Advanced Techniques for Image Formation

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Advanced Techniques for Image Formation
Processing of Radar Data

• Dr. James Schmitz
• Veridian Engineering
• 5200 Springfield Pike, Suite 200
• Dayton, Ohio 45431

2
Overview

• Introduction
• FOPEN Radar
• FOPEN IFP Algorithm
• AFRL Distributed Center
• Parallelization of FOPEN IFP Algorithm
• Conclusions and Future Work

3
Introduction

• Veridian is a leading provider of
  information-based systems, integrated solutions
  and services to the U.S. government. The company
  specializes in mission-critical national security
  programs for the national intelligence community,
  Department of Defense, law enforcement, and other
  government agencies. Veridian operates at more
  than 50 locations, and employs more than 5,000
  computer scientists and software development
  engineers, systems analysts, scientists,
  engineers and other professionals.

4
Introduction
5
Introduction

• 2k Hz PRF, Two-Channel, XBand
• One Foot Resolution SAR
• Spotlight and Orbit Mode for data collection

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FOPEN Introduction
DARPA FOPEN Project directed by Lee Moyer
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FOPEN Introduction
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FOPEN IFP Overview

• Developed by Dr. Mehrdad Soumekh of the
  University of New York at Buffalo (Synthetic
  Aperture Radar Signal Processing, Soumekh, et
  al, Signal Processing of Wide Bandwidth and Wide
  Beamwidth P-3 SAR Data, AES, Vol. 37, No. 4,
  October 2001, pp. 1122-1141))

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RFI Suppression

• RFI caused by various television and
  communication channels
• Conventional methods place notches at RFI bands
  this result in undesirable side lobes
• Observation RFI sources exhibit some coherence
  in the slow-time domain
• Implication RFI sources appear isolated
  (peaked) in the Doppler domain
• RFI suppression can be achieved via 2D spectral
  thresholding of SAR data

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Wavefront Reconstruction

• Example bandwidth of 215-730 MHz and beamwidth
  angle of recorded data gt 50 degrees
• Processing 20,000 PRIs poses practical and
  implementation issues
• Can possess a beamwidth of over 100 degrees
  thus, the illuminated azimuth area is over 30 km.
  Prior to the Doppler FFT, an extensive
  zero-padding of the aperture is essential to
  prevent azimuth spatial aliasing
• Difficulties in HPC-based implementation
  distributed processors limited RAM corners
  turns, etc.

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Wavefront Reconstruction
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Wavefront Reconstruction

• To avoid spatial aliasing, the spatial frequency
  sampling density in the Stolt Interpolation
  should satisfy
• Range freq. sample spacing Dk_x lt 2p/Radiated
  Range
• Azimuth freq. sample spacing Dk_y lt
  2p/Radiated Azimuth
• This translates into a large image size of around
  
• Range samples 2000-3000 pixels
• Azimuth samples 1000-1500 pixels

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Wavefront Reconstruction

• Conventional (Imprudent) Solution Downsample the
  slow-time data (by a 41 factor)
• This would result in slow-time Doppler aliasing
• This would not solve the azimuth spatial aliasing
  due to the large azimuth range (if zero-padding
  is not used)
• Solution Subaperture Processing

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Subaperture Digital Spotlighting

• Analogous to spotlight SAR, use DSP to reduce the
  size of the illuminated target area (in both
  range and azimuth) this is referred to as
  Digital Spotlighting
• Digital spotlighting uses a classical azimuth
  compression method (similar to polar format
  processing) to form a crude/unfocused map of
  the target scene applies a 2D filter to extract
  SAR signature of the desired area
• A two-dimensional filtering method is used on
  motion compensated (to scene center) phase
  history (MCPH) data in range-Doppler domain
  within subapertures to extract SAR signature of a
  desired subpatch of radiated area this is called
  digital-spotlighting
• This operation reduces sizes of processed arrays
  (zero-padding in synthetic aperture domain is not
  needed), and formed image

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Subaperture Digital Spotlighting
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Outline
Phase/Range Error Model

• Phase/Range Error Model
• Dependence on radar/platform
• Dependence on target coordinates
• 2D Auto-Calibration Via a Spatially-Varying
  Filtering
• AM-PM modeling of phase-contaminated SAR signal
• Mapping of the phase error signal into the SAR
  image spectral domain
• Estimating the Spatially-Varying Filter
  Parameters Via a 2D Global Fitting and an Image
  Sharpness Measure

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Outline
Phase/Range Error Model

• PGA-based auto-focusing is not suitable for
  wide-bandwidth wide-beamwidth SAR
• 2D in-scene target auto-calibration is feasible
  not robust
• A range error-based (model-based) 2D
  auto-calibration, incorporating GPS errors, radar
  phase imperfections and elevation variations, is
  developed
• Implementation A 2D spectral filter subpatch
  entropy minimization global fitting

