG data in the Wavelets Domain
 +
** Two Methods for Image Enhancement
  
−
          <li> <a href="http://www-stat.stanford.edu/%7Ewavelab/"> Wavelab
+
* Watermarking/Halftoning
−
at Stanford </a> </li>
+
** Introduction of IWT to wavelet-based watermarking and its effect on performance
−
          <li> <a href="http://www.mathworks.com/products/wavelet/"> The
+
** Inverse Halftoning using Wavelets
−
Mathworks  Matlab Wavelet Toolbox</a> </li>
 
−
          <li> <a
 
−
href="http://www.math.yale.edu/pub/wavelets/software/xwpl/html/xwpl.html">X-Windows
 
−
Wavelet Packet Lab </a> </li>
 
  
−
          <li> <a href="http://www.wavelsoftware.com/">WaveL Software</a>
+
* Communications
−
</li>
+
** Wavelets Based MC-CDMA System
−
          <li> <a
+
** MMSE Estimation Multi-user detection for CDMA System based on Wavelet Transform
−
href="http://www.cs.ubc.ca/nest/imager/contributions/bobl/wvlt/top.html">
 
−
Imager Wavelet Library at UBC </a> </li>
 
−
          <li> <a
 
−
href="http://www.cs.dartmouth.edu/~sp/liftpack/lift.html"> Liftpack</a>
 
−
      </li>
 
  
−
             
+
== Statement for Students with Disabilities ==
−
      </ul>
 
−
    </li>
 
−
      <li> People                   
 
−
      <ul>
 
−
  <li> <a href="http://iaks-www.ira.uka.de/home/klappi/people.html"> People
 
−
          </a>      </li>
 
−
             
 
−
      </ul>
 
−
  </li>
 
  
−
     
+
Any student requesting academic accommodations based on a disability
−
  </ul>
+
is required to register with Disability Services and Programs (DSP)
−
               
+
each semester. A letter of verification for approved accommodations
−
  <h3> Material covered (Note: based on the material covered in Fall'04,
+
can be obtained from DSP. Please be sure the letter is delivered to me
−
subject to change)</h3>
+
(or to TA) as early in the semester as possible. DSP is located in STU
−
       
+
301 and is open 8:30 a.m.--5:00 p.m., Monday through Friday. The
−
  <ul>
+
phone number for DSP is (213) 740-0776.
−
    <li>
 
−
<b> Weeks 1 and 2 </b>
 
−
Introduction and Motivation. Signal representation using bases.
 
−
Hilbert spaces. Orthogonal, bi-orthogonal basis and overcomplete
 
−
expansions.  
 
−
Example: representing finite energy continuous signals using Haar basis.
 
−
Example of construction of Haar basis
 
−
      <li> <b> Week 3</b>
 
  
−
  Bases for discrete signals. Finite and infinite dimensional spaces.
 
−
      </li>
 
−
      <li> <b> Week 4</b> Overcomplete expansions. Searching for the
 
−
  best representation. Matching pursuits and variations. Compressed
 
−
  sensing.
 
−
  </li>
 
−
      <li> <b> Weeks 5 and 6</b>
 
−
  Multirate signal processing. Filterbanks
 
−
  and discrete wavelet transforms. Time domain, frequency domain
 
−
  and polyphase domain representations.
 
−
      <li> <b> Week 7-8</b> 2-Channel orthogonal filterbanks. Iterated
 
−
  filterbanks. Bi-orthogonal filterbanks. Lifting
 
−
  factorizations. Multichannel filterbanks. Modulated filterbanks.
 
−
  </li>
 
  
−
      <li> <b> Weeks 9 and 10</b> Multidimensional wavelets. Edgelets,
+
== Statement on Academic Integrity ==
−
  bandlets, ridgelets and other extensions. Lifting for video
 
−
          representation.
 
