Table of contents for Biosignal and medical image processing / John L. Semmlow.


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C hapter   1  Introduction    ............................................................................................... 1
1.1   Typical M  easurem   ent  System  s.............................................................. ........................
1.1.1   T ran sd u cers........................................................................................ ........... . .   2
1.1.2   Further Study: The Transducer..........................                  ...................3
1.1.3   A nalog  Signal Processing    ............................................ ............. ...........................4
1.2   Sources   of Variability: N  oise................................................................................................
1.2 .1  E lectron ic  N oise  .................................................. ................................................ 8
1.2.2   Signal-to-N  oise  R atio......................................................... ............................ 9
1.3   A nalog  Filters: Filter  Basics  .................................................. ......... .................. 10
1.3.1   Filter  Types........................................                   ...................  10
1.3.2   Filter  Bandw  idth  ......................................................... ................................ 11
1.3 .3  Filter  O rd er  ........................................................................... .............................. 12
1.3.4   Filter  Initial Sharpness ..................... ......................................    12
1.4   Analog-to-Digital Conversion: Basic Concepts .............................................................. 14
1.4.1   Analog-to-Digital Conversion Techniques..................             ................... 15
1.4.2   Q uantization   Error  ............................................................................................  16
1.4.3   Further Study: Successive Approximation Analog-to-Digital Conversion..... 17
1.5   T im e  Sam p ling : Basics......................... ..........   ........ .............................. ............. 19
1.5.1   Further Study: Buffering and Real-Time Data Processing ..............................21
1.6   D ata  B an k s  ................................................................................... ..... ............. . . .......... 22
P ro b lem s................................................................................................. ............. . . ....   2 3
Chapter    2  Basic  Concepts .......................................................................................... 25
2.1   N oise  ....................................  .............................. ............................................ ......... 25
2.1.1   Ensem   ble  Averaging.................. ................................. ................................... 27
2.1.2   MATLAB       Implementation..................................... ...............................28
2.2   Data Functions and Transforms ............................................................................29
2.2.1   Comparing Waveforms: Vector Representation...........................................30
2.2.2   Signal Analysis: Transformation and Basis Functions...............................32
2.3   Convolution, Correlation, and Covariance ...................               ..    .......................35
2.3.1   Convolution and the Impulse Response ...........................................................35
2.3.2   Covariance and Correlation ..............................................................39
2.3.3   Covariance, Correlation, and Autocorrelation Matrices....................................40
2.3.4   MATLAB" Implementation ..............................................    ...................42
2.4   Sampling Theory and Finite Data Considerations ...................                  ....... ............ 46
2 .4 .1  E d g e  E ffects  ..................................................... .......................... ........................ 5 1
P roblem  s............................................................................................... ........ ............53
Chapter 3 Spectral Analysis: Classical Methods.................................................55
3.1   In troduction  ............................... ....................... ................................. ........................ 55
3.2   Fourier Transform: Fourier Series Analysis ...................................... ..................57
3.2.1   Periodic  Functions   ...............  .. .................................. ... .................... . 57
3.2.1.1  Sym   m etry  .................................................... ...................................... 60
3.2.2   D iscrete-Tim e  Fourier Analysis   .............................................. ..................62
3.3   A periodic  Functions   .......................................................................................... . ..... 65
3.3.1   Frequency Resolution .................................           ...................66
3.4   MATLAB' Implementation: Direct FFT...............           ...........................................   67
3.5   Truncated Fourier Analysis: Data Windowing ..................................................   70
3.6   MATLAB' Implementation: Window Functions ............................       ........................ 73
3.7   Power Spectrum .................................................................................... 75
3.8   MATLAB' Implementation: The Welch Method for
Pow  er Spectral Density   Determ   ination  ............................................ ... ................   78
P ro b le m s ............................................................................................... .. ......... .. ........ 8 1
C h ap ter  4  D igital  Filters.................................................................................................83
