ULTRASOUND IMAGING USING A BIAS-SWITCHABLE ROW-COLUMN ARRAY TRANSDUCER

Abstract

An ultrasonic image is obtained from a bias-switchable row-column array transducer. A row channel data set is obtained by applying a bias voltage pattern to groups of row electrodes, the bias voltage pattern being chosen such that row electrodes within each group have the same bias voltage; transmitting a waveform along each of the plurality of row electrodes; and recording received column signals from each of the plurality of column electrodes. A column channel data set is obtained by applying a bias voltage pattern to groups of column electrodes, the bias voltage pattern being chosen such that column electrodes within each group have the same bias voltage; transmitting a waveform along each of the plurality of column electrodes; and recording received row signals from each of the plurality of row electrodes.

Claims

1. A method for ultrasound imaging using a bias-switchable row-column array transducer having a plurality of row electrodes and a plurality of column electrodes that are not parallel to the row electrodes, the method comprising: performing one or more row transmit events, each transmit event comprising: identifying groups of row electrodes within the plurality of row electrodes; applying a bias voltage pattern to the groups of row electrodes, the bias voltage pattern being chosen such that row electrodes within each group of row electrodes have the same bias voltage; transmitting a waveform along each of the plurality of row electrodes; and recording received column signals from each of the plurality of column electrodes; obtaining a row channel dataset for each of the groups of row electrodes using the received column signals from each of the one or more row transmit events; performing a column imaging sequence having one or more transmit events, each transmit event comprising: identifying groups of column electrodes within the plurality of column electrodes; applying a bias voltage pattern to the groups of column electrodes, the bias voltage pattern being chosen such that columns within each group of column electrodes have the same bias voltage; transmitting a waveform along each of the plurality of column electrodes; and recording received row signals from each of the plurality of row electrodes; obtaining a column channel dataset for each of the groups of column electrodes using the received row signals; and generating an ultrasonic image based on the row channel data set and the column channel dataset.

2. The method of claim 1, wherein the groups of rows comprise multiple adjacent rows and/or the groups of columns comprise multiple adjacent columns.

3. The method of claim 1, wherein, for each of the row imaging sequence and the column imaging sequence, the bias voltage patterns are derived from an invertible matrix.

4. The method of claim 3, wherein the invertible matrix is a Hadamard matrix.

5. The method of claim 3, wherein the invertible matrix is a scalar.

6. The method of claim 1, wherein: the bias voltage pattern comprises positive biases and negative biases; and waveforms having a negative bias are inverted copies of waveforms having a positive bias.

7. The method of claim 1, wherein adjacent waveforms are scaled or delayed.

8. The method of claim 1, further comprising the steps of generating a row image from the row channel dataset, generating a column image from the column channel data set, and combining the row image and the column image to generate the ultrasonic image.

9. The method of claim 1, further comprising the steps of obtaining a plurality of row data sets and a plurality of channel data sets, generating a plurality of row images and column images, and combining and averaging the plurality of row images and column images to obtain a combined ultrasonic image.

10. The method of claim 9, wherein the row images and the column images are combined and averaged using phase information.

11. The method of claim 9, further comprising the step of applying temporal or spatio-temporal filtering over the plurality of row data sets and the plurality of channel data sets.

12. The method of claim 1, wherein the step of generating an ultrasonic image comprises applying a ghost artifact removal algorithm and/or a wall-filtering operation.

13. The method of claim 12, wherein the wall-filtering operation is an infinite impulse response filter, a finite impulse response filter, an eigenfilter, or a singular value decomposition filter.

14. The method of claim 1, wherein the ultrasonic image is a three-dimensional power Doppler image, a color Doppler image, a vector-flow image, a strain image, or a displacement-estimation image.

15. The method of claim 1, wherein the waveforms are transmitted to produce one of a plane wave, a cylindrically-diverging wave, or a cylindrically-converging wave.

16. The method of claim 1, further comprising the step of inputting the ultrasonic image into an algorithm for rendering, the algorithm for rendering comprising a generative adversarial network or cycle-consistent generative adversarial network trained on paired or unpaired data from another imaging modality.

