This three-day course is designed is designed for engineers, scientists, technicians, implementers, and managers who need to understand basic and advanced methods of signal and image processing and analysis techniques for the measurement and imaging sciences. This course will jump start individuals who have little or no experience in the field to implement these methods, as well as provide valuable insight, new methods, and examples for those with some experience in the field.

1. Slides From ATI Professional Development Short Course
SIGNAL AND IMAGE PROCESSING AND ANALYSIS FOR
SCIENTISTS AND ENGINEERS
Instructor:
Don J . Roth, Ph.D.
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3. Who Am I
• Dr. Donald J. Roth is the Nondestructive Evaluation (NDE) Team
Lead at NASA Glenn Research Center as well as a senior research
engineer with over 27 years of experience in NDE
• His primary areas of expertise over his career include research and
development in ultrasonics, thermography, x‐ray, computed
tomography, and terahertz imaging
• Served as the deputy discipline expert in NDE for the NASA
Engineering and Safety Center.
• Heavily involved in development of NDE‐dedicated software (full
data and control system architectures, and signal and image
processing software systems)
• Dr. Roth has published many articles and several book chapters over
this period. His NDE Wave & Image Processor software is available
as a public download at https://technology.grc.nasa.gov/software/
• Dr. Roth consults privately on signal and image processing and
analysis, data visualization, NDE‐related subjects, and LabVIEW
development
2

4. Who This Course is Designed For
• This course is designed for engineers, scientists,
technicians, implementers, and managers who
need to understand current practice and next
generation signal and image processing and
analysis techniques for scientific signal processing
and imaging
• Fields where this course would be quite
applicable would be Nondestructive Evaluation,
Diagnostic Medical Imaging, Radar, Sonar,
Security, Earthquake and Acoustic Emission
studies, Digital Filtering, Spectral Analysis, and
many others 3

5. The course uses the following model for
much of the time
• Discuss Concept
• Show Interactive Software Example of
Concept
– Students get software examples on CD as part of
the course
• Show Real World / Case History Example

6. Digital Signal Processing (DSP)
• “Signal” = set of numbers
• “Signal” can be 1‐d (generally Amplitude vs. time) or 2‐d
(Image)
• Signals can originally be either Digital (Discrete) or Analog
(Continuous)
– Phonograph vs. CD Player
– Analog signals are converted to digital domain via Analog‐to‐Digital
converter
• After acquiring data, DSP answers the question: What next?
5

7. Smoothing Windows to Reduce Spectral Leakage
• Windowing reduces discontinuities
at boundary of signal thus reducing
spectral leakage
• Multiply the signal by a finite‐length x
window whose amplitude tapers
smoothly and gradually towards
zero at edges
– Changes shape of signal
• Or perform convolution of the FFT
spectrum of the original signal with =
the FFT spectrum of the window
– Changes signal’s frequency
spectrum
• Windowing
Reduces
Time Domain Frequency
Domain
Amplitude
of smearing
Multiplication Convolution
frequencies
Convolution Multiplication 6

8. Smoothing Windows Software Demo
Turn 2nd
Signal off
Turn Filter off
Select Windows,
Change wave
Types & freq
For window
comparison
7

9. Limitations of the FFT
• No information about how frequencies evolve over time
• Not suitable for analyzing impulsive signals that occur
intermittently on top of nominal signal
8

10. Advantages of Time‐Frequency Analysis
• Time‐frequency representation shows how frequency components of
a signal evolve over time
• Linear Chirp • Reversed Linear Chirp
9

11. Short‐Time Fourier Transform
• Used to characterize the
Energy Density of a signal as a
function of time and frequency
for dynamic signals
– those signals that have
frequency content changing
with time such as dispersive
signals [acoustic emission,
ultrasonic guided waves]
10

12. Short‐Time Fourier Transform Software Demo
(Note: Other methods of Joint‐Time Frequency Analysis Provide Better
Resolution as we shall see later)
11

13. Practical (Non‐ideal) Filter
• Ideal Filter has
Characteristics
– gain = 1 (0 dB) in passband (PB)
– gain = 0 (‐∞ dB) in the stopband (SB) • Non‐abrupt transition
• In practice, there is always finite
• Passband / Stopband ripple
transition region between passband
and stopband and/or ripple in both
bands
– Gain of filter changes gradually, rather
than abrupty, from 1 to 0
• dB = 20log(A0(f)/Ai(f)) describes PB
ripple and SB attenuation
– A0(f) = output amplitude at particular Stopband ripple
frequency
– Ai(f) = input amplitude at particular
frequency
– e.g. SB attenuation = ‐60 dB; (A0(f)/Ai(f))
• Ramifications of Non‐idealness:
= 0.001 =10‐3 Filtering does not work perfectly for
Signals and images
12

