1. The Fast Curvelet Transform
Very Fast
The Fast Curvelet Transform
Brian Eriksson

2. Curvelet Transform
Coefficient Value = 0
Zero

3. Coefficient Value << 1
Curvelet Transform
Coefficient Value << 1
Very Small

4. Coefficient Value >> 1
Curvelet Transform
Coefficient Value >> 1
Very Large

5. Algorithm Construction
Take FFT of image
Divide into coronization segments

6. Algorithm Construction
For each segment, wrap around the origin
Take Inverse FFT

7. Optimization Strategies
Double Precision to Single Precision
Loop Unrolling
Subword Parallel Instructions
Integer Instructions – MMX Intrinsics
Wrapping Indices
Floating Point Instructions – SSE1 Intrinsics
Corona Filtering
Normalization

8. Optimization Costs Larger Code Original = 874 lines
Optimized = 2660 lines
Time
Double to Single Precision Error

9. Results Matlab Version Original C Version SSE/MMX C Version 7.551
Total transform (forward+inverse) time in seconds:
Matlab Version
Original C Version
SSE/MMX C Version
7.551
5.691
3.201