17. The method of claim 1, further comprising the step of injecting ultrasound contrast agents into a specimen to be imaged.

18. The method of claim 17, further comprising the step of performing centroid localization of contrast agent signatures in the ultrasonic image.

19. The method of claim 20, wherein the step of performing centroid localization of contrast agent signatures is repeated to obtain a plurality of super-localization images, and the plurality of super-localization images being combined to form a super-resolution ultrasound image or a velocity image.

20. A system for ultrasound imaging comprising: an array transducer having a plurality of row electrodes and a plurality of column electrodes that are not parallel to the row electrodes, the plurality of row electrodes being separated from the column electrodes by a dielectric layer; a voltage source; a signal generator; a controller that is programmed with instructions to: identify groups of row electrodes within the plurality of row electrodes and groups of column electrodes within the plurality of column electrodes; perform one or more row transmit events, each transmit event comprising: applying a bias voltage pattern to the plurality of row electrodes, the bias voltage pattern being applied such that the row electrodes within each group of row electrodes have the same bias voltage; transmitting a waveform along each of the plurality of row electrodes; and recording received column signals from each of the plurality of column electrodes; obtain a row channel dataset for each of the groups of row electrodes using the received column signals; perform one or more column transmit events, each transmit event comprising: applying a bias voltage pattern to the plurality of column electrodes, the bias voltage pattern being applied such that groups of column electrodes of the plurality of column electrodes have the same bias voltage; transmitting a waveform along each of the plurality of column electrodes; and recording received row signals from each of the plurality of row electrodes; obtain a column channel dataset for each of the groups of column electrodes using the received row signals; and generating an ultrasonic image based on the row channel data set and the column channel dataset.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0030] These and other features will become more apparent from the following description in which reference is made to the appended drawings, the drawings are for the purpose of illustration only and are not intended to be in any way limiting, wherein:

[0031] FIG. 1a through 1c are Power Doppler images of blood flow phantom 100 in a tube.

[0032] FIGS. 2a and 2b are perspective views of Hadamard bias patterns applied to an 8×8 row-column array.

[0033] FIGS. 3a and 3b are perspective views of Hadamard bias patterns applied to an 8×8 row-column array with a linear delay profile applied to produce a plane wave at an angle.

[0034] FIG. 4 depicts a row-column array with sixteen columns binned into groups of four columns.

[0035] FIG. 5a is an inverse Hadamard matrix applied to a row-column array transducers with 8 groups of columns and 128 rows.

[0036] FIG. 5b is a row-acquired image produced by the array of FIG. 5a.

[0037] FIG. 5c is an inverse Hadamard matrix applied to a row-column array transducers with 128 columns and 8 groups of rows.

[0038] FIG. 5d is a column-acquired image produced by the array of FIG. 5c.

[0039] FIG. 6 is an image produced by combining the column-acquired and row-acquired images.

[0040] FIG. 7a shows an image of a point-spread function in a first direction

[0041] FIG. 7b shows an image of a point-spread function in a second direction

[0042] FIG. 7c shows an image of the combined images from FIGS. 7a and 7b.

[0043] FIG. 8a shows a column-acquired image of blood vessels.

[0044] FIG. 8b shows an image of a combined column- and row-acquired image of blood vessels.

[0045] FIG. 9a shows a cross-sectional view of a blood vessel with an ensemble size of N=1

[0046] FIG. 9b shows a cross-sectional view of a blood vessel with an ensemble size of N=20.

[0047] FIG. 9c through 9e depict images obtained along a first axis, a second axis, and by combining the first and second axes, with a single normal plane wave.

[0048] FIG. 9f through 9h depict images obtained along a first axis, a second axis, and by combining the first and second axes, with angled beams at −7, 0, and 7 degrees.

[0049] FIG. 10a through 10c depict images obtained using shift-invariant point-spread function models along a first axis, a second axis, and a combination of the first and second axes.

[0050] FIG. 10d depict a cross-sectional image of two blood vessels.

[0051] FIG. 11a through 11c depict images obtained using shift-invariant point-spread function models along a first axis, a second axis, and a combination of the first and second axes.

[0052] FIG. 11d depict a cross-sectional image of two blood vessels.

