Computed Tomography Reconstruction

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Computed Tomography Reconstruction
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Background

• FDK Algorithm on planar detector array
• Double precision not used
• 512x512x370 volume
• 750 projection slices 366x304

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Key Optimizations

• Sine/cosine in constant memory
• -use_fast_math
• Computation Reduction
• Block size
• Texture memory
• Storage
• Interpolation

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-use_fast_math

• Reduction in float division time
• __fdividef(x,y)
• Problematic if
• 2126 lt y lt 2128
• x 8
• Output is identical
• Uses more registers

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Computation Reduction

• Value of a does not vary in z
• Compute multiple output voxels in each thread to
  reuse a
• Tradeoff Additional register usage for fewer
  overall computation

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Computation Reduction cont.
for x for y for p calculate a
for z calculate b
sum(z) proj(a,b) end end
for z voxel(x,y,z) sum(z)
end end end

• for x
• for y
• for z
• for p
• calculate a
• calculate b
• sum proj(a,b)
• end
• voxel(x,y,z) sum
• end
• end
• end

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Slices per Thread
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Block size
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Texture Memory

• Filtered projections stored in 2D texture memory
• Lack of 3D textures forced tiling in host
• Fetching from texture memory is faster than
  global memory due to caching
• Takes advantage of 2D locality because threads in
  a block access projection data in close proximity

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Texture Memory

• Interpolation
• Linear filtering
• Fewer registers
• Less computation
• Fewer memory accesses

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Interpolation
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Verification

• Visual verification
• Difference images
• Intensity profiles
• RMS error (when appropriate)

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Visual Verification

• Texture filtering
• Difference Images
• Manual filtering

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Performance
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OP Rate

• Theoretical OP rate
• Calculated OP rate

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Extension Micro CT

• 1000x1000x466 volume (1.77GB)
• 321 projection slices 1000x520 (636MB)
• Input Output does not fit into device memory
• Scheme Place all projection data into texture
  memory and compute 16 slices at a time

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Improvements and Future Work

• 3D Texture Memory
• Characterize bottleneck
• Need better documentation
• maxrregcount
• Texture cache
• Big data
• Find balance between amount of projection data in
  memory vs slices computed per kernel

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Any Thoughts?
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Questions?
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Appendix - Gold Code (no SSE)
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Fast Math