chapter 6: real-time image formation. display b, m, doppler image processing doppler processing...
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Chapter 6: Real-Time Image Formation
display
B, M, Doppler image
processing
Doppler processing
digital receive beamformer
system controlkeyboard
beamformer control
digital transmit beamformer DAC
high voltage
amplifier
ADCvariable
gain
T/R switch
array
body
All digital
Generic Ultrasonic Imaging System
• Transmitter:– Arbitrary waveform.– Programmable transmit voltage.– Arbitrary firing sequence.– Programmable apodization, delay control and
frequency control.
Digital Waveform Generator
D/A HV Amp Transducer Array
Control
OR
Transmit Waveform• Characteristics of transmit waveforms.
0 2 4 6 8-60
-40
-20
0
-2 -1 0 1 2-1
0
1
MHz
dBN
orm
aliz
ed
Am
plitu
de
Spectra
Waveforms
s
Generic Ultrasonic Imaging System
• Receiver:– Programmable apodization, delay control and
frequency control.– Arbitrary receive direction.
• Image processing:– Pre-detection filtering.– Post-detection filtering.
• Full gain correction: TGC, analog and digital.• Scan converter: various scan format.
Generic Receiver
beam former
filtering (pre-detection)
envelope detection
filtering(post-detection)
mapping and other processing
scan conversion
display
adaptive controls
A/D
Pre-detection Filtering
Z
t
X
Pre-detection Filtering
• Pulse shaping. (Z)
• Temporal filtering. (t)
• Beam shaping. (X)– Selection of frequency range. (ZX)
– Correction of focusing errors. (XX’)
B x z T x z R x z A d( , ) ( , , ) ( , , ) ( )
|C(x)|
|p(x’,z)|
-a a1
2a
/2ax'/z
F.T.
Pulse-echo effective apertures
0
2 11
2|)(|)( RR
jkx
exCxC DynTx DynRx
0
0.5
1
0
0.5
1DynRx
1FixedRx
0
5
10
0
5
10
• The pulse-echo beam pattern is the multiplication of the transmit beam and the receive beam
• The pulse-echo effective aperture is the convolution of transmit and receive apertures
For C.W.
R=Ro
R≠Ro
Post-Detection Filtering
• Data re-sampling (Acoustic Display).• Speckle reduction (incoherent averaging).• Feature enhancement.• Aesthetics.• Post-processing:
– Re-mapping (gray scale and color).– Digital gain.
Envelope Detection
• Demodulation based:
S t A t f t A t ej f t( ) ( )cos Re ( ) 2 02 0
A t LPF S t f( ) ( )cos 2 0
D t abs A t( ) ( ( ))rf signal
envelop
Envelope Detection
• Hilbert Transform
S t j H T S t A t e
D t abs S t j H T S t
j f t( ) . . ( ) ( )
( ) ( ) . . ( ) /
2
2
2 0
ff0-f0
ff0
-f0
ff0H.T.
ttht
fjfHT
1
)(
)sgn()(
Beam Former Design
Implementaiton of Beam Formation
• Delay is simply based on geometry.
• Weighting (a.k.a. apodization) strongly depends on the specific approach.
Beam Formation - Delay
• Delay is based on geometry. For simplicity, a constant sound velocity and straight line propagation are assumed. Multiple reflection is also ignored.
• In diagnostic ultrasound, we are almost always in the near field. Therefore, range focusing is necessary.
Beam Formation - Delay
• Near field / far field crossover occurs when f#=aperture size/wavelength.
• The crossover also corresponds to the point where the phase error across the aperture becomes significant (destructive).
82
2
R
a
Phased Array Imaging
Rc
x
c
xRxt ii
irx 2
cossin),,(
22 SymmetrySymmetry
Transducer
Delay
Tx
Rx
Rx
Dynamic Focusing
Delay
R
Fix
Dynamic
• Dynamic-focusing obtains better image quality but implementation is more complicated.
Focusing Architecture
summ
ation
1
N
delay line
delay line
delay controller
transducer array
Delay Pattern
Delay
Timen0
k0
n
Rct
x
ct
xroundk
s
i
s
in )
2
cossin(
22
• Delays are quantized by sampling-period ts.
Missing Samples
TimeTime
DelayDelay Delay-Change Delay-Change
BeamformerBeamformerHuman Human BodyBody
t1t2
Beam Formation
n t n tx
c t ti( ) ( )cos
1 2
2 2
21 2
11 1
n tx
c
x
c ti i( )sin cos
2 2
2
delay controller
input
output
Beam Formation - Delay
• The sampling frequency for fine focusing quality needs to be over 32*f0(>> Nyquist).
• Interpolation is essential in a digital system and can be done in RF, IF or BB.
2
1320 0f f
2 32 1125 / . o
Delay Quantization
• The delay quantization error can be viewed as the phase error of the phasors.
1
0
)cos(N
nnA
1
0
2
2
2N
nA nd
dA
Delay Quantization
• N=128, 16 quantization steps per cycles are required.• In general, 32 and 64 times the center frequency is
used.
2
1sin 2
12
222
n
N
NA
241
24
22
Beam Formation - Delay
• RF beamformer requires either a clock well over 100MHz, or a large number of real-time computations.
• BB beamformer processes data at a low clock frequency at the price of complex signal processing.
element i ADC interpolation digital delay summ
ation
Beam Formation - RF
• Interpolation by 2:
Z-1
Z-1
MU
X
1/2
Beam Formation - RF
• General filtering architecture (interpolation by m):
Delay
Filter 1
Filter 2
Filter m-1
MU
X
Fine delay control
FIFO
Coarse delay control
Autonomous Delay Control
n0 n1
A=n0+1n=1j=1
A<=0?