4 .1  In tro d u ctio n  ................................................................................ ........................ . ..........   83
4.2   Z -Transform    ............................................. .....................................  ........ ......................... 83
4.2.1   Digital Transfer Function................................. ............   .......... 84
4.2.2   MATLABŪ Implementation.....................................    . ....................86
4.3   Finite  Im pulse  Response   (FIR) Filters.............................................. ..... ................ 88
4.3.1   FIR  Filter  D esign  ...............................................................................................  89
4.3.2   Derivative Operation: The Two-Point Central Difference Algorithm..............93
4.3.3   MATLABŪ Implementation...........................................................95
4.3.4   Filter Design and Application Using the MATLABŪ
Signal Processing    Toolbox  ....................................................... ...................98
4.3.4.1   Single-Stage FIR Filter Design......................................99
4.3.4.2   Two-Stage   FIR  Filter Design............................................................  100
4.4   Infinite  Im pulse  Response  (IIR) Filters........................................ ........................ 106
4.4.1   MATLABŪ Implementation IIR Filters................      .......    ................... 107
4.4.2   Single-Stage  IIR  Filter D esign  ........................................ .. .......................... 107
4.4.3   Two-Stage IIR Filter Design: Analog Style Filters......................................... 109
Problem   s......... ............... ............... ................................... ............... ...............  11
Chapter 5 Spectral Analysis: Modern Techniques ...................................................115
5.1   Param  etric  M ethods  ................................................................. .......................... ... 115
5.1.1   Yule-W  alker  Equations  ........................................ .. ................................... 120
5.1.2   MATLAB" Implementation ............................................... ...................   122
5.2   Nonparametric Analysis: Eigenanalysis Frequency Estimation ................................ 127
5.2.1   MATLABŪ Implementation ........................................ 128
Problem   s............................................................... ....................................... . 136
Chapter 6 Time-Frequency Analysis ........................................................... ........ 139
6.1   Basic Approaches .................................. ................................ .................... 139
6.2   Short-Term Fourier Transform: The Spectrogram ....................................................... 139
6.2.1   MATLABý Implementation: The Short-Term Fourier Transform................. 140
6.3   Wigner-Ville Distribution: A Special Case of Cohen's Class .................................. 147
6.3.1   Instantaneous Autocorrelation Function .............................. ............. .... 147
6.4   Choi-Williams and Other Distributions .................................. 152
6.4.1   Analytic Signal ................................................................... ............   153
6.5   MATLABŪ Implementation .............................. ....    ............... ................... 154
6.5.1   Wigner-Ville Distribution ......................................................... 154
6.5.2   Choi-Williams and Other Distributions....................................................... 157
P rob lem s.............................................................. ................................. . ........ .......... 163
Chapter 7 Wavelet Analysis ......................................................................................... 165
1     Introduction    .......................................... .............................. ..........................................  165
72    Continuous Wavelet Transform....................................... .......................................  167
7.2.1   Wavelet Time-Frequency Characteristics ................................   ................... 168
7.2.2   MATLABŪ Implementation...............................................     ........................ 171
73    Discrete   W  avelet Transform     ........................................ ........................................  174
7.3.1   Filter  Banks  .................................................. ....................  .... .................. .. 175
7.3.1.1 Relationship between Analytical Expressions and
F ilter  B an k s  .................... ... .......................................... ...................... 179
7.3.2   MATLABŪ Implementation.................................................... 180
7 3.2.1   D en oisin g  ........................................................ ................................... 185
73.2.2    Discontinuity Detection................................................................... 187
74    Feature Detection: Wavelet Packets ......................                              ................. 189
P roblem  s.............................................................. ................................................. . . .  193
Chapter 8 Advanced Signal Processing Techniques: Optimal and
A daptive    Filters  .................................................................................................... 195
8.1   Optimal Signal Processing: Wiener Filters ........................................ .................. 195
8.1.1   MATLABŪ Implementation............................................................................ 198
8.2   A daptive   Signal Processing........................................................................................... 202
8.2.1 Adaptive Line Enhancement (ALE) and Adaptive Interference
Su p p ression .................................................................................................... ... ..... 205
