SIMD Implementation of Discrete Wavelet Transform Jake Adriaens Diana Palsetia

Outline Motivation Goal 2D Discrete Wavelet Transform Daubechies Lifting Approach Conclusion

Motivation Increasing focus on multimedia has lead new image coding called JPEG-2000 JPEG-2000 over JPEG Achieves higher compression rate Computationally more intensive Replaces low-complexity and memory efficient block DCT with Discrete Wavelet Transform

Goal Improve computation of DWT Transform Lowering memory access Align memory Apply loop transformation techniques Extracting Parallelism Compute independent data in parallel

2D Discrete Wavelet Transform Subband Decomposition of 1-D signal 2-D DWT 1-D DWT on each row followed by 1-D DWT on each column

DWT Schemes Daubechies wavelet function is passed x samples to calculate wavelet coefficient require a temporary array hence not memory efficient

DWT Schemes (continued) Lifting Scheme memory efficient compared to Daubechies Use correlation in data to remove the redundancy Original 1-D sequence is split in even and odd indexed sequence Values are iteratively modified by predict and update step s: update step d: predict step P: predict weights U: update weights

JPEG Codec Analysis using JasPer Table 1: RunTime using GNU profiler for 1792x1200 bitmap image

Approach Initial: modify JPEG-2000 to incorporate SIMD implementation using SSE2 Current: Implement C based DWT algorithm (Daubechies 4 and Daubechies 4 with lifting) Take the original algorithm and apply subword parallel functions using SSE2 instruction set Compare Speedup of original algorithm with SSE2 implementation

Conclusion DWT Superior to DCT (multi-resolution analysis) Computationally complex Implement Wavelet Transform Schemes Use SIMD instruction for optimization Compare Performance

References Daubechies D4 Wavelet Transform ubechies/index.html ubechies/index.html M. Rabbani, and R. Joshi, “An overview of JPEG 2000 still image compression standard”, Signal Processing: Image Communication, vol. 17, pp3-48, 2002 A. Shabahrami, B. Juurlink, S. Vassiliads, “Performance Comparison of SIMD Implementations of Discrete Wavelet Transform”,