DASMTX3 Delay-And-Sum matrix for 3-D imaging

DASMTX3 returns a Delay-And-Sum matrix for linear 3-D beamforming.

Contents

Syntax

M = DASMTX3(SIG,X,Y,Z,DELAYS,PARAM) returns the numel(X) -by- numel(SIG) delay-and-sum DAS matrix. The matrix M can be used to beamform SIG (RF or I/Q signals) at the points specified by X, Y, and Z.

Because the signals in SIG are not required (only its size is needed) to create M, the following syntax is recommended:

M = DASMTX3(size(SIG),X,Y,Z,DELAYS,PARAM)

!IMPORTANT! -- With this syntax, use M = DASMTX3(1i*size(SIG),...) to return a complex DAS matrix for I/Q data.

DELAYS are the transmit time delays (in s). The number of elements in DELAYS must be the number of elements in the array (which is equal to size(SIG,2)). If a sub-aperture was used during transmission, use DELAYS(i) = NaN if element # i of the linear array was off.

PARAM is a structure that contains the parameter values required for DAS beamforming (see below for details).

DASMTX3 versus DAS3

DASMTX3 is called by DAS3. DASMTX3 thus returns the same beamformed results as DAS3.

bfSIG = das3(SIG,x,y,z,delays,param)

M = dasmtx3(size(SIG),x,y,z,delays,param);

bfSIG = M*SIG(:);

bfSIG = reshape(bfSIG,size(x));

M is a large sparse matrix. Computing M can be much more cost-effective than using DAS if you need to beamform several SIG matrices, because M needs to be determined only once. In 3-D ultrasound imaging with a significant number of elements, however, DASMTX3 can generate tall sparse DAS matrices when beamforming large volume data! To avoid memory issues, consider chunking your datasets to create several smaller sparse matrices.

Let us consider that a series SIG{1}, SIG{2} ... SIG{N} of ultrasound matrices have been generated by sending similar wavefronts with the same ultrasound array. These signals SIG{i} are stacked in a 3D array sig3D so that sig3D(:,:,i) = SIG{i}. To beamform these data with a delay-and-sum approach, the following can be used.

To obtain the DAS matrix, use dasmtx3:

M = dastmtx3([size(sig3D,1) size(sig3D,2)],x,y,z,delays,param) or

M = dastmtx3(1i*[size(sig3D,1) size(sig3D,2)],...) for I/Q data.

The beamformed signals are then calculated by a matrix multiplication:

bfSIG3D = M*reshape(sig3D,[],size(sig3D,3))

It is necessary to reshape the beamformed matrix array:

bfSIG3D = reshape(bfSIG3D,size(x,1),size(x,2),[])

You can also consider saving the DAS matrix M in a MAT file and loading it when needed. The previous syntax is generally much faster than:

for k = 1:N, bfSIG{k} = das3(SIG{k},x,y,z,delays,param); end

Other syntaxes

DASMTX3(SIG,X,Y,Z,PARAM) uses DELAYS = param.TXdelay.

DASMTX3(...,METHOD) specifies the interpolation method. The available methods are decribed in NOTE #3 below.

[M,PARAM] = DASMTX3(...) also returns the structure PARAM with the default values.

The structure PARAM

PARAM is a structure that contains the following fields:

Notes

Conventional axes are used:

The X-axis is PARALLEL to the transducer. The Z-axis is PERPENDICULAR to the transducer and points downward (Z = 0 at the level of the transducer, Z increases as depth increases). The Y-axis is such that the coordinates are right-handed. These axes are represented in the following figure.

DASMTX3 uses a standard delay-and-sum. It is a linear operator. Phase rotations are included if I/Q (complex) signals are beamformed.

By default DASMTX3 uses a linear interpolation to generate the DAS matrix. To specify the interpolation method, use DASMTX3(...,METHOD), with METHOD being:

The linear interpolation (it is a 2-point method) returns a matrix twice denser than the nearest-neighbor interpolation. It is 3, 4, 5, 6 times denser for 'quadratic', 'lanczos3', '5points', 'lanczos5', respectively (they are 3-to-6-point methods).

The DAS matrix

The DAS matrix is very sparse. It is complex when beamforming I/Q signals, which should be the preferred approach.

Here is an example of a DAS matrix:

Example: Two-way PSF for a focused wave by a 32x32 matrix array

This example shows how to simulate RF signals then beamform I/Q signals

Create a 3-MHz matrix array with 32x32 elements.

param = [];
param.fc = 3e6;
param.bandwidth = 70;
param.width = 250e-6;
param.height = 250e-6;

Specify the x- and y-coordinates of the elements.

pitch = 300e-6; % pitch (in m)
[xe,ye] = meshgrid(((1:32)-16.5)*pitch);
param.elements = [xe(:).'; ye(:).'];

Use TXDELAY3 to calculate the transmit delays for a focused wave.

x0 = 0; y0 = 0; z0 = 3e-2;
txdel = txdelay3(x0,y0,z0,param);

Plot the transducer with VIEWXDCR.

p = viewxdcr(param);
p.FaceVertexCData = txdel(:)*1e9;
title('32\times32-element matrix array')
c = colorbar('SouthOutside');
c.Label.String = 'TX delays (ns)';

Calculate the pressure field with PFIELD3.

n = 24;
[xi,yi,zi] = meshgrid(linspace(-5e-3,5e-3,n),linspace(-5e-3,5e-3,n),...
    linspace(0,6e-2,4*n));
RP = pfield3(xi,yi,zi,txdel,param);

Have a look at the RMS pressure field.

figure
slice(xi*1e2,yi*1e2,zi*1e2,RP,0,0,3)
set(gca,'zdir','reverse')
zlabel('[mm]')
shading flat
axis equal
colormap([1-hot;hot])
hold on
plot3(xe(:)*1e2,ye(:)*1e2,0*xe(:),'.')
title('Focused field by the 32{\times}32 matrix array')

Simulate RF signals by using SIMUS3.

[RF,param] = simus3(x0,y0,z0,1,txdel,param);

Demodulate the RF signals with RF2IQ.

IQ = rf2iq(RF,param);

Create a 3-D grid for beamforming.

lambda = 1540/param.fc;
[xi,yi,zi] = meshgrid(-2e-2:lambda:2e-2,-2e-2:lambda:2e-2,...
    2.5e-2:lambda/2:3.2e-2);

Create the DAS matrix with DASMTX3.

M = dasmtx3(1i*size(IQ),xi,yi,zi,txdel,param);
figure
spy(M(1:10000,1:10000))
title(['A close up of the ' int2str(size(M,1)) '\times',...
    int2str(size(M,2)) ' DAS matrix'])

Beamform the I/Q signals.

IQb = M*IQ(:);
IQb = reshape(IQb,size(xi));

Obtain the log-envelope.

env = abs(IQb);
I = 20*log10(env/max(env(:)));

Display the two-way PSF.

figure
I(1:round(size(I,1)/2),1:round(size(I,2)/2),:) = NaN;
for k = [-40:10:-10 -5 -1]
    isosurface(xi*1e2,yi*1e2,zi*1e2,I,k)
end
view(-60,40)
colormap([1-hot;hot])
c = colorbar;
c.Label.String = 'dB';
box on, grid on
zlabel('[cm]')
title('PSF at the focal point [dB]')

See also

cite, das3, dasmtx, simus3, txdelay3

References

About the author

Damien Garcia, Eng., Ph.D.
INSERM researcher
Creatis, University of Lyon, France

websites: BioméCardio, MUST

Date modified

Published with MATLAB® R2022a