[0053] FIG. 12 is a schematic of a row-column array used for imaging.

[0054] FIG. 13a is an example of an object function

[0055] FIG. 13b is an example of a super-localization output with ghost artifacts.

[0056] FIG. 14a is an example of a HEX-US image after ghost artifact removal.

[0057] FIG. 14b is an example of a super-localization output of an image.

[0058] FIG. 15 is a schematic diagram of an ultrasonic detection system.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0059] Ultrafast Volumetric 3D Imaging may be used to provide acoustic angiography. TOBE (top orthogonal to bottom electrodes) arrays could scale to large sizes providing widefield acoustic angiography. Ultrafast Power Doppler imaging, or other 3D imaging, with a row-column array may be obtained using orthogonal plane wave compounding. However, such an array may not be bias-switchable, resulting in undesirable imaging artifacts. It is also possible to reconstruct Power Doppler images by repeating image-plane acquisitions with a TOBE array using Scheme 1 (row column imaging without bias switching, including virtual line source imaging methods), or using Fast Orthogonal Row-Column Electronic Scanning (FORCES), Ultra-Fast Row Column

[0060] Electronic Scanning (uFORCES), or Simultaneous Azimuthal and Fresnel Elevational (SAFE) compounding. FORCES, uFORCES, and SAFE compounding methods require a bias-switchable TOBE array. FIG. 1a through FIG. 1c are examples of Power Doppler images of blood flow phantoms 100 in a tube 102 using FORCES imaging. FIG. 1a, FIG. 1b, and FIG. 1c depict side, perspective, and end views, respectively. A limitation of these approaches is the imaging time needed (>1 sec/Vol). Using Scheme 1, out-of-plane resolution may be sub-optimal away from the transmit focus and if using diverging waves from a virtual line source, SNR may be poor. SAFE compounding and FORCES require a lot of coherent compounding, which may not work well with significant tissue/blood motion. FORCES and uFORCES have only one-way elevational focusing (but two-way in-plane focusing). uFORCES B-scanning may be faster than FORCES, with a requirement for coherent compounding over only a few sparse transmit events, but Power Doppler volumetric imaging is still relatively slow. A fast volumetric Power Doppler imaging method that may achieve high quality at thousands of frames per second may enable long ensemble times and thus high sensitivity.

[0061] Referring to FIG. 15, an ultrasonic imaging system may include a transducer array 100 connected to a controller 102. The transducer array 100 generates ultrasonic signals that are used to image a sample 104. In response to received signals, controller 102 generates an ultrasonic image, which may then be displayed on a display 106. Controller 102 may be a general purpose processor or other suitable computer device, and may include an internal storage device or may be connected to an external storage device. The image may be stored and transmitted to another device, may be displayed on an integrally formed display, remote display, personal electronic device, or the like.

[0062] Theory

[0063] 3D Power Doppler

[0064] Signals may be recorded from every element of a bias-switchable row-column array with boosted SNR by using multiple Hadamard-based column biasing patterns while receiving from rows. It may take a long time to form a single image with this approach, and multiple images are needed in a Doppler ensemble to form a Power Doppler image. The discussion below may also apply to other 3D imaging schemes, such as color Doppler image, vector-flow image, strain image, or displacement-estimation image.

[0065] Let g.sub.r be the RF or IQ beamformed 3D image acquired using rows, for a potentially sparse channel aperture encoding. Under the approximation of a linear shift-invariant system, this can modeled as a convolution between an object function ƒ and point-spread function PSF.sub.r (x), along with additive electronic noise: g.sub.r(x, t)=PSF.sub.r(x)*ƒ(x, t)+n.

[0066] The object function may change over time, as is the case with bloodflow and will be modelled as a zero-mean random process. A similar model can be developed for the data acquired with columns : g.sub.c(x, t)=PSF.sub.c(x)*ƒ(x, t)+n.

