Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time...
Transcript of Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time...
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Chapter 6: Real-Time Image Formation
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display
B, M, Doppler image
processingDoppler
processing
digital receive beamformer
beamformercontrol
digital transmit beamformer
high voltage
amplifierDAC
system controlkeyboard
ADCvariable
gain
T/R switch
arraybody
All digital
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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
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OR
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Transmit Waveform• Characteristics of transmit waveforms.
0 2 4 6 8-6 0
-4 0
-2 0
0
-2 -1 0 1 2-1
0
1
MHz
dBN
orm
aliz
ed
Am
plitu
de
Spectra
Waveforms
µs
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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.
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Generic Receiver
beam former
filtering (pre-detection)
envelope detection
filtering(post-detection)
mapping and other processing
scan conversion
display
adaptive controls
A/D
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Pre-detection Filtering
Z
t
X
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Pre-detection Filtering• Pulse shaping. (Z)• Temporal filtering. (t)• Beam shaping. (X)
– Selection of frequency range. (Z X)
– Correction of focusing errors. (X X’)B xz T x z Rx z A d( ,) ( , ,)( , ,)()′ = ′ ′∫ ω ω ω ω
|C(x)|
|p(x’,z)|
-a a1
2a
λ/2ax'/z
F.T.
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Pulse-echo effective apertures• 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
−
= 0
2 112|)(|)( RR
jkx
exCxCFor C.W.
DynTx DynRx
0
0.5
1
0
0.5
1DynRx
1FixedRx
0510
0510
R=Ro
R≠Ro
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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.
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Envelope Detection
• Demodulation based:
{ }S t At ft Atej ft( ) ( )cos Re ()= =2 0
2 0π π
{ }A t LPFSt f( ) ( )cos= 2 0π
D t absAt( ) ( ())=rf signal
envelop
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Envelope Detection
• Hilbert Transform
{ }{ }( )
S tjHT St Ate
D t absSt jHT St
j ft( ) .. ( ) ( )
( ) ( ) .. ( )/
+ ⋅ =
= + ⋅
2
2
2 0π
ff0-f0
ff0
-f0
ff0t
tht
fjfHT
π1)(
)sgn()(
−=
−=
H.T.
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Beam Former Design
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Implementaiton of Beam Formation
• Delay is simply based on geometry.• Weighting (a.k.a. apodization) strongly
depends on the specific approach.
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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.
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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 λ=
Ra
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Phased Array Imaging
Rcx
cxRxt ii
irx 2cossin),,(
22 θθθ +−=
Transducer
Delay
Tx
Rx
θ
Rx
SymmetrySymmetry
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Dynamic Focusing
• Dynamic-focusing obtains better image quality but implementation is more complicated.
Fix
DynamicDelay
R
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Focusing Architecture
summ
ation
1
N
delay line
delay line
delay controller
transducer array
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Delay Pattern
Delay
Timen0
k0
τθθ∆=+−= n
Rctx
ctxroundk
s
i
s
in )
2cossin(
22
• Delays are quantized by sampling-period ts.
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Missing Samples
TimeTime
DelayDelay DelayDelay--Change Change
BeamformerBeamformer
t2
Human Human BodyBody
t1
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Beam Formation ∆τ ∆τ∆τ
delay controller
input
output
n t n tx
c t ti( ) ( )cos
1 2
2 2
21 2
11 1
− = = −
θτ∆
n tx
c
x
c ti i( )sin cos
≈ − +θ
τθ
τ∆ ∆
2 2
2
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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.
∆∆τ θπ
= ≤2
1
320 0f f
2 32 1125π/ .≈ o
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Delay Quantization
• The delay quantization error can be viewed as the phase error of the phasors.
∑−
=
=1
0)cos(
N
nnA φ
∑−
=
=
1
0
22
2N
nA nd
dAφσφ
σ
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Delay Quantization
21sin2 =φ
12
222 φσσ φφ
∆==
n
NN
A241
24
22 <∆⇒<
∆⋅= φφσ
• N=128, 16 quantization steps per cycles are required.• In general, 32 and 64 times the center frequency is used.
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Beam Formation - Delay
element i ADC interpolation digital delay summ
atio n
• 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.
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Beam Formation - RF
• Interpolation by 2:
Z-1
Z-1
MU
X
1/2
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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
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Autonomous Delay ControlAutonomous vs. Centralized
A=n0+1−φ∆n=1j=1
A<=0?
