Adaptive imaging preliminary speckle correlation analysis
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Adaptive Imaging Preliminary: Speckle Correlation Analysis. sample volume. transducer. Speckle Formation. Speckle results from coherent interference of un-resolvable objects. It depends on both the frequency and the distance. Speckle Second-Order Statistics.

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Adaptive Imaging Preliminary: Speckle Correlation Analysis

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Adaptive Imaging Preliminary:Speckle Correlation Analysis


sample volume

transducer

Speckle Formation

  • Speckle results from coherent interference of un-resolvable objects. It depends on both the frequency and the distance.


Speckle Second-Order Statistics

  • The auto-covariance function of the received phase-sensitive signals (i.e., before envelope detection) is simply the convolution of the system’s point spread function if the insonified region is

    • macroscopically slow-varying.

    • microscopically un-correlated.


Speckle Second-Order Statistics

  • The shape of a speckle spot (assuming fully developed) is simply determined by the shape of the point spread function.

  • The higher the spatial resolution, the finer the speckle pattern, and vice versa.


Speckle Statistics

  • The above statements do not hold if the object has structures compared to or larger than the ultrasonic wavelength.

  • Rician distribution is often used for more general scatterer distribution.

  • Rayleigh distribution is a special case of Rician distribution.


van Cittert-Zernike Theorem

  • A theorem originally developed in statistical optics.

  • It describes the second-order statistics of the field produced by an in-coherent source.

  • The insonification of diffuse scatterers is assumed in-coherent.

  • It is different from the aforementioned lateral displacement.


van Cittert-Zernike Theorem

  • The theorem describes the spatial covariance of signals received at two different points in space.

  • For a point target, the correlation of the two signals should simply be 1.

  • For speckle, correlation decreases since the received signal changes.


van Cittert-Zernike Theorem

  • The theorem assumes that the target is microscopically un-correlated.

  • The spatial covariance function is the Fourier transform of the radiation pattern at the point of interest.


correlation

radiation pattern

van Cittert-Zernike Theorem


van Cittert-Zernike Theorem

  • The theorem states that the correlation coefficient decreases from 1 to 0 as the distance increases from 0 to full aperture size.

  • The correlation is independent of the frequency, aperture size, …etc.


van Cittert-Zernike Theorem

  • In the presence of tissue inhomogeneities, the covariance function is narrower since the radiation pattern is wider.

  • The decrease in correlation results in lower accuracy in estimation if signals from different channels are used.


van Cittert-Zernike Theorem

correlation

distance


van Cittert-Zernike Theorem

RF Signals

Channel

Time (Range)


van Cittert-Zernike Theorem(Focal length 60mm vs. 90mm)


van Cittert-Zernike Theorem(16 Elements vs. 31 Elements)


van Cittert-Zernike Theorem(2.5MHz vs. 3.5MHz)


van Cittert-Zernike Theorem(with Aberrations)


correlation coefficient

displacement

L/2

Lateral Speckle Correlation


Lateral Speckle Correlation

  • Assuming the target is at focus, the correlation roughly decreases linearly as the lateral displacement increases.

  • The correlation becomes zero when the displacement is about half the aperture size.

  • Correlation may decrease in the presence of non-ideal beam formation.


Lateral Speckle Correlation

14.4 mm Array


Lateral Speckle Correlation


Lateral Speckle Correlation


Lateral Speckle Correlation


Lateral Speckle Correlation: Implications on Spatial Compounding


Speckle Tracking

  • Estimation of displacement is essential in many imaging areas such as Doppler imaging and elasticity imaging.

  • Speckle targets, which generally are not as ideal as points targets, must be used in many clinical situations.


Speckle Tracking

  • From previous analysis on speckle analysis, we found the local speckle patterns simply translate assuming the displacement is small.

  • Therefore, speckle patterns obtained at two instances are highly correlated and can be used to estimate 2D displacements.


Speckle Tracking

  • Displacements can also be found using phase changes (similar to the conventional Doppler technique).

  • Alternatively, displacements in space can be estimated by using the linear phase shifts in the spatial frequency domain.


Speckle Tracking

  • Tracking of the speckle pattern can be used for 2D blood flow imaging. Conventional Doppler imaging can only track axial motion.

  • Techniques using phase information are still inherently limited by the nature of Doppler shifts.


