ECSE4963 Introduction to Subsurface Sensing and Imaging Systems

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ECSE-4963Introduction to Subsurface Sensing and
Imaging Systems

• Lecture 2 Introduction to MATLAB
• Kai Thomenius1 Badri Roysam2
• 1Chief Technologist, Imaging technologies,
• General Electric Global Research Center
• 2Professor, Rensselaer Polytechnic Institute

Center for Sub-Surface Imaging Sensing
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Review of Last Lecture

• Subsurface imaging Course Focus
• Many applications to Biology, Medicine, Industry,
  Homeland Security
• Probes, media, and probe-media interactions
• Methods by which we examine contents of hidden
  volumes
• Wave theory the common thread
• Common to electromagnetic and acoustic probing
• This Class
• Overview of Matlab tools

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Outline of Course Topics

• THE BIG PICTURE
• What is subsurface sensing imaging?
• Why a course on this topic?
• EXAMPLE THROUGH TRANSMISSION SENSING
• X-Ray Imaging
• Computer Tomography
• COMMON FUNDAMENTALS
• propagation of waves
• interaction of waves with targets of interest 

• PULSE ECHO METHODS
• Examples
• MRI
• A different sensing modality from the others
• Basics of MRI
• MOLECULAR IMAGING
• What is it?
• PET Radionuclide Imaging
• IMAGE PROCESSING CAD

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Sources

• These slides have been collected from a number of
  sources
• www.cs.cornell.edu/Courses/cs401/2001fa
• www.soes.soton.ac.uk/MSc/current/matlab.ppt
• Matlab File Exchange
• www.mathworks.com/matlabcentral/fileexchange/loadC
  ategory.do
• While there, download the following MATLAB
  Programming Style Guidelines by Richard Johnson

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Matlab History

• Matlab stands for Matrix Laboratory
• Created by Dr. Cleve Moler in the 1970s, then a
  professor at U. of New Mexico
• Now Dr. Moler is Chief Scientist Mathworks, Inc.
• Mathworks is now a major computer company
• Developed from LAPACK--a series of routines for
  numerical linear algebra
• Consequences
• is funny, / is even funnier
• Matlab does linear algebra really well

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Starting Up

• On Windows
• Launch from START, or find matlab.exe double
  click
• On UNIX/Linux
• Open a terminal, type matlab
• Problems
• Command not found--check your path
• Splash window of 6.X hangs--try matlab -nojvm

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Matlab Windows

• As of 6.0, Matlab has lots of windows inside a
  Desktop
• The Workspace is the center of the Matlab
  universe
• Holds your data
• Waits for your commands
• (other windows are fluff)
• 5.X only has workspace

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Basic Math

• Matlab is a command-line calculator
• Simple arithmetic operators
• - /
• Basic functions
• sin(), log(), log10(), exp(), rem()
• Constants
• pi, e

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Big deal, a calculators 20

• Matlab is a fully-functional programming language
• This means we get variables
• name value
• Name can be anything made of letters, numbers,
  and a few symbols (_). Must start with a letter
• End line with to avoid output
• Can also use to put multiple commands on a
  line
• List with who
• Delete with clear
• More info with whos

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1D Arraysa.k.a. Vectors

• An array is anything you access with a subscript
• 1D arrays are also known as vectors
• Everything (nearly) in Matlab is a double array
• Create arrays with brackets
• Separate elements with commas or spaces
• Access with ()s

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Regular arrays

• We can create regularly spaced arrays using
• Asten produces st, st1, st2, en
• A15 is 1 2 3 4 5
• A-3.52 is -3.5 -2.5 -1.5 0.5 1.5---note,
  stops before 2!
• What happens if en lt st ?
• Can also insert a step size Aststepen
• A026 is 0 2 4 6
• A5-2.50 is 5 -2.5 0

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Accessing vectors

• Matlab arrays start at 1
• In most languages (C, Java, F77) can only access
  arrays one element at a time
• a(1)1 a(2)2.5 a(3)-3 etc.
• In Matlab, can access several elements at a time
  using an array of integers (aka an index)
• a(15) is a(1),a(2),a(3),a(4),a(5)
• a(5-21) is a(5), a(3), a(1)

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Accessing vectors

• Index vectors can be variables
• A1010100 I129 A(I) gives
  10,30,50,70,90
• J2210A(J) gives 20,40,60,80,100
• What does A(I)A(J) do?

