Clutter filtering in color flow imaging

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Clutter filtering in color flow imaging
Hans TorpNorwegian University of Science and
Technology Trondheim, Norway
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Outline

• Methods for clutter filtering in color flow
  imaging
• IIR , FIR, regression filter
• General linear filtering basis functions
• Computational complexity
• Comparison FIR filter and regression filter

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Clutter filter in color flow imaging?
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Doppler Signal Model

• Signal vector for each sample volume

x x(1),,x(N)T

• Zero mean complex random process
• Three independent signal components

Signal Clutter White noise Blood
x c n b

• Typical clutter/signal level 30 80 dB
• Clutter filter stopband suppression is critical!

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IIR filter with initialization
Frequency response
Power dB
Projection init
Frequency
Chebyshev order 4, N10
Chornoboy Initialization for improving IIR
filter response, IEEE Trans. Signal processing,
1992
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FIR Filters

• Discard the first M output samples, where M is
  equal to the filter order
• Improved amplitude response when nonlinear phase
  is allowed

0
-20
Power dB
-40
-60
-80
Frequency
Frequency response, order M 5, packet size N10
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Regression Filters

• Subtraction of the signal component contained in
  a K-dimensional clutter space

x x(1),,x(N)
y x - c
Linear regression first proposed by Hooks al.
Ultrasonic imaging 1991
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Why should clutter filters be linear?

• No intermodulation between clutter and blood
  signal
• Preservation of signal power from blood
• Optimum detection (Neuman-Pearson test) includes
  a linear filter

• Any linear filter can be performed by a matrix
  multiplication of the N - dimensional signal
  vector x

y Ax

• This form includes all IIR filters with linear
  initialization, FIR filters, and regression
  filters

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Frequency response Linear Filters
y Ax

• Definition of frequency response function
• power output for single frequency input signal

1
2
Ho
w

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(
Ae
-p lt w lt p
w
N


T
w
w
-
N
i
i
)
1
(

e
e
e
1
L
w
Note 1. The output of the filter is not in
general a single frequency signal (This is only
the case for FIR-filters)
Note 2. Frequency response only well defined for
complex signals
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FIR filter matrix structure
FIR filter order M5 Packet size N10 Output
samples N-M 5
Improved clutter rejection
Increasing filter order
- Increased estimator variance
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Regression Filters

• Subtraction of the signal component contained in
  a K-dimensional clutter space

y x - c
A
Choise of basis function is crucial for filter
performance
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Fourier basis functions
ikn/N
b (k)1/sqrt(N)e
n
n 0,.., N-1 are orthonormal, and equally
distributed in frequency
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Fourier Regression Filters
Frequency response
0
-20
Power dB
-40
-60
-80
Frequency
N10, clutter dim.3
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Legendre polynom basis functions
b0
b1
b2
b3
Gram-Schmidt process to obtain Orthonormal basis
functions -gt Legendre polynomials
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Polynomial Regression Filters
b0
Frequency responses, N10
b1
Power dB
b2
b3
Frequency
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Frequency Response comparison
Power dB
Frequency
Polynomial regression and IIR filter with
projection initializarion have almost identical
performance, and are superior to FIR filters
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Computational complexity
multipications additions per packet
Full matrix multipication NN
Projection 1 basis function 2N
y A x
FIR-filter Order M (M1)(N-M)
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Real-time clutter filtering

• Data rate in color flow imaging
• 1 5 M samples/sec (complex samples)
• Processing speed test Pentium M 1.6 GHz, using
  Matlab R13, N8, M6
• Matrix multipication 13 Msamples/sec
• Projection filter, 3 basis functions 17
  Msamples/sec
• FIR filter 45 Msamples/sec
• Adaptive filters is much more computer demanding
• Double CPU-time with complex filter coefficients
• CPU-time for filter coefficient calculation
• Example Adaptive Eigenvector filter 2.1
  Msamples/sec

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SummaryComputational complexity ofclutter
filter algorithms

• Regression filters have 1 2 times longer
  computation time than FIR-filters
• A standard laptop computer is able to do
  real-time regression filtering using less than
  10 of available cpu-time
• Adaptive eigenvector filter requires 10 times
  more computation power than the regression filter