Improvement of CT Slice Image Reconstruction Speed Using

SIMD Technology

Xingxing Wu Yi Zhang

Instructor: Prof. Yu Hen Hu

Department of Electrical & Computer EngineeringUniversity of Wisconsin, Madison

Motivation CT Slice Image Reconstruction is a very important

part which will affect the reconstructed image quality and scanning speed

CT Slice Image Reconstruction is very time-consuming

Traditional methods for speedup: Specially designed hardware Parallel algorithm running on super computer

Explore a new method: SIMD implementation

Parallel-Beam FBP Image Reconstruction Algorithm

The Algorithm consists on three parts: data rebinning:

data filtering

back-projection

Parallel-Beam FBP Image Reconstruction Algorithm

Projection:

Data Rebinning:

Data Filtering:

Data Backprojection:

dxdytyxyxftP )sincos(),()(

)sin()( DPR

dwewjwwSjtQ wtj

2)sgn(

2)(2)(

)sgn(

2)(2)( 11 wjFwwSjFtQ

ddwewwSyxf wtj

0

2)(),(

CT Slice Image Reconstruction Is Very Time Consuming

A Whole Head Spiral Scanning will generate several GB projection data

Function Profiling

0102030405060708090

time (s)

Data Rebinning Data Filtering DataBackprojection

Can FBP Algorithm Benefit from SIMD? The Algorithm has the following features:

Small, highly repetitive loops that operate on sequential arrays of integers and floating-point values

Frequent multiplies and accumulates Computation-intensive algorithms Inherently parallel operations Wide dynamic range, hence floating-point based Regular memory access patterns Data independent control flow

Analysis of Data Dynamic Range and Quantization Errors Wide Dynamic Range

Relative Error Metric

32-Bit Single-Precision Floating Point and SSE2

N

i

DFPDFPi

DFPDFPi

N

ii

yy

yyxxRE

1

2

2

1

)(

)]()[(

Updated Algorithm to Fit SIMD

Update the algorithm to eliminate some conditional branches

Reduce the on-the-fly calculations which are not suitable for the SIMD implementation

Parallel Implementation of Data Filtering In SIMD

A0 A1 A2 A3 A4 A5 A6 A7

B0 B1 B2 B3 B4 B5 B6 B7

Rebinned Data

Weight

A0*B0+A4*B4 A1*B1+A5*B5 A2*B2+A6*B6 A3*B3+A7*B7 Filtered Data

* * * * * * * *

Parallel Implementation of Backprojection in SIMD

A0 A1 A2 A3

+0.5+0.5+0.5+0.5-0.5-0.5-0.5-0.5

B0 B1 B2 B3 C0 C1 C2 C3

D0 D1 D2 D3 E0 E1 E2 E3

F0 F1 F2 F3 G0 G1 G2 G3

H0 H1 H2 H3

Index Calculation

Index

Ceil (index)Floor (index)

Filtered Data

Weight

Reconstructed Image

(fetch data)

Optimization of The Implementation

Optimize Memory Access Ensure proper alignment to prevent data split across cache line

boundary: data alignment, stack alignment, code alignment Observe store-forwarding constraints Optimize data structure layout and data locality to ensure efficient

use of 64-byte cache line size and also reduce the frequency of memory loading and storing

Use prefetching cacheability instructions control appropriately Minimize bus latency by segmenting the reads and writes into

phases Replace Branches with Logic Operations Optimize Instruction Scheduling Optimize the Parallelism

Loop Unrolling Break dependence chains

Optimization of The Implementation

Optimize Instruction Selection avoid longer latency instruction avoid instructions that unnecessarily introduce dependence-related stalls

Optimize the Floating-point Performance avoid exceeding the representable range avoid change floating-point control/status register enable flush-to-zero and DAZ mode

Improvement of Performance

0102030405060708090

time (s)

Data Rebinning Data Filtering DataBackprojection

C Implementation

SIMD Implementation

The differences of the reconstructed image pixel values between C implementation and SIMD implementation are less than 0.01