y Tf n
SPARSITY DRIVEN ULTRASOUND IMAGING Ahmet Tuysuzoglu, J. Kracht, M. Cetin, R. Cleveland, W. C. Karl ABSTRACT
PROPOSED METHOD
Ultrasound imaging is an appealing imaging modality due to its non-invasive nature and low operational cost. It has been used commonly in medical imaging, e.g., cancer imaging, kidney stone imaging, and in nondestructive evaluation of materials. In both of these applications, producing high quality images from limited data is desirable. In this work, we focus on ultrasound image formation from sparse and reduced apertures. When the collected data come from such apertures, conventional ultrasound imaging strategies exhibited degraded resolution and artifacts. These artifacts hinder visual and automatic interpretation of the scenes. We propose a new sparsity-based approach to ultrasound imaging that overcomes the limitations of conventional methods.
EXPERIMENTS & RESULTS
fˆ
arg min J f
In sparse apertures the collected data lie in a small and potentially irregular portion of what would be considered a full aperture.
In reduced apertures, the collected data lie in a regular grid on an aperture that is smaller than the full aperture.
We propose a new method for ultrasound image reconstruction: •Model based inversion coupled with sparsity-based priors that offers •Improved resolution •Reduced artifacts (e.g. speckle, streaking) •Robustness to data loss (sparse and reduced aperture scenarios)
PROBLEM FORMULATION •We use the following Green’s function to model the scattered field in space in response to a point source of excitation:
jk r ' r
r
e ' 4 r r
J
f
The data for the measured model is collected from a 1mm diameter spherical scatter (Real parts are shown).
f
1 1
Smoothes homogeneous regions and preserves sharp transitions.
2 2
f
2 jk G
r
Tf
n
1
Beamforming reconstruction with full data
SDUI reconstruction with full data
BeamformingReduced Aperture
SDUI- Reduced Aperture
2. Experiments with the Channel: Results using full aperture:
Synthetic ground truth image for channel
Real part of channel data
Results using reduced and sparse apertures: BeamformingSparse Aperture
SDUI- Sparse Aperture
56% of full data
25% of full data
EXPERIMENTS & RESULTS The experiments are conducted at the Large Ultrasound Test Facility (LUTF) at Boston University Mechanical Engineering Department. Two types of experiments: a. Experiments with metal rods: 3/16 and 3/8 inches of diameter rods at 1 cm separation 3/16 and 3/8 inches of diameter rods at 0.5 cm separation b. Experiment with a channel that has U-shaped cross-section 1. Experiments with Rods:
14% of full data
6% of full data
Results using full aperture: Quantitative Performance Comparison of SDUI and Beamforming:
SDUI- 1cm separation
Beamforming- 1cm separation
Beamforming- 0.5cm separation
SDUI- 0.5cm separation
BeamformingReduced Aperture
SDUI- Reduced Aperture
Results using reduced and sparse apertures: Rods at 1 cm separation: BeamformingSparse Aperture
25% of full data
r f (r )dr
We discretize this model and take into account the measurement noise to obtain the following model:
SDUI- Reduced Aperture
1
To preserve strong scatterers and suppressing artifacts.
• is a discrete approximation to the 2-D derivative operator. • 1 and 2 are regularization parameters and they control the emphasis on the priors that f is sparse and the gradient of magnitude of f is sparse respectively. •The formulation starts from the back-scattered data and is not a postprocessing of a formed image.
Measured Model
y
2
2 1
BeamformingReduced Aperture
6% of full data
where r and r’ denote the source and observation location respectively.
•We relate the observed data y, and the reflectivity field using the following observation model: ' 2 '
y r
Tf
Data fidelity term incorporates the Green’s function model.
•Validation of the scattering model:
Theoretical Model
y
2
SDUI- Sparse Aperture
25% of full data
f
•Conventional ultrasound images display the raw time of flight observations and amplitude of the backscattered signal. •Such methods exhibit speckle noise and artifacts especially as data quality and quantity are reduced. •We consider sparse and reduced apertures:
G r
BeamformingSparse Aperture
We formulate the ultrasound imaging problem as the following optimization problem:
MOTIVATION
'
Rods at 0.5 cm separation:
Question: What kinds of prior information can we include? -Sparsity of some aspect of underlying field: Used in NMR, SAR, CT, Astronomical Imaging etc.
6% of full data
SDUI- Sparse Aperture
CONCLUSIONS In this work we have presented a new ultrasound image reconstruction method that produces images with higher resolution and higher signalto-noise ratio compared to conventional ultrasound imaging method, beamforming.