Adaptive Imaging Methods:Correlation-Based Approach


body wall

viscera

point of interest

v1 v2 v3

transducer array

Sound Velocity Inhomogeneities


Velocity (m/sec)

water

1484

blood

1550

myocardium

1550

fat

1450

liver

1570

kidney

1560

Sound Velocity Inhomogeneities


Sound Velocity Inhomogeneities

  • Sound velocity variations result in arrival time errors.

  • Most imaging systems assume a constant sound velocity. Therefore, sound velocity variations produce beam formation errors.

  • The beam formation errors are body type dependent.


Sound Velocity Inhomogeneities

  • Due to beam formation errors, mainlobe may be wider and sidelobes may be higher.

  • Both spatial and contrast resolution are affected.

no errors

with errors


beam formation

geometric delay

aligned

velocity variations

correction

Near Field Assumption

  • Assuming the effects of sound velocity inhomogeneities can be modeled as a phase screen at the face of the transducer, beam formation errors can be reduced by correcting the delays between channels.


Correlation-Based Aberration Correction

No Focusing


Correlation-Based Aberration Correction

Transmit Focusing Only


Correlation-Based Aberration Correction

Transmit and Receive Focusing


Correlation-Based Aberration Correction

Wire: Before Correction

Wire: After Correction


Correlation-Based Aberration Correction

Diffuse Scatterers: Before

Diffuse Scatterers: After


Correlation Based Method

  • Time delay (phase) errors are found by finding the peak of the cross correlation function.

  • It is applicable to both point and diffuse targets.


Correlation Based Method

  • The relative time delays between adjacent channels need to be un-wrapped.

  • Estimation errors may propagate.


Correlation Based Method

  • Two assumptions for diffuse scatterers:

    • spatial white noise.

    • high correlation (van Cittert-Zernike theorem).

filter

correlator

Dx


Correlation Based Method

  • Correlation using signals from diffuse scatterers under-estimates the phase errors.

  • The larger the phase errors, the more severe the underestimation.

  • Iteration is necessary (a stable process).


Alternative Methods

  • Correlation based method is equivalent to minimizing the l2 norm. Some alternative methods minimize the l1 norm.

  • Correlation based method is equivalent to a maximum brightness technique.


Baseband Method

  • The formulation is very similar to the correlation technique used in Color Doppler.


CORDIC

acc.

I

I

Q

Q

sign control

Q sign bit

acc.

CORDIC

acc.

Baseband Method


One-Dimensional Correction:Problems

  • Sound velocity inhomogeneities are not restricted to the array direction. Therefore, two-dimensional correction is necessary in most cases.

  • The near field model may not be correct in some cases.


One-Dimensional Correction:Problems


One-Dimensional Correction:Problems


Two-Dimensional Correction

  • Using 1D arrays, time delay errors can only be corrected along the array direction.

  • The signal received by each channel of a 1D array is an average signal. Hence, estimation accuracy may be reduced if the elevational height is large.

  • 2D correction is necessary.


Two-Dimensional Correction

  • Each array element has four adjacent elements.

  • The correlation path between two array elements can be arbitrary.

  • The phase error between any two elements should be independent of the correlation path.


(1,1)

(3,1)

(2,1)

corr

corr

corr

(1,2)

(2,2)

(3,2)

corr

corr

corr

(2,3)

(3,3)

(1,3)

corr

corr

corr

corr

corr

corr

Full 2D Correction


(1,1)

(3,1)

(2,1)

corr

corr

corr

(1,2)

(2,2)

(3,2)

corr

corr

corr

(1,3)

(3,3)

(2,3)

corr

corr

Row-Sum 2D Correction


Correlation Based Method: Misc.

  • Signals from each channel can be correlated to the beam sum.

  • Limited human studies have shown its efficacy, but the performance is not consistent clinically.

  • 2D arrays are required to improve the 3D resolution.


Displaced Phase Screen Model

  • Sound velocity inhomogeneities may be modeled as a phase screen at some distance from the transducer to account for the distributed velocity variations.

  • The displaced phase screen not only produces time delay errors, it also distorts ultrasonic wavefronts.


phase screen

Displaced Phase Screen Model

  • Received signals need to be “back-propagated” to an “optimal” distance by using the angular spectrum method.

  • The “optimal” distance is determined by using a similarity factor.