8.2.2   Adaptive Noise Cancellation (ANC)..................................        ..... ..................206
8.2.3   MATLABŪ Implementation..................................................... ...................... 207
8.3   Phase-Sensitive     D etection.................................................................. ....................  213
8.3.1   A M    M odulation.......................   ......................................... ......................... 213
8.3.2   Phase-Sensitive     D etectors........................... ...................................... ....... 215
8.3.3   MATLAB        Implementation .................................................. ................... 218
P roblem  s...... ........... . . ....................................................................... ........................  220
Chapter 9 Multivariate Analyses: Principal Component Analysis and
Independent Component Analysis.........................               ......................................223
9.1   Introduction: Linear Transformations ......................................................................... 223
9.2   Principal Component Analysis.............. ...................................... 226
9.2.1   Determination of Principal Components Using Singular Value
D ecom   p osition  .................................................... ............................................ 229
9.2.2   Order Selection: The Scree Plot.................................               ............... 230
9.2.3   MATLABŪ Implementation ........................................................................... 230
9.2.3.1   D ata  Rotation   ............................................................ .................... 230
9.2.4   PCA     Evaluation   .................................................................................................. 232
9.3   Independent Component Analysis .........................     ...................................... 236
9.3.1   MATLABŪ Implementation...................................       ................................... 241
P ro b lem s ...........................................................................................................   245
Chapter 10 Fundamentals of Image Processing: MATLABŪ Image
Processing     Toolbox ..................................................................... ...................... 247
10.1  Image Processing Basics: MATLABŪ Image Formats................................................ 247
10.1.1 General Image Formats: Image Array Indexing .........................................247
10.1.2 Data Classes: Intensity Coding Schemes .......................      .................... 48
10.1.3  D ata  Form ats  .............................................. ................................................  250
10.1.4  Data  Conversions   ....... .................................................................... 250
10 .2  Im ag e  D isp lay ...................................................................................... ......................... 2 53
10.3  Im age  Storage  and  Retrieval ............................................................. .................... 257
10.4  Basic  A rithm etic  O perations ............................................................ ....................  258
10.5  Advanced   Protocols: Block   Processing............................................ ................... 64
10.5.1 Sliding Neighborhood Operations..............................    ....................264
10.5.2  D istinct Block  O perations  ............ . ..................................... ..................... 268
Problem  s  ................. .............................. .. .........  ........................   272
Chapter 11 Spectral Analysis: The Fourier Transform ...........................................275
11.1  Two-Dim   ensional Fourier Transform    ............................................ ....................   275
11.1.1  M ATLA  BŪ  Im plem entation  .............................................. ................... ...  276
11.2  Linear  Filtering .......................................... .............................................................  279
11.2.1  M ATLABŪ    Im plem entation  .................. ................................... ...................280
11.2.2  F ilter  D esig n  ....................................................... .................. .......................  281
11.3  Spatial Transform  ations............................................... .......................... ..................  286
11.3.1  M ATLAB'    Im plem entation  ................................................................................ 288
11.3.1.1. Affine Transformations.......................................... 288
11.3.1.2 General Affine Transformations ........................... ..................290
11.3.1.3  Projective  Transform ations  .............. .................. ........................   292
11.4  Im age  R egistration ................................    ................................................ 296
11.4.1 Unaided Image Registration ........................................................297
11.4.2 Interactive Image Registration ...................................... 300
P rob lem s ........................................................................... .............. ...... ......... ... 302
Chapter 12 Image Segmentation ............................................................................305
12.1  Introduction  ......................................................................................... .................... 305
12.2  Pixel-Based  M ethods .......................................................................... ................... 305
12.2.1 Threshold Level Adjustment............................................           306
12.2.2 MATLAB' Implementation ................                             ................... 309
12.3  Continuity-Based   M  ethods  .................................................... ..............................   311