−
      </li>
 
−
      <li> <b> Week 11</b> Continuous time wavelets. Series
 
−
  expansions of continuous signals. Haar, Sinc, Meyer, Daubechies
 
−
  and Spline wavelets. Mallat algorithm. </li>
 
  
−
      <li> <b> Weeks 12 and 13</b> Applications. Compression. Classification. Graphics. </li>
+
USC seeks to maintain an optimal learning environment. General
−
     
+
principles of academic honesty include the concept of respect for the
−
  </ul>
+
intellectual property of others, the expectation that individual work
 +
will be submitted unless otherwise allowed by an instructor, and the
 +
obligations both to protect oneís own academic work from misuse by
 +
others as well as to avoid using anotherís work as oneís own. All
 +
students are expected to understand and abide by these
 +
principles. Scampus, the Student Guidebook, contains the Student
 +
Conduct Code in Section 11.00, while the recommended sanctions are
 +
located in Appendix A [http://www.usc.edu/dept/publications/SCAMPUS/gov/ http://www.usc.edu/dept/publications/SCAMPUS/gov/ ]
  
−
         
+
Students will be referred to the Office of Student Judicial Affairs
−
  <h3>Projects</h3>
+
and Community Standards for further review, should there be any
−
       
+
suspicion of academic dishonesty. The Review process can be found at
−
  <ul>
+
[http://www.usc.edu/student-affairs/SJACS/ http://www.usc.edu/student-affairs/SJACS/].
−
  <li> Project requirements:                 
 
−
      <ul>
 
−
        <li> Projects should be done individually.      </li>
 
−
          <li> Each project must involve using the wavelet transform as a
 
−
tool. A   signal is analyzed/classified, etc by computing its wavelet
 
−
transform and then the required task   (e.g. denoising/classification) is
 
−
performed in the transform domain.      </li>
 
−
 
 
−
          <li> The Matlab toolbox or C libraries can be used for the project.
 
−
C libraries are available at <a
 
−
href="http://www.cs.dartmouth.edu/%7Egdavis/wavelet/wavelet.html"> Dartmouth
 
−
          </a> and   <a
 
−
href="http://math.rutgers.edu/%7Eojanen/wavekit/"> Rutgers. </a>.     
 
−
        </li>
 
−
          <li> Whichever method is used, the source code will have to be
 
−
made    available along with the project report (only for the routines that
 
−
  you write, which could call those available in matlab or C.)    </li>
 
−
             
 
−
      </ul>
 
−
 
 
−
  </li>
 
−
      <li> Reporting requirements: a final report and a class presentation.
 
−
    </li>
 
−
      <li> <a href="./Projects596.html"> Project descriptions and references
 
−
      </a> </li>
 
−
      <li>  Test data for the projects </li>
 
−
      <li> <a href="./ee596_wavelet_toolbox.html"> Software packages</a>
 
−
 
 
−
    </li>
 
−
     
 
−
  </ul>
 
−
 
 
−
        <p> Examples of coding using JPEG and the latest version of JPEG 2000
 
−
(provided by Christos Chrysafis, HP Labs)      </p>
 
−
             
 
−
      <ul>
 
−
        <li><a href="./Images/original.gif"> Original Image </a>      </li>
 
−
          <li><a href="./Images/jpeg_40_1.gif"> JPEG Coded at 0.2 bpp (40:1
 
−
compression) </a>      </li>
 
−
 
 
−
          <li><a href="./Images/jpeg2000_40_1.gif"> JPEG2000 Coded at 0.2
 
−
bpp (40:1 compression)</a>      </li>
 
−
          <li><a href="./Images/jpeg_70_1.gif"> JPEG Coded at 0.11 bpp (70:1
 
−
compression)</a>      </li>
 
−
          <li><a href="./Images/jpeg2000_70_1.gif"> JPEG2000 Coded at 0.11
 
−
bpp (70:1 compression) </a>      </li>
 
−
             
 
−
      </ul>
 
−
 
 
−
                             
 
−
      <p> Demos on the web      </p>
 
−
             
 
−
      <ul>
 
−
<li>  <a href="http://www.andrew.cmu.edu/user/jelenak/"> Jelena Kovacevic's webpage</a> contains numerous pointers to books, projects, demos, applets, etc. </li>
 
