Signal & Image Processing & Analysis For Scientists and - ATI
Transcript of Signal & Image Processing & Analysis For Scientists and - ATI
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www.ATIcourses.com
Boost Your Skills with On-Site Courses Tailored to Your Needs The Applied Technology Institute specializes in training programs for technical professionals. Our courses keep you current in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highly competitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presented on-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our training increases effectiveness and productivity. Learn from the proven best. For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.asp For Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm
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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
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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
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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
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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?
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Smoothing Windows to Reduce Spectral Leakage• Windowing reduces discontinuities
at boundary of signal thus reducing spectral leakage
• Multiply the signal by a finite‐length 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
• WindowingReducesAmplitudeof smearingfrequencies
Time Domain Frequency Domain
Multiplication Convolution
Convolution Multiplication
x
=
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Smoothing Windows Software Demo
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Turn 2ndSignal off
Turn Filter off
Select Windows,Change waveTypes & freqFor windowcomparison
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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
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Advantages of Time‐Frequency Analysis• Time‐frequency representation shows how frequency components of
a signal evolve over time
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• Linear Chirp • Reversed Linear Chirp
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Short‐Time Fourier Transform• Used to characterize the
Energy Density of a signal as a function of time and frequencyfor dynamic signals – those signals that have
frequency content changing with time such as dispersive signals [acoustic emission, ultrasonic guided waves]
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Short‐Time Fourier Transform Software Demo
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(Note: Other methods of Joint‐Time Frequency Analysis Provide BetterResolution as we shall see later)
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Practical (Non‐ideal) Filter Characteristics• Ideal Filter has
– gain = 1 (0 dB) in passband (PB) – gain = 0 (‐∞ dB) in the stopband (SB)
• In practice, there is always finite 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 frequency
– Ai(f) = input amplitude at particular frequency
– e.g. SB attenuation = ‐60 dB; (A0(f)/Ai(f)) = 0.001 =10‐3
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Stopband ripple
• Non‐abrupt transition
• Passband / Stopband ripple
• Ramifications of Non‐idealness:Filtering does not work perfectly for Signals and images
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Practical Filter Software Demo
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Start at 10kFreq
Lowpass filter
Move cutoff freqto show attenuationand passing of sinewave
Change toDifferentFreqs andFilters (LP, HP)
Then try real worldSignals (HOP, Doppler) with LP& HP filters
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Wavelet Transform 1st Level Coefficients Software Demo
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• Note that Approx coeffs contain lower freqs and detail coeffs contain higher frequency
Show different Wavelets atLevel 1
See what Analysis Wavelet andAnalysis Scaling Look like
Show a 2nd / 3rd data set(blocks, noisy doppler)
Change to L1
(UWTrepresentation)
Change wavelets
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Wavelets for Filtering Signals Software Demo
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• Wavelet Decomposition/Reconstruction Based on Frequency
(UWTrepresentation)
Show a 2nd / 3rd data set(blocks, noisy doppler,And do reconstructions with various freq bands selected)
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Wavelet / Signal Processing ofTerahertz Signals
• FS Conditioning (for terahertz signal off of ET foam)
Within Gate• Wavelet Denoise• 40x Amplification• DC Subtract
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Signal Analysis ‐ Feature Extraction ExamplesSIMULATED VOIDS in FOAM – THz Inspection
Foam 1
Foam 1
Foam 1
Metal
Peak-centered gate
Outlier removal forContrast enhancement
Deeper
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Acoustic Emission Signal Analysis Demo
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ResultsControls
Help
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Model‐based Curve Fit Software Demos
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• 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.
Image
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• Pixelation in digital image
• Digital Camera Image• Photographic 35 film
Analog vs. Digital Image
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Lookup Table Transformation Example – Linear Contrast Expansion
• In the linear histogram of the source image, the gray‐level intervals [0, 49] and [191, 254] do not contain significant information
• Using the following LUT 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 concentration of pixels in the gray‐level range [50, 190]
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Image Gray Values
Nearly‐Unusedgrayscale
Use full range of grayscale
• Widening Gray Range = Contrast Expansion
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Histogram Equalization Example
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• Unwanted banding removed, material differences hilited, but noise added
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Lookup Table with Ranging Software Demo
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Change Range,Operator,And Image toSee effects ofDifferentoperations
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Image Math Software Demo
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Image Math – Logical Operators Example
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Image1
Image2
AND=
Intersection of two images
• Grayscale Image AND Grayscale Image
• Only way to understand is bydoing bitwise ANDing at each pixel
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2d FFT For Images
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2d FFT Software Filtering Demo
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ShowCamera Man,Lake, AluInclusions,Metal Images(these imageshave energy atlow and highSpatial freqs;Also CoinWith Jitter liveIf so desired)
Do LP & HPFilter using ROI mouse drawOn FFTFor metal image, can
also change Truncation Frequency= 10%, HP Filter)
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Linear Gradient Filter Software Demo
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Change Kernal#,Kernal size, andThen ImagesTo see effectsOf differentGradient filters
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Wavelets for Filtering Images• Wavelet Decomposition/Reconstruction Based on Frequency
• Note how wavelet coefficients above LL2 emphasize edges & / or topography
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• LL2 reconstruction greatly removes jagged edges
(DWTrepresentation)
Note: Zoom theCoin Image andReconstructed Image To See DetailRemoval Better
• UltrasonicImageOf KennedyHalf Dollar
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Compacted Soil Phase Analysis
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• Contrast Expand• Crop
• From Automated Clustering Analysis,Porosity (black phase) appearsTo be ~ 0.20 areal fractionFor slice image 181 (cropped region).This analysis also shows white phases as 0.098 areal fraction.
• Automated Analysis• Clustering Procedure can be used for multiphaseAnalysis – in this case, 3 phases
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Basic Morphology Operations Software Demo
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IllustrateErosion & DilationWith‘Salt&Pepper’And ‘Iron’Images
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