[0067] Wall-filtering may be performed on the beamformed RF data, which will produce temporally-filtered outputs {tilde over (g)}.sub.r, {tilde over (g)}.sub.c insensitive to stationary tissues. Given the object function may consist of stationary tissue ƒ.sub.t and moving blood ƒ.sub.b components: ƒ(x, t)=ƒ.sub.t(x)+ƒ.sub.b(x, t). Then, for example, {tilde over (g)}.sub.r≅PSF.sub.r(x)*{tilde over (ƒ)}.sub.b(x, t)+n.

[0068] The power Doppler image acquired with TOBE row acquisition, PD.sub.r={tilde over (g)}.sub.r{tilde over (g)}.sub.r*, may have good elevational resolution, but may have poor azimuthal resolution. Likewise, the Power Doppler image PD.sub.c={tilde over (g)}.sub.c{tilde over (g)}.sub.c* acquired with TOBE columns may have good azimuthal resolution, but may have poor elevational resolution. Here .Math. represents statistical ensemble averaging, which is approximated by slow-time averaging over a Doppler ensemble.

[0069] To achieve a power Doppler image with improved and more isotropic resolution, consider forming the image XPD={tilde over (g)}.sub.r{tilde over (g)}.sub.c*. Expanding, we have

XPD={tilde over (g)}.sub.r{tilde over (g)}.sub.c*=(PSF.sub.r(x)*ƒ(x,t)+n.sub.r)(PSF.sub.c(x)*ƒ(x,t)+n.sub.c)*

[0070] Now since the object function and the noise are uncorrelated, and the noise acquired with row acquisition and column acquisition will be uncorrelated:

[00001]$\mathrm{XPD}\cong .Math.\left({\mathrm{PSF}}_r\left(x\right)*f_b\left(x,t\right)\right){\left({\mathrm{PSF}}_c\left(x\right)*f_b\left(x,t\right)\right)}^{*}.Math.==.Math.\left(\int {\mathrm{PSF}}_r\left(x^{\prime }\right)f_b\left(x-x^{\prime },t\right){\mathrm{dx}}^{\prime }\right){\left(\int {\mathrm{PSF}}_c\left(x^{″}\right)f_b\left(x-x^{″},t\right){\mathrm{dx}}^{″}\right)}^{*}.Math.=\int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right).Math.f_b\left(x-x^{\prime },t\right)f_b^{*}\left(x-x^{″},t\right).Math.{\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}$

[0071] The object spatio-temporal autocorrelation R.sub.ƒƒ(x, x′|t, t′)≡ƒ(x, t)ƒ*(x′, t′) may be modeled as temporally wide-sense stationary, and spatially statistically uncorrelated but spatially varying:

R.sub.ƒƒ(x,x′|t, t′)=R.sub.ƒ(x|t−t′)δ(x−x′)

where δ is a delta function and R.sub.ƒ(x|t−t′)≡ƒ(x, t)ƒ*(x, t′). Now in the above, ƒ.sub.b(x−x′, t)ƒ.sub.b*(x−x″, t) must be evaluated. This may be written as:

ƒ.sub.b(x−x′,t)ƒ.sub.b*(x−x″,t)=R.sub.b(x−x′|0)δ(x″−x′)

[0072] This then simplifies the integration as:

[00002]$\mathrm{XPD}\cong \int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right)R_b\left(x-x^{\prime }.Math.0\right)\delta \left(x^{″}-x^{\prime }\right){\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}=\int {\mathrm{PSF}}_r\left(x^{″}\right){\mathrm{PSF}}_c\left(x^{″}\right)R_b\left(x-x^{″}.Math.0\right){\mathrm{dx}}^{″}={\mathrm{PSF}}_r\left(x\right){\mathrm{PSF}}_c\left(x\right)*R_b\left(x.Math.0\right)={\mathrm{PSF}}_{\mathrm{rc}}\left(x\right)*R_b\left(x.Math.0\right)$

[0073] Here PSF.sub.rc(x)=PSF.sub.r(x)PSF.sub.c(x) is the new point-spread function, and may have more isotropic resolution compared to PSF.sub.r(x) or PSF.sub.c(x) alone.

[0074] Now a spatially-varying zero-temporal lag autocorrelation can be written as an integral over the power spectral density: R.sub.b(x|0)=∫S.sub.b(x, ƒ)dƒ. Thus,

XPD≅PSF.sub.rc(x)*∫S.sub.b(x,ƒ)dƒ

and represents an image of the scattering power due to moving blood, as resolved by a point-spread function with improved isotropic resolution.