Displaced Phase Screen Model


TSC + BPTime-shift compensation with back-propagation


TSC + BPTime-shift compensation with back-propagation


TSC + BPTime-shift compensation with back-propagation


TSC + BPTime-shift compensation with back-propagation


Abdominal Wall Measurements


Abdominal Wall Measurements


Abdominal Wall Measurements


Displaced Phase Screen Model

  • After the signals are back-propagated, correlation technique is then used to find errors in arrival time.

  • It is extremely computationally extensive, almost impossible to implement in real-time using current technologies.


Wavefront Distortion

  • Measurements on abdominal walls, breasts and chest walls have shown two-dimensional distortion.

  • The distortion includes time delay errors and amplitude errors (resulting from wavefront distortion).


phase

phase

f

f

Phase Conjugation

phase screen at face of transducer

displaced phase screen


Phase Conjugation


Phase Conjugation

No aberration

At 0 mm

At 20 mm

At 40 mm

At 60 mm


Phase Conjugation

  • Simple time delays result in linear phase shift in the frequency domain.

  • Displaced phase screens result in wavefront distortion, which can be characterized by non-linear phase shift in the frequency domain.


Phase Conjugation

  • Non-linear phase shift can be corrected by dividing the spectrum into sub-bands and correct for “time delays” individually.

  • In the limit when each sub-band is infinitesimally small, it is essentially a phase conjugation technique.


End 4/13/2005


Some of the Recent Developments


Real-Time In Vivo Imaging[15]


Real-Time In Vivo Imaging


Real-Time In Vivo Imaging


Real-Time In Vivo Imaging


Real-Time In Vivo Imaging


Real-Time In Vivo Imaging

Distribution of time delay corrections


Clinical Imaging Using 1-D Array [16]


Clinical Imaging Using 1-D Array

Before Correction

After Correction


Clinical Imaging Using 1-D Array

Before Correction

After Correction


Clinical Imaging Using 1-D Array

Channel Data

Complex Scattering Structures


Real Time Adaptive Imaging with 1.75D, High Frequency Arrays [17]

1D and 2D Least Squares Estimation


Real Time Adaptive Imaging with 1.75D, High Frequency Arrays

Before Correction

After Correction


Real Time Adaptive Imaging with 1.75D, High Frequency Arrays

Before Correction

After Correction


Real Time Adaptive Imaging with 1.75D, High Frequency Arrays

Original

1 iteration

4 iterations


Real Time Adaptive Imaging with 1.75D, High Frequency Arrays

Original

Receive Only


2D Correction Using 1.75d Array On Breast Microcalcifications [18]


2D Correction Using 1.75d Array On Breast Microcalcifications


2D Correction Using 1.75d Array On Breast Microcalcifications

(also with a 60% brightness improvement)


2D Correction Using 1.75d Array On Breast Microcalcifications


2D Correction Using 1.75d Array On Breast Microcalcifications

  • 1D

  • 1D with correction

  • 1.75D

  • 1.75D with correction


Adaptive Imaging Methods:Aperture Domain ProcessingParallel Adaptive Receive Compensation Algorithm


Single Transmit Imaging

  • Fixed direction transmit, all direction receive


Measuring Source Profile


Removing Focusing Errors


Focusing Errors

With Aberrations

No Aberrations


Single Transmit Imaging

With Aberrations

No Aberrations


PARCA

With Correction

No Correction


Simplifications:1. DFT vs. Single Transmit Imaging2. Weighting vs. Complex Computations


DFT vs. Single Transmit Imaging

Single Transmit Imaging

DFT


Adaptive Weighting


Adaptive Weighting


Coherent

Speckle

Incoherent

Aberrated

Frequency Domain Interpretation of the Aperture Data

*P.-C. Li and M.-L. Li, “Adaptive Imaging Using the Generalized Coherence Factor”,

IEEE UFFC, Feb., 2003.


Coherent sum (DC)

The larger, the better?

Total energy (times N)

N: the number of array channels used in beam sum

C(i,t) : the received signal of channel i

Coherence Factor (CF)

  • A quantitative measure of coherence of the received array signals.


Determination of the Optimal Receive Aperture Size

Object of Interest

Enhance

Unwanted Sidelobes

Suppress

Optimize the receive aperture size

Classify “object types”


Experimental Results: Tissue Mimicking Phantoms

1X

0

2X

Azimuth

28.6 mm

Range

Original

96.2 mm

–40

40

Adaptive Receive Aperture

Dynamic range: 60 dB


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