1. Clutter filtering in color flow imaging
Hans Torp Norwegian University of Science and Technology
Trondheim, Norway
Disposisjon:
Signal-model 2D -> 1D (?)
Hvorfor lineært filter? -> lineær transf., Matrise, Eks. FIR-filter
Shift invarianse
Frequency response. Advantage complex signals
Basis functions and transformation to obtain diagonal matrix
Regression filter. Linear regression (Hooks). Polynomial regression
Discrete Legendre polynomials. Show freq. Resp. basis and filter
Fourier basis, and regression filter. Fourier basis with zeropadding. How to obtain zero in freq. Response
Kahrunen-Loeven transform- generelt
Modellbasert: Gaussisk og rektang. Frekv. Respons. Adaptiv
Deteksjonsproblemet
Estimering av hastighet – bias . ML-estimering av hastighet
Computatonal complexity
General linear filter matrix. Regression filter, compare FIR
Compex/real coefficients. Adaptive filter

2. 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
Clutterfilter in Doppler/cfi, history (brief)
Signal model 2D -> 1D Doppler signal
Properties:
- linearity
-shift invariance
Performance criteria:
Frequency response
Detection
Velocity estimation
Basis types:
Fourier
Extended Fourier (spør Kjell!)
Legendre
Karuhen Leuwe
Performance advantages:
Best frequency response
Optimum detection
Disadvantages:
Bias in velocity estimation
Computational complexity
Max N FIR-filter av orden N+1
Ta med bilde av DSP-kort i System 5

3. Clutter filter in color flow imaging?
Beam k-1
Beam k
Beam k+1

4. Doppler Signal Model x = [x(1),…,x(N)]T x = c + n + b
Signal vector for each sample volume:
-0.6
-0.4
-0.2
0.2
0.4
0.6 20 40 60 80
100
Blood velocity [m/s]
Doppler spectrum [dB]
Clutter
Blood
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!
Hans Torp
NTNU, Norway

5. IIR filter with initialization
Frequency response
-80
-60
-40
-20
Steady state
Step init.
Discard first samples
Power [dB]
Projection init*
0.1
0.2
0.3
0.4
0.5
Frequency
Chebyshev order 4, N=10
*Chornoboy: Initialization for improving IIR filter response, IEEE Trans. Signal processing, 1992

6. FIR Filters å = - M k z b H ) (
Discard the first M output samples, where M is equal to the filter order
Improved amplitude response when nonlinear phase is allowed
-20
Linear phase
Power [dB]
-40
Minimum phase
-60
-80
0.1
0.2
0.3
0.4
0.5
Frequency
Frequency response, order M= 5, packet size N=10

7. Regression Filters x y c y = x - c b3 Signal space x = [x(1),…,x(N)]
Clutter space b1 b2 b3 x y c
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

8. 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 *
Matrix A
Input vector x
Output vector y
y = Ax
This form includes all IIR filters with linear initialization, FIR filters, and regression filters

9. Frequency response Linear Filters
y = Ax
Definition of frequency response function
= power output for single frequency input signal 1 Ho 2 ( w ) = Ae
; -p < w < p w N [ ] T w e = 1 e i w e i ( N - 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

10. FIR filter matrix structure
FIR filter order M=5
Packet size N=10
Output samples: N-M= 5
+ Improved clutter rejection
Increasing filter order
- Increased estimator variance
Hans Torp
NTNU, Norway

11. å Regression Filters x y c y = x - c x b I y ÷ ø ö ç è æ - = A b3
Signal space
Clutter space b1 b2 b3 x y c
Subtraction of the signal component contained in a K-dimensional clutter space:
y = x - c x b I y ÷ ø ö ç è æ - = å K i H 1 A
Choise of basis function is crucial for filter performance

12. Fourier basis functions
i*k*n/N
b (k)=1/sqrt(N)e n
n= 0,.., N-1
are orthonormal, and equally distributed in frequency

13. Fourier Regression Filters
Frequency response
DFT
Set low frequency
coefficients to zero
Inverse DFT
-20
Power [dB]
-40
-60
-80
0.1
0.2
0.3
0.4
0.5
Frequency
N=10, clutter dim.=3

14. Legendre polynom basis functions
Gram-Schmidt process to obtain
Orthonormal basis functions
-> Legendre polynomials

15. Polynomial Regression Filters
b0 =
Frequency responses, N=10
-80
-60
-40
-20
b1 =
b2 =
Power [dB]
b3 =
0.1
0.2
0.3
0.4
0.5
Frequency

16. Frequency Response comparison
-80
-60
-40
-20
Polynom regression
Power [dB]
IIR projection init.
FIR minimum phase
0.1
0.2
0.3
0.4
0.5
Frequency
Polynomial regression and IIR filter with projection initializarion
have almost identical performance, and are superior to FIR filters

17. Computational complexity
# multipications
+ additions
per packet
M=5 *
Filter matrix
Input signal vector
Output signal vector
Packet size
N=8
Full matrix
multipication:
N*N * -
Basis vector
Projection
1 basis function
2*N
y = A* x
FIR-filter
Order M
(M+1)*(N-M) 
M+1
N-M

18. 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, N=8, M=6
Matrix multipication: Msamples/sec
Projection filter, 3 basis functions: 17 Msamples/sec
FIR filter 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

19. Summary Computational complexity of clutter 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