[0075] In practice, the system may not be linear shift-invariant, so the convolution model above may only be an approximation that is valid locally. However, numerical simulations may be used to validate the approach described herein. The advantage of the above approach is that row- and column-acquired images may be acquired quickly with sacrificed elevational or azimuthal resolutions, respectively, but the above approach can lead to high-quality volumetric power Doppler images in a rapid way.

[0076] Biasing and Pulsing Schemes to Implement HEX-Power Doppler

[0077] One simple way to read out from every element of a row-column array is to bias one column at a time while recording signals from every row. An alternative method is to apply Hadamard biasing patterns to columns while reading out signals from rows. After aperture decoding using an inverse Hadamard matrix, signals from every element of the array may be recovered, with improved signal-to-noise ratio compared to the approach of biasing one column at a time. FIG. 2a and FIG. 2b depict examples of first and second Hadamard bias patterns applied to an 8×8 row-column array transducer 20, that produce a plane wave 22 at a first angle.

[0078] For larger row-column arrays, the time required for these approaches increases. Moreover, these approaches does not involve a transmission strategy. To achieve a widefield plane wave (or diverging wave) transmission, when columns are biased with a particular Hadamard biasing pattern, signals may be transmitted along columns. When a negative bias voltage is present the polarity of the transmit waveform may be inverted so that the emitted acoustic wave from that column is identical to the emitted wave from a column with a positive bias and a positive polarity transmit signal. When the delay for each column is constant, a normal plane wave emission may result. When a linear delay profile is applied, a tilted plane wave emission may result. FIG. 3a and FIG. 3b depict examples of a first and second Hadamard bias patterns applied to an 8×8 row-column array transducer 20 with a linear delay profile applied, that produce a plane wave 22 at a second angle.

[0079] To improve volumetric imaging speeds, columns (or rows) may be binned prior to bias encoding. In one example, shown in FIG. 4, a row-column array transducer 20 is shown with sixteen columns binned into four groups of columns 24 with four columns in each group. A bias pattern is applied to the groups of columns according to the second row of the following Hadamard Matrix:

[00003]$H=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]$

[0080] In another example, for a 128×128 array, if columns may be binned into 8 groups of 16, and bias patterns from an 8×8 Hadamard matrix are applied to the groupings, only 8 transmit events are needed, but with the consequence of reading out from an effective 8×128 array. This will result in poor azimuthal but excellent elevational focusing.

[0081] Other grouping schemes may be possible besides simple binning, and in different sizes or numbers. In addition, other bias patterns may also be used. The matrix may be invertible, and/or may be a scalar.

[0082] The bias voltage pattern may use positive biases and negative biases, where the waveforms sent to the row or column electrodes that have a negative bias are inverted copies of the waveforms sent to the row or column electrodes having a positive bias (or vice versa). The waveforms may be scaled or delayed relative to one another.

[0083] A single normal plane wave may be sufficient to achieve fine resolution but more plane wave compounding may improve contrast and resolution at the expense of imaging speed.

[0084] HEX-PD Simulations:

[0085] In one simulation, Field II was used to generate plane wave emissions and scattering data collected from elements of a Hadamard-bias-encoded TOBE array. The data was then reconstructed using a custom delay-and sum plane-wave beamforming algorithm accounting for a constant plane wave delay then a custom delay from a scatterer to each element of the array. 64×64 and 128×128 10 MHz lambda-pitch arrays were simulated.

[0086] The HEX-PD methodology is discussed below, along with some simulation results. Shift-invariant convolution-based models are shown first, and then some results of a shift-variant model are shown.

[0087] FIG. 5a depicts the application of an inverse Hadamard matrix for aperture decoding on row-column array transducer 20 with 8 groups of columns 24 and 128 rows; an example of a row-acquired image g.sub.r is shown in FIG. 5b. FIG. 5c depicts the application of an inverse Hadamard matrix for aperture decoding on row-column array transducer 20 with 128 columns and 8 groups of rows 26; an example of a column-acquired image g.sub.c is shown in FIG. 5d. FIG. 6 depicts the X-Power Doppler image XPD={tilde over (g)}.sub.r{tilde over (g)}.sub.c*.