12.3.1 MATLAB" Implementation .......................................... 312
12.4  M u ltith resh old in g  ........................................................................ ................................ 317
12.5  M orphological O  perations......................................................................... ..........  319
12.5.1  M ATLAB' Im    plem entation  ............................................................... ................ 321
12.6  Edge-Based   Segm  entation  ............................................................................................... 326
12.6.1  H ough  Transform   .................................................. ................ .... ............. 327
12.6.2 MATLAB' Implementation ...............................   .....    ....... ............ 328
Problems.................. ..........      .................................. 332
Chapter 13 Image Reconstruction ............................................................................... 335
13.1 Introduction ....    ....................................................................................................335
13.1.1 CT, PET, SPECT.................................................................................................. 335
13.1.2  Filtered  Back-Projection  ........................................... ............ .... ............. 339
13.1.3  Fan  Beam   G eom etry ............................................................... ...................  341
13.1.4  M ATLABO    Im plem entation  ................................................... ..................342
13.1.4.1  Radon  Transform   ..................................................... ..................342
13.1.4.2 Inverse Radon Transform: Parallel Beam Geometry ........................  342
13.1.4.3  Radon and Inverse Radon Transform: Fan Beam Geometry............344
13.2 Magnetic Resonance Imaging.....................     .......................346
13.2.1  B asic  P rin cip les  ................................................................................. ................. .... 346
13.2.2 Data Acquisition: Pulse Sequences ........................................ .................349
13.3  Functional M   R I .............................................................................................. ................. 351
13.3.1 MATLABŪ Implementation.............................................................................. 352
13.3.2 Principal Component and Independent Component Analyses.................... 354
P roblem  s.............................................................. ................................ ............ . . . .....   359
Chapter 14 Classification I: Linear Discriminant Analysis and Support
Vector   M achines   .................................................................................................361
14.1  In tro d u ction ............................................................. .................................... . ............   361
14.1.1  C lassifier  D esign  ..................................................... ................................... 364
14.2  Linear  D iscrim inators ...................................................... ...................  365
14.3 Evaluating Classifier Performance.....................                      ...................... 371
14.4 Higher Dimensions: Kernel Machines ....................................... 376
14.5 Support Vector Machines ....................................................... . ..................... 378
14.5.1 MATLABŪ Implementation.......................        .........  ..........................381
14.6 Machine Capacity: Overfitting or "Less Is More"......................................................... 385
14.7  C lu ster  A n aly sis  .................................................................................. .. ................ 389
14.7.1  The k-Nearest Neighbor Classifier........    ................................389
14.7.2  The k-Means Clustering Classifier..............     ................................. ................ 391
Problem   s..... .............. .. ............... ............................................................................ 396
Chapter 15 Adaptive Neural Nets ...........................................   ...............................399
15.1  Introdu ction ................................................................... ............. .......................... 399
15.1.1  N euron  M odels  ..................................................... ........................... ........ 399
15.2 McCullough-Pitts Neural Nets ...............     .................................. ......................403
15.3 Gradient Descent Method or Delta Rule ........................................ 407
15.4 Two-Layer Nets: Backpropagation ...................    .......................... 411
15.5  T h ree-L ayer  N ets  ................................................... ..................................................... 416
15.6  T rain in g  Strateg ies............................................................................................................. 419
15.6.1  Stopping  Criteria: Cross-Validation    .............................................................. 419
15.6.2  M om  en tum  ................................................ .................................................  420
15.7  M ultiple  C lassifications...................................................................... ................... 426
15.8  M ultiple  Input Variables ...................................................................................................428
Problem   s................................ .  ........................... ................................... .........429



Library of Congress subject headings for this publication: Imaging systems in medicine, Image processing, Diagnostic imaging Digital techniques, Image Processing, Computer-Assisted methods, Signal Processing, Computer-Assisted instrumentation, Biosensing Techniques, Image Interpretation, Computer-Assisted methods