# Improvement of CT Slice Image Reconstruction Speed Using SIMD by COi98Y

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```									Improvement of CT Slice Image
Reconstruction Speed Using
SIMD Technology

Xingxing Wu            Yi Zhang

Instructor: Prof. Yu Hen Hu

Department of Electrical & Computer Engineering
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
   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:
P (t )   f ( x, y ) ( x cos  y sin   t )dxdy

   Data Rebinning:
R ( )  P  ( D sin  )

   Data Filtering:
                 j       
Q (t )         j 2wS ( w)     sgn(w) e j 2wt dw

 2       
  j   
Q (t )  F 1 j 2wS (w)F 1  sgn(w) 
 2    
   Data Backprojection:

f ( x, y)    S (w) w e j 2wt dwd


0  
                     

CT Slice Image Reconstruction
Is Very Time Consuming

A Whole Head Spiral Scanning will generate several GB projection data
Function Profiling

90
80
70
60
50
time (s)
40
30
20
10
0
Data Rebinning   Data Filtering       Data
Backprojection
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
N

 [( xi  x)  ( yiDFP  y
DFP
)] 2
RE    i 1
N

 ( yiDFP  y
DFP 2
)
i 1

   32-Bit Single-Precision Floating Point and
SSE2
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     Rebinned Data

*        *     *      *       *     *      *     *

B0      B1    B2     B3      B4    B5     B6    B7       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
Index                  A0 A1 A2 A3       Index
Calculation
-0.5-0.5-0.5-0.5        +0.5 +0.5
+0.5 +0.5

Floor (index) B0 B1 B2 B3           C0 C1 C2 C3 Ceil (index)

(fetch data)
Filtered Data   D0 D1 D2 D3                     E0 E1 E2 E3

Weight        F0 F1 F2 F3                     G0 G1 G2 G3

Reconstructed Image               H0 H1 H2 H3
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
   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
90
80
70
60
C Implementation
50
time (s)
40                                                    SIMD Implementation
30
20
10
0
Data Rebinning Data Filtering       Data
Backprojection

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

```
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