[0088] Referring to FIG. 7a through FIG. 7c, results of HEX-PD 3D PSF simulations with 10 MHz 128×128 TOBE array are shown. FIG. 7a shows PSF.sub.r with 8 transmission events, FIG. 7b shows PSF.sub.c with 8 transmission events, and FIG. 7c shows PSF.sub.r×PSF.sub.c.

[0089] Referring to FIG. 8a and FIG. 8b, results of HEX-PD 3D PSF simulations of blood vessels with 10 MHz 128×128 TOBE array are shown. FIG. 8a shows the column acquired image with 8×128 TOBE, 8 transmission events, and an ensemble size of N=10. FIG. 8b depicts the HEX-PD image using the column-acquired image and the row-acquired image (not shown). FIG. 9a and FIG. 9b show the effects of ensemble size and HEX-PD compounding. FIG. 9a depicts a blood vessel cross section with and ensemble size of N=1, and FIG. 9b depicts the same blood vessel cross section with an ensemble size of N=20.

[0090] In some examples, plane wave compounding may be used, which may offer a slight advantage over imaging without plane wave compounding. FIG. 9a depicts a 2D image obtained with 1 plane wave per orientation, 16 transmission events per image, and coherent compounding over 8 transmission events. FIG. 9b depicts a 2D image obtained with 3 plane waves per orientation, 48 transmission events per image, and coherent compounding over 16 transmission events. FIG. 9c, FIG. 9d, and FIG. 9e depict a 3D PSF.sub.r, PSF.sub.c, and PSF.sub.r×PST.sub.c image, respectively, with a single normal plane wave. FIG. 9f, FIG. 9g, and FIG. 9h depict a 3D PSF.sub.r, PSF.sub.c, and PSF.sub.r ×PST.sub.c , image, respectively, with angled beams at −7, 0, and 7 degrees.

[0091] Table 1 below shows some potential HEX-PD volumetric imaging rates and sensitivities with examples of potential applications.

TABLE-US-00001 TABLE 1 Potential HEX-PD volumetric imaging rates and sensitivities Volume X Sensitivity PRF Res. Field of Ensemble Rate vs traditional Potential Array (KHz) (mm) view (cm) size (Vol/s) Doppler Application 128 × 128, 5 MHz 16 0.5 4 × 4 × 5 40 25 4 Carotid 1024 × 1024, 8 MHz 16 0.2 16 × 16 × 4 1000 1 100 Breast 256 × 256, 30 MHz 50 0.07 1.3 × 1.3 × 1 500 50 50 Small animal 48 × 64, 2.5 MHz 5 1 10 × 10 × 15 30 3 3 Cardiac

[0092] Shift-Variant Simulations

[0093] The previous simulations relied on shift-invariant point-spread function models. The following simulation results include non-shift-varying models. X-Y image planes at a fixed 20 mm depth from a 64×64 10 MHz array.

[0094] FIG. 10a through FIG. 10d depict a first shift-variant simulation HEX-PD Shift-Variant Simulations with 64×64 10 MHz TOBE array, with a group size of 8 and a focal depth of 20 mm. FIG. 10a, FIG. 10b, and FIG. 10c depict a PSF.sub.r, PSF.sub.c, PSF.sub.r×PSF.sub.c, and a blood vessel cross section image (N=10), respectively. FIG. 11a through FIG. 11d depict a second shift-variant simulation HEX-PD Shift-Variant Simulations with 64×64 10 MHz TOBE array, with a group size of 8 and a focal depth of 20 mm. FIG. 10a, FIG. 10b, and FIG. 10c depict a PSF.sub.r, PSF.sub.c, PSF.sub.r×PSF.sub.c, and a blood vessel cross section image (N=10), respectively.

[0095] Super-Resolution Contrast Imaging

[0096] Super-resolution contrast ultrasound works by super-localizing microbubble contrast agent signals and accumulating their positions over an extended observation time. Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging.