−
        <li><a href="http://www.math.sc.edu/%7Esjohnson/wvlib/demo/"> Wavelet
 
−
Library Demo at South Carolina </a>      </li>
 
−
 
 
−
          <li><a href="http://cm.bell-labs.com/cm/ms/who/wim/cascade/"> Bell
 
−
Labs: Wim Sweldens' Wavelet Cascade Applet </a>      </li>
 
−
          <li><a
 
−
href="http://bigwww.epfl.ch/demo/fractsplines/demoprep.html"> Biomedical
 
−
Group at EPFL - Fractional Splines Demo </a>      </li>
 
−
          <li><a href="http://www.ics.forth.gr/%7Eliapis/demo/"> Texture
 
−
Classification  Demo </a> </li>
 
−
          <li><a href="http://www-db.stanford.edu/IMAGE/">  SIMPLIcity Content
 
−
Based Image Retrieval - Search </a> </li>
 
−
 
 
−
          <li><a
 
−
href="http://www.ai.polymtl.ca/webLab/SMART/Facet1DocD/Facet1DocD.html">
 
−
Wavelet-Based View Synthesis </a>      </li>
 
−
          <li><a
 
−
href="http://telin.rug.ac.be/%7Efrooms/links/wavelets.html"> More links...
 
−
          </a><a> </a></li>
 
−
          <li><a
 
−
href="http://www.google.com/search?q=Wavelet+Press+Releases"> A measure
 
−
of Wavelet popularity?</a></li>
 
−
             
 
−
      </ul>
 
−
 
 
−
  <h3>Sample Project Topics (from Fall'01) - Organized by areas </h3>
 
−
       
 
−
  <ul>
 
−
    <li> Coding                   
 
−
      <ul>
 
−
  <li>  Implementation of a Pyramidal Image Coder  </li>
 
−
          <li> Compression of finite-length discrete-time signals using flexible
 
−
adaptive wavelet packets&lt; </li>
 
−
 
 
−
          <li> Wavelet Descriptors for Planar Curves  </li>
 
−
          <li> Sinusoidal Modeling of Audio Signals Using Frame-Based Perceptually
 
−
Weighted Matching Pursuits     </li>
 
−
          <li>  Low Complexity Motion Estimation Algorithm for Long-term
 
−
Memory  Motion Compensation Using Hierarchical Motion Estimation      </li>
 
−
          <li>  Global/Local Motion Compensation for 3D Video Coding Based
 
−
on Lifting Techniques      </li>
 
−
             
 
−
      </ul>
 
−
 
 
−
    </li>
 
−
      <li> Classification/Recognition                   
 
−
      <ul>
 
−
  <li> Shift Invariant Texture Classification by Using Wavelet Frame </li>
 
−
          <li> Texture Feature Extraction with Non-Separable Wavelet Transforms
 
−
</li>
 
−
          <li>  Comparison of Two Wavelet-Based Image Watermarking Techniques
 
−
</li>
 
−
 
 
−
          <li> Application of Wavelet Transform in Analysis of Fractal Signals
 
−
</li>
 
−
          <li>  Human-Face Detection and Location in Color Images Using Wavelet
 
−
      Decomposition    </li>
 
−
          <li>  Music/Speech Classifier using Wavelets       </li>
 
−
          <li> Wavelet Decomposition for the Analysis of Heart Rate Variability
 