A=A+∆n+n0j=j+1
A=A+j−φ∆n=∆n+1 N bump
n0 n1
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Beam Formation - BB
A(t-τ)cos2πf0(t-τ)
A(t-τ)cos2πf0(t-τ)e-j2πfdt
magnitude
ff0-fd-f0-fd
ff0-fd
LPF(A(t-τ)cos2πf0(t-τ)e-j2πfdt)
ff0-f0
rf
baseband
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Beam Formation - BB
{ }
( )
I LPFAt f t ft
LPFA t
f ft f f f t f
A tf ft f
d
d d d d
d d
= − −
=−
− − − + + − +
=−
− − −
( )cos ( )cos
( )cos(( )( ) )cos(( )( ) )
( )cos(( )( ) )
τ π τ π
τ π τ τ π τ τ
τ π τ τ
2 2
22 2
22
0
0 0
0
{ }
( )
Q LPF At f t ft
LPFA t
f ft f f f t f
A tf ft f
d
d d d d
d d
= − − −
=−
− − − − + − +
=−
− − −
( )cos ( )sin
( )sin(( )( ) )sin(( )( ) )
( )sin(( )( ) )
τ π τ π
τ π τ τ π τ τ
τ π τ τ
2 2
22 2
22
0
0 0
0
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Beam Formation - BBelement i A DC demod/
LPFtime delay/
phase rotation
I Q
I
Q
BBtA t
e ej ft j fd( )( ) ( )=− − −τ π τ π τ
22 2∆
O tA t
e ei i
i
Nj ft jfi i d i i( )
( ) ( ) ( )=− + ′
=
− + ′ − −∑τ τ π τ τ π τ θ
21
2 2∆
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Beam Formation - BBelement i A DC demod/
LPFtime delay/
phase rotation
I Q
I
Q
∆∆∆ ∆
τ θπ
= ≤2
1
32f f
• The coarse time delay is applied at a low clock frequency, the fine phase needs to be rotated accurately (e.g., by CORDIC).
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∆Σ-Based Beamformers
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Why ∆Σ ?
• High Delay Resolution -- 32 f0 (requires interpolation)
• Multi-Bit Bus
Current ProblemsCurrent Problems
• High Sampling Rate -- No Interpolation Required
• Single-Bit Bus -- Suitable for Beamformers with Large Channel-Count
∆Σ∆Σ AdvantagesAdvantages
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Conventional vs. ∆Σ
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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.
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Advantages of ∆Σ 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.
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Block-Diagram of the ∆Σ ModulatorQuantizer
D/A
_yx Integrator
eLPF ↓ x*
Single-Bit
• Over-Sampling • Noise-Shaping
• Reconstruction
• The SNR of a 32 f0, 2nd-order, low-passed ∆Σ modulator is about 40dB.
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Property of a ∆Σ 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*
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A Delta-Sigma Beamformer
Σ
Transducer TGC ∆Σ A/DShift-Register
Delay-Controller / MUX
Transducer TGC
Shift-Register
Delay-Controller / MUX
. . .
SingleSingle--BitBit
LPF
∆Σ A/D
• No Interpolation• Single-Bit Bus
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A
-70
-60
-50
-40
-30
-20
-10
0B
D C
Results
A. RF
B. Repeat
C. Insert-Zero
D. Sym-Hold
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Cross-Section-Views of Peak 3
-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)
![Page 45: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/45.jpg)
Scan Conversion
• Acquired data may not be on the display grid.
Acquired grid
Display grid
![Page 46: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/46.jpg)
Scan Conversion
sinθ
R
x
y
acquired converted
![Page 47: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/47.jpg)
Scan Conversion
original gridraster gridacquired 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
![Page 48: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/48.jpg)
Moiré Pattern
![Page 49: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/49.jpg)
Scan Conversion
original data buffer
interpolation display buffer
addresses and coefficients generation
display
![Page 50: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/50.jpg)
Temporal Resolution (Frame Rate)
• Frame rate=1/Frame time.• Frame time=number of lines * line time.• Line time=(2*maximum depth)/sound
velocity.• Sound velocity is around 1540 m/s.• High frame rate is required for real-time
imaging.
![Page 51: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/51.jpg)
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.
![Page 52: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/52.jpg)
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.
![Page 53: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/53.jpg)
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.
![Page 54: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/54.jpg)
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
![Page 55: Chapter 6: Real-Time Image Formationcc.ee.ntu.edu.tw/~ultrasound/€¦ · Chapter 6: Real-Time Image Formation . display B, M, Doppler image ... D/A HV Amp Transducer Array Control.](https://reader033.fdocuments.us/reader033/viewer/2022051809/601133a21f0b1623fc4f8ff4/html5/thumbnails/55.jpg)
Parallel Beamformation
• Simultaneously transmit multiple beams.• Interference between beams, spatial
ambiguity.
t1/r1 t2/r2
t1/r1t2/r2