[0097] A row-column array may be used for super-resolution imaging, however such an approach may require a non-bias-switchable array and a large number of transmit events to form a 3D image. This approach is shown in FIG. 12, in which N transmit events for an N×N array are required to form one 3D image. In contrast, the approach described herein may require only 16 transmit events for arrays of size 128×128 or even larger, and may achieve ultrafast imaging rates, leading to shortened image acquisition time. Moreover, because larger arrays can be used with high numerical aperture focusing, finer-resolution can be achieved prior to super-localization, meaning that agent distribution may not need to be as sparse, and thus lead to more super-localization image frames to accumulate for high quality and fast 3D super-resolution acoustic angiography.

[0098] Hadamard-Encoded X-Ultrasound (HEX-US) Super-Resolution Method

[0099] Hadamard-Encoded X-ultrasound imaging may be used to form ultrafast volumetric images of sparse contrast agents, perform artifact removal and super-localization in 3D over a large number of images to form a super-resolution acoustic angiography image.

[0100] When the object function of interest is contrast agents, ƒ.sub.c(x, t)=Σ.sub.ia.sub.iδ(x−x.sub.i(t)), then including tissue and blood, the total object function may be ƒ(x, t)=ƒ.sub.t(x)+ƒ.sub.b(x, t)+ƒ.sub.c(x, t), with ƒ.sub.c>>ƒ.sub.b. An example of an object function is shown in FIG. 13a. The product of dominant moving object function components may be defined as

[00004]$f_c\left(x,t\right)f_c^{*}\left(x^{\prime },t\right)=\left(\underset{i}{.Math.}{a}_i\delta \left(x-x_i\left(t\right)\right)\right)\left(\underset{j}{.Math.}{a}_j\delta \left(x^{\prime }-x_j\left(t\right)\right)\right)=\underset{i}{.Math.}\underset{j}{.Math.}{a}_i{a}_j\delta \left(x-x_i\left(t\right)\right)\delta \left(x^{\prime }-x_j\left(t\right)\right)$

[0101] But the product of two delta functions is zero unless their arguments are identical so ƒ.sub.c(x, t)ƒ.sub.c*(x′, t)=Σ.sub.iΣ.sub.ja.sub.ia.sub.jδ(x−x.sub.i(t))δ(x−x′−(x.sub.i(t)−x.sub.j(t))). The argument of the right delta function can be zero when i=j and x−x′=0 or when i≠j and x−x′−(x.sub.i(t)−x.sub.j(t))=0, so

[00005]$\begin{array}{c}{f}_c\left(x,t\right)f_c^{*}\left(x^{\prime },t\right)=\begin{array}{c}\underset{i}{.Math.}{a}_i^2\delta \left(x-x_i\left(t\right)\right)\delta \left(x-x^{\prime }\right)+\\ \underset{i\ne j}{.Math.}{a}_i{a}_j\delta \left(x-x_i\left(t\right)\right)\delta \left(x^{\prime }-x_j\left(t\right)\right)\end{array}\\ =\begin{array}{c}\delta \left(x-x^{\prime }\right)\underset{i}{.Math.}{a}_i^2\delta \left(x-x_i\left(t\right)\right)+\\ \underset{i\ne j}{.Math.}{a}_i{a}_j\delta \left(x-x_i\left(t\right)\right)\delta \left(x^{\prime }-x_j\left(t\right)\right)\end{array}\\ =\begin{array}{c}{f}_c^2\left(x,t\right)\delta \left(x-x^{\prime }\right)+\\ \underset{i\ne j}{.Math.}{a}_i{a}_j\delta \left(x-x_i\left(t\right)\right)\delta \left(x^{\prime }-x_j\left(t\right)\right)\end{array}\end{array}\mathrm{And}{f}_c\left(x-x^{\prime },t\right)f_c^{*}\left(x-x^{″},t\right)=f_c^2\left(x-x^{\prime },t\right)\delta \left(x^{\prime }-x^{″}\right)+\underset{i\ne j}{.Math.}{a}_i{a}_j\delta \left(x-x^{\prime }-x_i\left(t\right)\right)\delta \left(x-x^{″}-x_j\left(t\right)\right)$

