Chapter 6: Real-Time Image Formationhome.ee.ntu.edu.tw/classnotes/us1/CHAPTER6.pdf · Chapter 6:...
Transcript of Chapter 6: Real-Time Image Formationhome.ee.ntu.edu.tw/classnotes/us1/CHAPTER6.pdf · Chapter 6:...
Chapter 6: Real-Time Image Formation
display
B, M, Doppler image
processing
Doppler processing
digital receive beamformer
system control keyboard
beamformer control
digital transmit beamformer DAC
high voltage
amplifier
ADC variable
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
dB
Nor
mal
ized
A
mpl
itude
Spectra
Waveforms
µs
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. (ZàX’)
– Correction of focusing errors. (XàX’) |C(x)|
|p(x’,z)|
-a a 1
2a
λ/2a x'/z
F.T.
Pulse-echo effective apertures
DynTx DynRx"
0"
0.5"
1"
0"
0.5"
1"DynRx"
1"FixedRx"
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 à Display). • Speckle reduction (incoherent averaging). • Feature enhancement. • Aesthetics. • Post-processing:
– Re-mapping (gray scale and color). – Digital gain.
Envelope Detection
• Demodulation based:
rf signal"
envelop
Envelope Detection
• Hilbert Transform
f f0 -f0
f f0
-f0
f f0 H.T.
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).
Phased Array Imaging
Symmetry
Transducer
Delay
Tx
Rx
θ
R x
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
Time n0
k0
• Delays are quantized by sampling-period ts.
Missing Samples
Time
Delay Delay-Change
Beamformer Human Body
t1 t2
Beam Formation Δτ Δτ Δτ
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.
Delay Quantization
• The delay quantization error can be viewed as the phase error of the phasors.
Delay Quantization
• N=128, 16 quantization steps per cycles are required. • In general, 32 and 64 times the center frequency is
used.
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.
e l e m e n t i A D C i n t e r p o l a t i o n d i g i t a l d e l a y s u m m
a t i o n
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+1−φ Δn=1 j=1
A<=0?
A=A+Δn+n0 j=j+1
A=A+j−φ Δn=Δn+1 N bump
Autonomous vs. Centralized
Beam Formation - BB
A(t-τ)cos2πf0(t-τ)
A(t-τ)cos2πf0(t-τ)e-j2πfdt
magnitude
f f0-fd -f0-fd
f f0-fd
LPF(A(t-τ)cos2πf0(t-τ)e-j2πfdt)
f f0 -f0
rf
baseband
Beam Formation - BB
Beam Formation - BB e l e m e n t i A D C d e m o d /
L P F t i m e d e l a y /
p h a s e r o t a t i o n
I Q
I
Q
Beam Formation - BB e l e m e n t i A D C d e m o d /
L P F t i m e d e l a y /
p h a s e r o t a t i o n
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).
ΔΣ-Based Beamformers
Why ΔΣ ?
• 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
ΔΣ Advantages
Current Problems
Conventional vs. ΔΣ
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 ΔΣ 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 ΔΣ Modulator Quantizer
D/A
_ y x Integrator
e LPF ↓ x*
Single-Bit
• Over-Sampling • Noise-Shaping
• Reconstruction
• The SNR of a 32 f0, 2nd-order, low-passed ΔΣ modulator is about 40dB.
Noise Shaped ΔΣ Modulator
Signal and Noise Transfer Function
Noise Shaping Transfer Functions • For first order noise shaping, 1.5 bits (9 dB) is
gained when the sampling frequency is doubles. • For second order noise shaping, 2.5 bits (15 dB) is
gained when the sampling frequency is doubles.
Property of a ΔΣ 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"
0"dB"
Frequency"
1" 1024"-0.5"
0"
0.5"
1" 1024"-1"
0"
1"
1" 256" 512" 768" 1024"-0.5"
0"
0.5"
Sample"
Waveform Spectrum
x
y
x*
A Delta-Sigma Beamformer
• No Interpolation • Single-Bit Bus
Transducer TGC ΔΣ A/D
Shift-Register
Delay-Controller / MUX
Transducer TGC
Shift-Register
Delay-Controller / MUX
. . .
Single-Bit
LPF
ΔΣ A/D
A. RF
B. Repeat
C. Insert-Zero
D. Sym-Hold
A "
-70"
-60"
-50"
-40"
-30"
-20"
-10"
0"B"
D "C"
Results
-20" -10" 0" 10" 20"
-80"
-60"
-40"
-20"
0"RF"
dB"
-20" -10" 0" 10" 20"
-80"
-60"
-40"
-20"
0"Repeat"
dB"
-20" -10" 0" 10" 20"
-80"
-60"
-40"
-20"
0"Insert-Zero"
dB"
Width (mm)"-20" -10" 0" 10" 20"
-80"
-60"
-40"
-20"
0"Symmetric-Hold"
dB"
Width (mm)"
Cross-Section-Views of Peak 3
Generic Receiver
beam former
filtering (pre-detection)
envelope detection
filtering(post-detection)
mapping and other processing
scan conversion
display
adaptive controls
A/D
Scan Conversion
• Acquired data may not be on the display grid.
Acquired grid
Display grid
Scan Conversion
sinθ
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
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
velocity. • Sound velocity is around 1540 m/s. • High frame rate is required for real-time
imaging.
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 r2 t
t
r1 r2
Parallel Beamformation
• Simultaneously transmit multiple beams. • Interference between beams, spatial
ambiguity.
t1/r1 t2/r2
t1/r1 t2/r2
Term Report
• “The Applications of K-Space in Pulse-Echo Ultrasound”, W.F. Walker and G.E. Trahey, IEEE Trans. on UFFC, vol. 45-3, pp. 541-558, 1998.