A=A+n+n0
j=j+1
A=A+jn=n+1 N bump
Autonomous vs. Centralized
Beam Formation - BB
A(t-)cos2f0(t-)
A(t-)cos2f0(t-)e-j2fdt
magnitude
ff0-fd-f0-fd
ff0-fd
LPF(A(t-)cos2f0(t-)e-j2fdt)
ff0-f0
rf
baseband
Beam Formation - BB
I LPF A t f t f t
LPFA t
f f t f f f t f
A tf f t f
d
d d d d
d d
( )cos ( )cos
( )cos (( )( ) ) cos (( )( ) )
( )cos (( )( ) )
2 2
22 2
22
0
0 0
0
Q LPF A t f t f t
LPFA t
f f t f f f t f
A tf f t f
d
d d d d
d d
( )cos ( )sin
( )sin (( )( ) ) sin (( )( ) )
( )sin (( )( ) )
2 2
22 2
22
0
0 0
0
Beam Formation - BB
BB tA t
e ej f t j fd( )( ) ( )
22 2
element i A DC demod/LPF
time delay/phase rotation
I Q
I
Q
O tA t
e ei i
i
Nj f t j fi i d i i( )
( ) ( ) ( )
21
2 2
Beam Formation - BB
element i A DC demod/LPF
time delay/phase rotation
I Q
I
Q
• The coarse time delay is applied at a low clock frequency, the fine phase needs to be rotated accurately (e.g., by CORDIC).
2
132f f
-Based Beamformers
Why ?
• High Delay Resolution -- 32 f0 (requires interpolation)
• Multi-Bit Bus
• High Sampling Rate -- No Interpolation Required
• Single-Bit Bus -- Suitable for Beamformers with Large Channel-Count
AdvantagesAdvantages
Current ProblemsCurrent Problems
Conventional vs.
Advantages of Over-Sampling
• Noise averaging.
• For every doubling of the sampling rate, it is equivalent to an additional 0.5 bit quantization.
• Less requirements for delay interpolation.
• Conventional A/D not ideal for single-bit applications.
Advantages of Beamformers
• Noise shaping.
• Single-bit vs. multi-bits.
• Simple delay circuitry.
• Integration with A/D and signal processing.
• For hand-held or large channel count devices.
Block-Diagram of the Modulator
Quantizer
D/A
_yx
Integrator
e
LPF x*
Single-Bit
• Over-Sampling • Noise-Shaping
• Reconstruction
• The SNR of a 32 f0, 2nd-order, low-passed modulator is about 40dB.
Property of a Modulator
0 0.5-60
-40
-20
0
0 0.5-60
-40
-20
0
0 0.1 0.2 0.3 0.4 0.5-60
-40
-20
0dB
Frequency
1 1024-0.5
0
0.5
1 1024-1
0
1
1 256 512 768 1024-0.5
0
0.5
Sample
WaveformWaveform SpectrumSpectrum
xx
yy
x*x*
A Delta-Sigma Beamformer
• No Interpolation
• Single-Bit Bus
Σ
Transducer TGC A/D
Shift-Register
Delay-Controller / MUX
Transducer TGC
Shift-Register
Delay-Controller / MUX
. . .
Single-BitSingle-Bit
LPF
A/D
A. RF
B. Repeat
C. Insert-Zero
D. Sym-Hold
A
-70
-60
-50
-40
-30
-20
-10
0B
D C
Results
-20 -10 0 10 20
-80
-60
-40
-20
0RF
dB
-20 -10 0 10 20
-80
-60
-40
-20
0Repeat
dB
-20 -10 0 10 20
-80
-60
-40
-20
0Insert-Zero
dB
Width (mm)-20 -10 0 10 20
-80
-60
-40
-20
0Symmetric-Hold
dB
Width (mm)
Cross-Section-Views of Peak 3
Scan Conversion
• Acquired data may not be on the display grid.
Acquired grid
Display grid
Scan Conversion
sin
R
x
y
acquired converted
Scan Conversion
original grid
raster grid
acquired data
display pixel
a(i,j)
a(i,j+1)
a(i+1,j)
a(i+1,j+1)
p
)1,1(
)1,(),1(),(),(
1,1,,
1,,,,1,,,,,
jiac
jiacjiacjiacnmp
jinm
jinmjinmjinm
Moiré Pattern
Scan Conversion
original data buffer
interpolation display buffer
addresses and coefficients generation
display
Temporal Resolution (Frame Rate)
• Frame rate=1/Frame time.• Frame time=number of lines * line time.• Line time=(2*maximum depth)/sound vel
ocity.• Sound velocity is around 1540 m/s.• High frame rate is required for real-time i
maging.
Temporal Resolution
• Display standard: NTSC: 30 Hz. PAL: 25 Hz (2:1 interlace). 24 Hz for movie.
• The actual acoustic frame rate may be higher or lower. But should be high enough to have minimal flickering.
• Essence of real-time imaging: direct interaction.
Temporal Resolution
• For an actual frame rate lower than 30 Hz, interpolation is used.
• For an actual frame rate higher than 30 Hz, information can be displayed during playback.
• Even at 30 Hz, it is still possibly undersampling.
Temporal Resolution
• B-mode vs. Doppler.
• Acoustic power: peak vs. average.
• Increasing frame rate:– Smaller depth and width.– Less flow samples.– Wider beam width.– Parallel beam formation.
Parallel Beamformation
• Simultaneously receive multiple beams.• Correlation between beams, spatial ambiguity.• Require duplicate hardware (higher cost) or time
sharing (reduced processing time and axial resolution).
r1 r2t
t
r1 r2
Parallel Beamformation
• Simultaneously transmit multiple beams.
• Interference between beams, spatial ambiguity.
t1/r1 t2/r2
t1/r1
t2/r2