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Column vectors

• row vectors are 1-by-n
• column vectors are n-by-1
• Row/column distinction doesnt exist in most
  languages, but VERY IMPORTANT in MATLAB
• Create column vectors with semi-colons
• Can force to column vector with ()
• Convert column-to-row and back with transpose ()
• Can access the same way as row vectors

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2D arrays--matrices

• From using commas/spaces and semi-colons
• A1 2 3 4 5 6 7 8 9
• A(j,k) jth row, kth column
• A(23,12) rows 2 through 3 and columns 1
  through 2
• A(1,3,4, ) all of rows 1, 3 and 4
• A(, 1) first column

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Size matters

• A is m-by-n means A has m rows and n columns
• m,nsize(A) gets size of A
• length(a) gets length of vectors.
• A(13,2)v, v better have length 3
• A(125,23)B, B better be 3-by-2

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Array Arithmetic

• CAB
• if A and B are the same size, C(j,k)A(j,k)B(j,k)
  
• If A is a scalar, C(j,k)AB(j,k)
• Same for -

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Array Multiplication

• Multiplication is weird in Matlab
• Inherited from linear algebra
• To multiply by a scalar, use
• To get C(j,k)A(j,k)B(j,k) use .
• Also applies to . and ./

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Matrix Multiplication CAB

• A is m-by-p and B is p-by-n then C is m-by-n
• C(i,j) a(i,1)b(1,j)a(i,2)b(2,j)
  a(i,p)b(p,j)
• Another view
• C(i,j)a(i,)b(,j)
• 1-by-p p-by-1 answer is 1-by-1

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ND arrays

• Until V5, Matlab arrays could only be 2D
• Now has unlimited dimensions
• Aones(2,3,2)
• A is a 3D array of ones, with 2 rows, 3 columns,
  and 2 layers
• A(,,1) is a 2-by-3 matrix
• squeeze command is very important

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What kind of graphics is possible in Matlab?
Polar plot t0.012pi
polar(t,abs(sin(2t).cos(2t)))
Line plot x00.055,ysin(x.2),plot(x,y)
Stem plot x 00.14, y
sin(x.2).exp(-x) stem(x,y)
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What kind of graphics is possible in Matlab?
Surface plot zpeaks(25), surf(z),
colormap(jet)
Mesh plot zpeaks(25), mesh(z)
Contour plot
zpeaks(25),contour(z,16)
Quiver plot
28 January 2003, Matlab tutorial Joanna Waniek
(jowa_at_soc.soton.ac.uk)
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Iteration

• For loops in Matlab use index-notation
• for jststepen
• ltcommands involving jgt
• end
• Example uv
• tot0
• for j1length(u)
• tottotu(j)v(j)
• end

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Conditionals

• Conditional statements control flow of a program
• if(logic)
• ltcommands executed if truegt
• else
• ltcommands executed if falsegt
• end
• Matlab also has switch
• switch(j)
• case a ltcommands if ajgt
• case b ltcommands if bjgt
• otherwise ltdefault commandsgt
• end

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Logic--searching with find

• Find--searches for the truth (or not false)
• b1 0 -1 0 0
• Ifind(b)
• I1 3 --b(I) is an array without zeros
• Ifind(ones(3,1) 1 2 32)
• I 4 5 6
• I,Jfind(ones(3,1) 1 2 32)
• I 1 2 3
• J 2 2 2

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Programming

• Matlab programs are stored in m-files
• Text files containing Matlab commands and ending
  with .m
• Script m-files--commands executed as if entered
  on command line
• Function m-files--analogous to subroutines or
  methods, maintain their own memory (workspace)

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Functions

• First line of file must be function
  outputsfname(inputs)
• outputs and inputs can be blank
• Comments immediately following are returned by
  help
• Functions must be in current directory or in
  Matlabs search path

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Summary

• Matlab
• Very widely used mathematical modeling tool
• Brief introduction to MATLABs key concepts
• Arrays, vectors, matrices, their addressing
• Graphics w. MATLAB
• Iteration program flow
• Conditionals
• Next Class
• Projection Imaging X-rays

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Instructor Contact Information

• Badri Roysam
• Professor of Electrical, Computer, Systems
  Engineering
• Office JEC 7010
• Rensselaer Polytechnic Institute
• 110, 8th Street, Troy, New York 12180
• Phone [phone]
• Fax [phone]
• Email roysam_at_ecse.rpi.edu
• Website http//www.rpi.edu/roysab
• NetMeeting ID (for off-campus students)
  128.113.61.80
• Secretary Betty Lawson, JEC 7012, (518) 276
  8525, lawsob_at_.rpi.edu

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Instructor Contact Information

• Kai E Thomenius
• Chief Technologist, Ultrasound Biomedical
• Office KW-C300A
• GE Global Research
• Imaging Technologies
• Niskayuna, New York 12309
• Phone [phone]
• Fax [phone]
• Email thomeniu_at_crd.ge.com, thomenius_at_ecse.rpi.edu
  
• Secretary TBD