−
</li>
 
−
          <li> Wavelet-based fMRI dynamic activation detection </li>
 
−
 
 
−
          <li> Wavelet analysis of evoked potentials </li>
 
−
          <li>  Detection of Microcalcifications in Mammograms using Wavelet
 
−
Transforms     </li>
 
−
          <li>  Wavelet-based Tone Classification for Thai      </li>
 
−
    </li>
 
−
             
 
−
      </ul>
 
−
    </li>
 
−
 
 
−
      <li> Denoising                     
 
−
      <ul>
 
−
  <li> Comparison of Denoising via Block Weiner Filtering in Wavelet Domain
 
−
with Existing Ad-hoc Linear and Non-linear Denoising Techniques  </li>
 
−
          <li> Wavelet-domain filtering of data with Poisson noise  </li>
 
−
          <li> Contrast Enhancement and De-noising using Wavelets </li>
 
−
          <li>  Wavelet Denoising Applied to Time Delay Estimation  </li>
 
−
 
 
−
          <li> Comparison of image denoising using Wavelet Shrinkage vs.
 
−
MMSE  using an exponential decay autocorrelation model </li>
 
−
          <li> Threshold Denoising Effects on Covariance Matrices  </li>
 
−
          <li>  Comparing Performance of Different  Wavelet De-noising algorithms
 
−
with Basic Noise Removal  Techniques  </li>
 
−
          <li> Information Driven Denosing of MEG data in the Wavelets Domain
 
−
  </li>
 
−
          <li>  Two Methods for Image Enhancement<a
 
−
href="./ChongKim.html">  </a>      </li>
 
−
 
 
−
             
 
−
      </ul>
 
−
    </li>
 
−
      <li> Watermarking/Halftoning                     
 
−
      <ul>
 
−
  <li> Introduction of IWT to wavelet-based watermarking and its effect
 
−
on performance </li>
 
−
          <li> Inverse Halftoning using Wavelets      </li>
 
−
             
 
−
      </ul>
 
−
 
 
−
    </li>
 
−
      <li> Communications                     
 
−
      <ul>
 
−
  <li> Wavelets Based MC-CDMA System </li>
 
−
          <li>    MMSE Estimation Multi-user detection for CDMA System based
 
−
on Wavelet Transform<a href="EE596_Wu.htm">  </a>      </li>
 
−
             
 
−
      </ul>
 
−
 
 
−
  </li>
 
−
     
 
−
  </ul>
 
−
           
 
−
  <h3>Homeworks</h3>
 
−
       
 
−
  <ul>
 
−
         
 
−
  </ul>
 
−
 
 
−
<li>  &copy;1996-2006 Antonio Ortega.&nbsp;</li>
 
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Latest revision as of 13:47, 26 January 2016

EE 596, Wavelets, Spring 2016

Course Description: The theory and application of wavelet decomposition of signals. Includes subband coding, image compression, multiresolution signal processing, filter banks, and time-frequency tilings.

Prerequisites: EE 483, Introduction to Digital Signal Processing and EE 441, Applied Linear Algebra for Engineering, or equivalent courses. Please note that the course will assume some knowledge of standard DSP concepts as well as of some basic linear algebra. If you took these two courses some time ago it would be a good idea to review some of the key material early in the semester.

Instructor

Antonio Ortega

Signal and Image Processing Institute
Department of Electrical Engineering
University of Southern California
3740 McClintock Ave., EEB 436
Los Angeles, CA 90089-2564

Tel: (213) 740-2320
Fax: (213) 740-4651
Email: antonio DOT ortega AT sipi DOT usc DOT edu

Schedule

  • Lectures Tuesday and Thursday, 11-12:20pm, KAP 158
  • Office hours Tuesday and Thursday, 1:30-3:00pm, EEB 436, and by appointment.
  • Midterm 1 Thursday Feb 18, in class (tentative)
  • Midterm 2 Thursday Mar 24, in class (tentative)
  • Final There will be no final exam

Grading

Each midterm will account for 30% of the grade. 30% will be based on a project and the remaining 10% will be based on class participation and homeworks. The final project report and project presentations will be due on Monday May 9th (tentative).