[0102] With wall-filtering (to remove stationary tissue, sometimes referred to as clutter-filtering) resulting in a sequence images with stationary tissue primarily rejected, the contrast ultrasound 3D HEX-ultrasound image is:

[00006]${\tilde{g}}_r\left(x,t\right){\tilde{g}}_c^{*}\left(x,t\right)=\left({\mathrm{PSF}}_r\left(x\right)*f_c\left(x,t\right)\right){\left({\mathrm{PSF}}_c\left(x\right)*f_c\left(x,t\right)\right)}^{*}=\int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right)f_c\left(x-x^{\prime },t\right)f_c^{*}\left(x-x^{″},t\right){\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}=\int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right)f_c^2\left(x-x^{\prime },t\right)\delta \left(x^{\prime }-x^{″}\right){\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}+\int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right)\underset{i\ne j}{.Math.}{a}_i{a}_j\delta \left(x-x^{\prime }-x_i\left(t\right)\right)\delta \left(x-x^{″}-x_j\left(t\right)\right){\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}=\int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{\prime }\right)f_c^2\left(x-x^{\prime },t\right){\mathrm{dx}}^{\prime }+\underset{i\ne j}{.Math.}{a}_i{a}_j\int \int {\mathrm{PSF}}_r\left(x^{\prime }\right){\mathrm{PSF}}_c\left(x^{″}\right)\delta \left(x-x^{\prime }-x_i\left(t\right)\right)\delta \left(x-x^{″}-x_j\left(t\right)\right){\mathrm{dx}}^{\prime }{\mathrm{dx}}^{″}$

[0103] But by the sifting property of the delta functions, the second term becomes:

[00007]$ϵ=\underset{i\ne j}{.Math.}{a}_i{a}_j{\mathrm{PSF}}_r\left(x-x_i\left(t\right)\right){\mathrm{PSF}}_c\left(x-x_j\left(t\right)\right)$

[0104] But, if the agents are sparse such that the distance between any agents is much greater than the width of a PSF, then this term is negligible since the product of sufficiently separated PSFs is close to zero. Moreover, the scattering amplitudes and RF PSFs can be bipolar or even complex, thus the sum above may tend to a zero-average. Thus, we have:

{tilde over (g)}.sub.r{tilde over (g)}.sub.c*≈PSF.sub.r(x)PSF.sub.c(x)*ƒ.sub.c.sup.2(x,t)+ϵ=PSF.sub.rc(x)*ƒ.sub.c.sup.2(x,t)+ϵ

[0105] Where ϵ is a ghost artifact residual. FIG. 13b depicts an example of the super-localization output with ghost artifacts. This represents the power of the sparse microbubble distribution as resolved by an improved row-column point-spread function plus some weak ghost artifacts that could be removed by thresholding or by a more intelligent algorithms as follows.

[0106] Ghost Artifact Removal Algorithm

[0107] For each detected contrast agent signature, check to see if there are agent signatures directly above and directly to the side in the an x-y image plane (for a fixed depth or projected to an xy-plane from a depth interval). If there are, then the contrast agent signature in question could be a ghost artifact. Discard the weakest signature then move to check the other agent signatures. FIG. 14a depicts a HEX-US image after ghost artifact removal.

[0108] Superlocalization and Super-Resolution

[0109] If the signal PSF.sub.rc(x)*ƒ.sub.c.sup.2(x, t) is sufficiently distinct from the background, or if ghost artifacts can be sufficiently removed, then the agent signals may be super-localized by finding the centroids in the envelope-detected image and 3D super-resolution imaging can be performed by accumulating centroid positions over many observation times. FIG. 14b depicts a super-localization output.

[0110] Linear Scatterers

[0111] The Hadamard aperture coding and decoding assumes that the scatterers imaged are linear scatterers. However, microbubbles may be nonlinear scatterers. They may be sufficiently linear to implement the technique. The nonlinear components may not unmix appropriately and lead to artifacts but they will be weak and unfocused.

[0112] The scope of the following claims should not be limited by the preferred embodiments set forth in the examples above and in the drawings, but should be given the broadest interpretation consistent with the description as a whole.