COLLABORATORS
PROPOSED METHOD
Ultrasound imaging is an appealing imaging modality due to its non-invasive nature and low operational cost. It has been used commonly in medical imaging, e.g., cancer imaging, kidney stone imaging, and in nondestructive evaluation of materials. In both of these applications, producing high quality images from limited data is desirable. In this work, we focus on ultrasound image formation from sparse and reduced apertures. When the collected data come from such apertures, conventional ultrasound imaging strategies exhibited degraded resolution and artifacts. These artifacts hinder visual and automatic interpretation of the scenes. We propose a new sparsity-based approach to ultrasound imaging that overcomes the limitations of conventional methods.
EXPERIMENTS & RESULTS
fˆ
arg min J f
In sparse apertures the collected data lie in a small and potentially irregular portion of what would be considered a full aperture.
In reduced apertures, the collected data lie in a regular grid on an aperture that is smaller than the full aperture.
We propose a new method for ultrasound image reconstruction: •Model based inversion coupled with sparsity-based priors that offers •Improved resolution •Reduced artifacts (e.g. speckle, streaking) •Robustness to data loss (sparse and reduced aperture scenarios)
PROBLEM FORMULATION •We use the following Green’s function to model the scattered field in space in response to a point source of excitation:
jk r ' r
r
e ' 4 r r
J
f
The data for the measured model is collected from a 1mm diameter spherical scatter (Real parts are shown).
f
1 1
Smoothes homogeneous regions and preserves sharp transitions.
2 2
f
2 jk G
r
Tf
n
1
Beamforming reconstruction with full data
SDUI reconstruction with full data
BeamformingReduced Aperture
SDUI- Reduced Aperture
2. Experiments with the Channel: Results using full aperture:
Synthetic ground truth image for channel
Real part of channel data
Results using reduced and sparse apertures: BeamformingSparse Aperture
SDUI- Sparse Aperture
56% of full data
25% of full data
EXPERIMENTS & RESULTS The experiments are conducted at the Large Ultrasound Test Facility (LUTF) at Boston University Mechanical Engineering Department. Two types of experiments: a. Experiments with metal rods: 3/16 and 3/8 inches of diameter rods at 1 cm separation 3/16 and 3/8 inches of diameter rods at 0.5 cm separation b. Experiment with a channel that has U-shaped cross-section 1. Experiments with Rods:
14% of full data
6% of full data
Results using full aperture: Quantitative Performance Comparison of SDUI and Beamforming:
SDUI- 1cm separation
Beamforming- 1cm separation
Beamforming- 0.5cm separation
SDUI- 0.5cm separation
BeamformingReduced Aperture
SDUI- Reduced Aperture
Results using reduced and sparse apertures: Rods at 1 cm separation: BeamformingSparse Aperture
25% of full data
r f (r )dr
We discretize this model and take into account the measurement noise to obtain the following model:
SDUI- Reduced Aperture
1
To preserve strong scatterers and suppressing artifacts.
• is a discrete approximation to the 2-D derivative operator. • 1 and 2 are regularization parameters and they control the emphasis on the priors that f is sparse and the gradient of magnitude of f is sparse respectively. •The formulation starts from the back-scattered data and is not a postprocessing of a formed image.
Measured Model
y
2
2 1
BeamformingReduced Aperture
6% of full data
where r and r’ denote the source and observation location respectively.
•We relate the observed data y, and the reflectivity field using the following observation model: ' 2 '
y r
Tf
Data fidelity term incorporates the Green’s function model.
•Validation of the scattering model:
Theoretical Model
y
2
SDUI- Sparse Aperture
25% of full data
f
•Conventional ultrasound images display the raw time of flight observations and amplitude of the backscattered signal. •Such methods exhibit speckle noise and artifacts especially as data quality and quantity are reduced. •We consider sparse and reduced apertures:
G r
BeamformingSparse Aperture
We formulate the ultrasound imaging problem as the following optimization problem:
MOTIVATION
'
Rods at 0.5 cm separation:
Question: What kinds of prior information can we include? -Sparsity of some aspect of underlying field: Used in NMR, SAR, CT, Astronomical Imaging etc.
6% of full data
SDUI- Sparse Aperture
CONCLUSIONS In this work we have presented a new ultrasound image reconstruction method that produces images with higher resolution and higher signalto-noise ratio compared to conventional ultrasound imaging method, beamforming.
COLLABORATORS