Lectures

  • Lecture 1 (1/12/16)
    • Introduction, goals, historical perspective
  • Lecture 2 (1/14/16)
    • Uncertainty principle
    • Practical time frequency localization example
  • Lecture 3 (1/19/16)
    • Signal spaces
    • Piecewise constant signals and Haar Wavelets
    • Bases
  • Lecture 4 (1/21/16)
    • Norms, Spaces, subspaces, orthogonal complements,
  • Lecture 5 (9/11/12)
    • View lecture 4-5 from 2010
    • successive approximation
  • Lecture 6 (9/13/12)
    • Haar Wavelet construction, discrete time Haar construction example
  • Lecture 7 (9/18/12)
    • View lecture 6-7 from 2010
    • Bi-orthogonal bases, overcomplete representations
  • Lecture 8 (9/20/12)
    • View Lecture 8-9 from 2010
  • No Lecture on 9/25/12
  • Lecture 9 (9/27/12)
    • View Lecture 10 from 2010
    • Criteria to select a representation in an overcomplete set
    • Why is sparsity useful?
    • Least squares solution, brute force search
  • Lecture 10 (10/2/12)
    • Matching pursuits and Orthogonal Matching Pursuits
    • Why does l1 promote sparsity?
    • Basis pursuit
  • Lecture 11 (10/4/12)
    • Compressed sensing
    • Discussion of compressed sensing requirements and applications
  • Lecture 12 (10/9/12)
    • View Lectures 11-12 from 2010
    • Multirate signal processing
    • Modulation domain representation of filterbanks
  • Lecture 13 (10/11/12)
    • Time domain representation, polyphase domain representation
  • Lecture 14 (10/16/12)
    • Polyphase domain representation, QMF solutions
  • Lecture 15 (10/18/12)
    • Review session -- Problems
  • Midterm #1 (10/23/12)
  • Lecture 16 (10/25/12)
    • View lectures 13-15, 2010
    • Orthogonal filterbank solutions
  • Lecture 17 (10/30/12)
    • View Lecture 16-17, 2010
    • Adaptive bases
    • Wavelet packets
    • Examples
  • Lecture 18 (11/1/12)
    • Bi-orthogonal conditions and solutions
  • Lecture 19 (11/6/12)
    • View lectures 18-20, 2010
    • Lifting
  • Lecture 20 (11/8/12)
    • Multichannel transforms
    • Multidimensional transforms

Texbooks

Required:

  • Martin Vetterli and Jelena Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995. This textbook is now available electronically at http://www.waveletsandsubbandcoding.org
  • Martin Vetterli , Jelena Kovacevic and Vivek K. Goyal, Foundations of Signal Processing, Cambridge University Press, 2014, available electronically at http://www.waveletsandsubbandcoding.org
  • Jelena Kovacevic, Vivek K. Goyal and Martin Vetterli, Fourier and Wavelet Signal Processing, Cambridge University Press, to be published, available electronically at http://www.waveletsandsubbandcoding.org
  • Matlab Wavelet Toolbox, This toolbox is available on the student computer accounts.

Recommended:

  • Gilbert Strang and Truong Q. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1995
  • Stephane Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd Ed., Academic Press - Elsevier, 2009
  • P. P. Vaidyanathan, Multirate Systems and Filter Banks , Prentice Hall, 1993

Material Covered (Subject to Change)

  • Weeks 1 and 2 Introduction and Motivation. Signal representation using bases. Hilbert spaces. Orthogonal, bi-orthogonal basis and overcomplete expansions. Example: representing finite energy continuous signals using Haar basis. Example of construction of Haar basis
  • Week 3 Bases for discrete signals. Finite and infinite dimensional spaces.
  • Week 4 Overcomplete expansions. Searching for the best representation. Matching pursuits and variations. Compressed sensing.
  • Weeks 5 and 6 Multirate signal processing. Filterbanks and discrete wavelet transforms. Time domain, frequency domain and polyphase domain representations.
  • Week 7 and 8 2-Channel orthogonal filterbanks. Iterated filterbanks. Bi-orthogonal filterbanks. Lifting factorizations. Multichannel filterbanks. Modulated filterbanks.
  • Weeks 9 and 10 Multidimensional wavelets. Edgelets, bandlets, ridgelets and other extensions. Lifting for video representation.
  • Week 11 Continuous time wavelets. Series expansions of continuous signals. Haar, Sinc, Meyer, Daubechies and Spline wavelets. Mallat algorithm.
  • Weeks 12, 13, 14 and 15 Applications. Compression. Classification. Graphics. Class Projects.