14. Practical Filter Software Demo
Start at 10k
Freq
Lowpass filter
Move cutoff freq
to show attenuation
and passing of sine
wave
Change to
Different
Freqs and
Filters (LP, HP)
Then try real world
Signals (HOP,
Doppler) with LP
& HP filters
13

15. Wavelet Transform 1st Level Coefficients Software Demo
Show different Wavelets at
Level 1
See what Analysis Wavelet and
Analysis Scaling Look like
Show a 2nd / 3rd data set
(blocks, noisy doppler)
(UWT
representation)
Change wavelets
Change to L1
• Note that Approx coeffs contain lower freqs and detail coeffs contain higher frequency
14

16. Wavelets for Filtering Signals Software Demo
• Wavelet Decomposition/Reconstruction Based on Frequency
Show a 2nd / 3rd data set
(blocks, noisy doppler,
And do reconstructions with
various freq bands selected)
(UWT
representation)
15

17. Wavelet / Signal Processing of
Terahertz Signals
• FS Conditioning (for terahertz signal off of ET foam)
Within Gate
• Wavelet Denoise
• 40x Amplification
• DC Subtract
16

18. Signal Analysis ‐ Feature Extraction Examples
SIMULATED VOIDS in FOAM – THz Inspection
Foam 1
Foam 1 Peak-centered gate
Foam 1
Outlier removal for
Metal
Contrast enhancement
Deeper
17

19. Acoustic Emission Signal Analysis Demo
Controls Results
Help
18

20. Model‐based Curve Fit Software Demos
19

21. Image
• Image: A spatial
representation of an object;
usually means recorded
image (egs. Of brightness /
intensity) such as video
image, digital image, or
picture.
• For the digital format, an
image can be thought of as
a collection of
measurements at different
spatial positions that form a
2d array.
20

22. Analog vs. Digital Image
• Photographic 35 film • Digital Camera Image
• Pixelation in digital image
21

23. Lookup Table Transformation Example – Linear Contrast
Expansion
• In the linear histogram of the Image Gray Values
source image, the gray‐level
intervals [0, 49] and [191, 254]
do not contain significant
information
Nearly‐Unused
• Using the following LUT grayscale
transformation, any pixel with a
value less than 49 is set to 0,
and any pixel with a value
greater than 191 is set to 255
• The interval [50, 190] expands
to [1, 254], increasing the
contrast of the regions with a Use full range of grayscale
concentration of pixels in the
gray‐level range [50, 190]
• Widening Gray Range = Contrast Expansion 22

24. Histogram Equalization Example
• Unwanted banding removed, material differences hilited, but noise added
23

25. Lookup Table with Ranging Software Demo
Change Range,
Operator,
And Image to
See effects of
Different
operations
24

26. Image Math Software Demo
25

27. Image Math – Logical Operators Example
• Grayscale Image AND Grayscale Image
Image1 Intersection of two images
=
AND
Image2
• Only way to understand is by
doing bitwise ANDing at each pixel
26

28. 2d FFT For Images
27

29. 2d FFT Software Filtering Demo
Show
Camera Man,
Lake, Alu
Inclusions,
Metal Images
(these images
have energy at
low and high
Spatial freqs;
Also Coin
With Jitter live
If so desired)
Do LP & HP
Filter using
ROI mouse draw
For metal image, can On FFT
also change
Truncation Frequency
= 10%, HP Filter)
28

30. Linear Gradient Filter Software Demo
Change Kernal#,
Kernal size, and
Then Images
To see effects
Of different
Gradient filters
29

31. Wavelets for Filtering Images
• Wavelet Decomposition/Reconstruction Based on Frequency
• LL2 reconstruction
greatly removes
jagged edges
• Ultrasonic
Image • Note how
Of Kennedy wavelet
Half Dollar coefficients above
(DWT LL2 emphasize
representation) edges & / or
topography
Note: Zoom the
Coin Image and
Reconstructed
Image To See Detail
Removal Better
30

32. Compacted Soil Phase Analysis
• Automated Analysis
• Clustering Procedure can be used for multiphase
Analysis – in this case, 3 phases
• Contrast Expand
• Crop
• From Automated Clustering Analysis,
Porosity (black phase) appears
To be ~ 0.20 areal fraction
For slice image 181 (cropped region).
This analysis also shows white
phases as 0.098 areal fraction.
31

33. Basic Morphology Operations Software Demo
Illustrate
Erosion &
Dilation
With
‘Salt&Pepper’
And ‘Iron’
Images
32

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SIGNAL AND IMAGE PROCESSING AND ANALYSIS FOR
SCIENTISTS AND ENGINEERS
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