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Phase/Range Error Model

• Radar Electronics Variations and/or
  imperfections of the radar electronics over time
  results in range/phase errors these include
• Range gate slip that results in a slow-time
  (aspect angle) dependent range error
• Imperfections in the generated chirp signal
  (non-linear instantaneous frequency) results in
  a slow-time varying and spatially-varying (in
  target domain) range error
• Imperfections in the radar beam pattern results
  in a slow-time varying and spatially-varying
  range error

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Phase/Range Error Model

• Platform GPS/INS errors result in a slow-time
  varying and spatially-varying range error
• Target Coordinates Variations in the elevation
  of the imaging scene result in a slow-time
  varying and spatially-varying range error
• The above-mentioned phase/range errors could be
  viewed as a (relatively) slow-fluctuating AM
  phase signal that modulates the SAR spherical PM
  signal
• The AM signal depends on the target slant-range
  and azimuth coordinates (x,y) as well as the
  SAR signal measurement domain (w,u)
• Phase of the AM signal is 2k r_e (x,y,u) ,
  where r_e (x,y,u) is the range error

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Spatially-Varying Filtering

• Using the Fourier properties of AM-PM signals and
  SAR Stolt mapping, the phase error AM signal is
  mapped into the target spectral domain (k_x,k_y)
  via
• 2k sqrt (k_x2k_y2)
• arctan (y-u)/x arctan (k_y/k_x)
• Ref. Soumekh, SAR Signal Processing, Chap 2
• Thus, 2D calibration with respect to the phase
  error AM signal can be achieved via a
  spatially-varying filtering on the formed SAR
  image

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Spatially-Varying Filtering

• A quadratic approximation to this filter has been
  used to compensate for variations in elevation of
  imaging scene
• The approximation-based quadratic filter is not
  suitable for wide-bandwidth wide-beamwidth SAR
  systems the user may be forced to lowpass filter
  the image in range and azimuth
• At a given point (x,y) in the formed image, the
  range error is modeled as a third order Fourier
  series function of the angular Doppler domain
• arctan (k_y/k_x)
• The (seven) coefficients of the Fourier series
  are estimated in small patches (500 m by 500 m)
  using a sharpness measure, e.g., minimum entropy
  (min-entr), maximum standard deviation (max-std),
  etc.

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Distributed Center

• The AFRL/SN Embedded Distributed Center is a high
  performance computer
• center funded by the DoD High Performance
  Computing Modernization Program and
• the Air Force Research Laboratory Sensors
  Directorate (AFRL/SN). The center was
• established to enhance research,development, and
  engineering capabilities through
• the use of state-of-the-art embedded high
  performance computing resources, support
• compute and visualization tools, and high-speed
  networking.
• The Embedded Distributed Center offers DoD users
  these unique features
• Embedded Compute Platform. Provides either an
  unclassified system offering
• 64 processors, with 205 gigaflops or a classified
  system with 96 processors, with
• 307 gigaflops of embedded computing power
  connected to the Defense
• Research Engineering Network (DREN).
• Multi-Level Restricted Access. Provides
  unclassified and classified compute platforms.
• Embedded Prototype/Test Site. Quickly transitions
  embedded research to leading-edge
• HPC field-ready platforms.
• Directly Supports DoD Operations. Supports the
  Signal and Image Processing
• Computational Technology Area.

 
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Distributed Center
Hardware Resources
Mercury MP-510 300 MHz Sun processor Front end 64
- 400MHz PowerPC G4 Processors 128mb per CPU 8GB
additional shared memory E3500 Development
System 2 400MHz processors 2 GB RAM 54 GB user
disk space (NFS mounted to Mercury)

• Software Resources Programming Tools
• C C compilers
• MPI and Mercury PAS parallel communication
  libraries
• MATLAB RTExpress
• Vector Signal Image Processing Library (VSIPL)
• Scientific Algorithm Library (SAL)
• MULTI IDE visual project management, programming
  debugging environment

 
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FOPEN IFP Computations

• Charter is to speed up formation process for a
  single image
• Autofocus parameter estimation takes the longest
  by far (100 hours in Matlab)
• Autofocus is composed of small discrete steps
  during parameter estimation
• These two factors make it a no-brainer to focus
  on.
• Algorithm ported to C and Distributed center by
  Brett Keaffaber and Jeremy Gwinnup of Veridian

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Autofocus Parallelization Overview

• Each worker node works on a subsection of the
  image
• One controller node directs workers to process a
  patch
• Up to 63 patches can be processed at once on
  hardware.
• Leverage native vector libraries to speed up
  tasks.
• Approx 8000 2D FFT operations performed per patch
• Iterative process clock speed dependant.

Basic Divide and Conquer!
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Autofocus Parallelization Results Issues

• Results

• Memory Consumption
• Need to fit individual pieces of the algorithm
  into 100MB of heap or less.
• Some parts of the algorithm need 800MB of
  resident memory (matlab version) to run.

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Conclusions Future Work

• Preliminary stages of parallelization of the code
• Have accomplished significant speedup in the
  algorithm using a brute-force approach to
  parallelization
• Continue to parallelize other parts of the
  process
• Gains can be made in deskewing the data and
  digital spotlighting