Projects

  • Project requirements:
    • Projects should be done individually.
    • Each project must involve using the wavelet transform as a tool. A signal is analyzed/classified, etc by computing its wavelet transform and then the required task (e.g. denoising/classification) is performed in the transform domain.
    • The Matlab toolbox or C libraries can be used for the project. C libraries are available at Dartmouth and Rutgers.
    • Whichever method is used, the source code will have to be made available along with the project report (only for the routines that you write, which could call those available in matlab or C.)
  • Reporting requirements: a final report and a class presentation.
  • Project descriptions and references
  • Test data for the projects
  • Software packages

Demos on the web

Sample Project Topics - Organized by Areas

  • Coding
    • Implementation of a Pyramidal Image Coder
    • Compression of finite-length discrete-time signals using flexible adaptive wavelet packets<
    • Wavelet Descriptors for Planar Curves
    • Sinusoidal Modeling of Audio Signals Using Frame-Based Perceptually Weighted Matching Pursuits
    • Low Complexity Motion Estimation Algorithm for Long-term Memory Motion Compensation Using Hierarchical Motion Estimation
    • Global/Local Motion Compensation for 3D Video Coding Based on Lifting Techniques
  • Classification/Recognition
    • Shift Invariant Texture Classification by Using Wavelet Frame
    • Texture Feature Extraction with Non-Separable Wavelet Transforms
    • Comparison of Two Wavelet-Based Image Watermarking Techniques
    • Application of Wavelet Transform in Analysis of Fractal Signals
    • Human-Face Detection and Location in Color Images Using Wavelet Decomposition
    • Music/Speech Classifier using Wavelets
    • Wavelet Decomposition for the Analysis of Heart Rate Variability
    • Wavelet-based fMRI dynamic activation detection
    • Wavelet analysis of evoked potentials
    • Detection of Microcalcifications in Mammograms using Wavelet Transforms
    • Wavelet-based Tone Classification for Thai
  • Denoising
    • Comparison of Denoising via Block Wiener Filtering in Wavelet Domain with Existing Ad-hoc Linear and Non-linear Denoising Techniques
    • Wavelet-domain filtering of data with Poisson noise
    • Contrast Enhancement and De-noising using Wavelets
    • Wavelet Denoising Applied to Time Delay Estimation
    • Comparison of image denoising using Wavelet Shrinkage vs. MMSE using an exponential decay autocorrelation model
    • Threshold Denoising Effects on Covariance Matrices
    • Comparing Performance of Different Wavelet De-noising algorithms with Basic Noise Removal Techniques
    • Information Driven Denosing of MEG data in the Wavelets Domain
    • Two Methods for Image Enhancement
  • Watermarking/Halftoning
    • Introduction of IWT to wavelet-based watermarking and its effect on performance
    • Inverse Halftoning using Wavelets
  • Communications
    • Wavelets Based MC-CDMA System
    • MMSE Estimation Multi-user detection for CDMA System based on Wavelet Transform

Statement for Students with Disabilities

Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m.--5:00 p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.


Statement on Academic Integrity

USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect oneís own academic work from misuse by others as well as to avoid using anotherís work as oneís own. All students are expected to understand and abide by these principles. Scampus, the Student Guidebook, contains the Student Conduct Code in Section 11.00, while the recommended sanctions are located in Appendix A http://www.usc.edu/dept/publications/SCAMPUS/gov/

Students will be referred to the Office of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty. The Review process can be found at http://www.usc.edu/student-affairs/SJACS/.

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