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examples.m
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% exemplary applications of
% the frequency-dependent F-number to
% coherent plane-wave compounding
%
% -------------------------------------------------------------------------
% REFERENCES:
% -------------------------------------------------------------------------
% [1] M. F. Schiffner and G. Schmitz,
% "Frequency-dependent F-number suppresses grating lobes and improves the lateral resolution in coherent plane-wave compounding,"
% IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 70, no. 9, pp. 1101-1117, Sep. 2023.
% DOI: <a href="matlab:web('https://doi.org/10.1109/TUFFC.2023.3291612')">10.1109/TUFFC.2023.3291612</a>
%
% [2] M. F. Schiffner and G. Schmitz,
% "Frequency-dependent F-number increases the contrast and the spatial resolution in fast pulse-echo ultrasound imaging,"
% 2021 IEEE Int. Ultrasonics Symp. (IUS), Xi'an, China, Sep. 2021, pp. 1-4.
% DOI: <a href="matlab:web('https://doi.org/10.1109/IUS52206.2021.9593488')">10.1109/IUS52206.2021.9593488</a>
% arxiv: <a href="matlab:web('https://arxiv.org/abs/2111.04593')">2111.04593</a>
% YouTube: <a href="matlab:web('https://www.youtube.com/watch?v=T6BoYRvQ6rg')">T6BoYRvQ6rg</a>
%
% -------------------------------------------------------------------------
% ABOUT:
% -------------------------------------------------------------------------
% author: Martin F. Schiffner
% date: 2023-07-14
% modified: 2023-11-15
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% clear workspace
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
close all;
clear;
clc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 0.) parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load RF data (tissue phantom)
load( 'data_RF.mat' );
% specify bandwidth
f_bounds = [ f_lb, f_ub ];
% specify time index of the sample extracted from the focused RF signal
index_t0 = 8;
% steering angles in rad
steering_angles_rad = deg2rad( steering_angles_deg );
% dependent parameters
positions_x = (-255.5:255.5) * element_pitch / 4;
positions_z = ( 64 + (0:511) ) * element_pitch / 4;
% dynamic range for all illustrations
dynamic_range_dB = 60;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 1.) typical usage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% typical usage of
% the Fourier-domain beamformer in
% coherent plane-wave compounding
%--------------------------------------------------------------------------
% 1.) compute images
%--------------------------------------------------------------------------
% specify cell array for results
images = cell( 1, numel( steering_angles_rad ) );
% iterate steering angles
for index_angle = 1:numel( steering_angles_rad )
% call Fourier-domain beamformer
images{ index_angle } = das_pw( positions_x, positions_z, data_RF( :, :, index_angle ), f_s, steering_angles_rad( index_angle ), element_width, element_pitch, c_avg, f_bounds, index_t0 );
end
% compute compound image
image_compound = sum( cat( 3, images{ : } ), 3 );
%--------------------------------------------------------------------------
% 2.) show results
%--------------------------------------------------------------------------
c_limits = [ -dynamic_range_dB, 0 ];
figure( 1 );
for index_angle = 1:numel( steering_angles_rad )
subplot( 1, numel( steering_angles_rad ), index_angle );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ index_angle } ) / max( abs( images{ index_angle }( : ) ) ) ), c_limits );
title( sprintf( 'Steering angle: %.0f°', steering_angles_deg( index_angle ) ) );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
end
figure( 2 );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( image_compound ) / max( abs( image_compound( : ) ) ) ), c_limits );
title( 'Coherent compounding' );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 2.) graphical abstract
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Reproduce the graphical abstract of [1].
% select steering angle of -20°
index_angle = 1;
% specify receive F-numbers
F_numbers_rx = { f_numbers.constant( 0 ), f_numbers.constant( 1.5 ), f_numbers.grating.angle_lb( 60, 1.5 ) };
str_titles = { 'Full aperture', 'Fixed', 'Proposed' };
%--------------------------------------------------------------------------
% 1.) compute images
%--------------------------------------------------------------------------
% specify cell array for results
images = cell( 1, numel( F_numbers_rx ) );
% iterate F-numbers
for index_F = 1:numel( F_numbers_rx )
% call Fourier-domain beamformer
images{ index_F } = das_pw( positions_x, positions_z, data_RF( :, :, index_angle ), f_s, steering_angles_rad( index_angle ), element_width, element_pitch, c_avg, f_bounds, index_t0, [], F_numbers_rx{ index_F } );
end
%--------------------------------------------------------------------------
% 2.) show results
%--------------------------------------------------------------------------
c_limits = [ -dynamic_range_dB, 0 ];
figure( 3 );
for index_F = 1:numel( F_numbers_rx )
subplot( 1, numel( F_numbers_rx ), index_F );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ index_F } ) / max( abs( images{ index_F }( : ) ) ) ), c_limits );
title( str_titles{ index_F }, 'Interpreter', 'none' );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 3.) apodization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% select steering angle of -20°
index_angle = 1;
% specify window functions
windows_rx = { windows.boxcar, windows.tukey( 0.2 ), windows.triangular, windows.hann };
%--------------------------------------------------------------------------
% 1.) compute images
%--------------------------------------------------------------------------
% specify cell array for results
images = cell( 1, numel( windows_rx ) );
% iterate window functions
for index_window = 1:numel( windows_rx )
% call Fourier-domain beamformer
images{ index_window } = das_pw( positions_x, positions_z, data_RF( :, :, index_angle ), f_s, steering_angles_rad( index_angle ), element_width, element_pitch, c_avg, f_bounds, index_t0, windows_rx{ index_window } );
end
%--------------------------------------------------------------------------
% 2.) show results
%--------------------------------------------------------------------------
c_limits = [ -dynamic_range_dB, 0 ];
figure( 4 );
for index_window = 1:numel( windows_rx )
subplot( 1, numel( windows_rx ), index_window );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ index_window } ) / max( abs( images{ index_window }( : ) ) ) ), c_limits );
title( sprintf( '%s', windows_rx{ index_window } ), 'Interpreter', 'none' );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 4.) normalization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% select steering angle of -20°
index_angle = 1;
% specify types of normalization
normalization_rx = { normalizations.off, normalizations.on };
%--------------------------------------------------------------------------
% 1.) compute images
%--------------------------------------------------------------------------
% specify cell array for results
images = cell( 1, numel( normalization_rx ) );
% iterate window functions
for index_normalization = 1:numel( normalization_rx )
% call Fourier-domain beamformer
images{ index_normalization } = das_pw( positions_x, positions_z, data_RF( :, :, index_angle ), f_s, steering_angles_rad( index_angle ), element_width, element_pitch, c_avg, f_bounds, index_t0, [], [], normalization_rx{ index_normalization } );
end
%--------------------------------------------------------------------------
% 2.) show results
%--------------------------------------------------------------------------
c_limits = [ -dynamic_range_dB, 0 ];
figure( 5 );
for index_normalization = 1:numel( normalization_rx )
subplot( 1, numel( normalization_rx ), index_normalization );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ index_normalization } ) / max( abs( images{ index_normalization }( : ) ) ) ), c_limits );
title( sprintf( 'Normalization: %s', normalization_rx{ index_normalization } ), 'Interpreter', 'none' );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 5.) bandwidth
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The frequency bounds specify
% the bandwidth for
% all computations.
%
% Smaller bandwidths reduce
% the computational costs at
% the expense of
% the image quality.
% select steering angle of -20°
index_angle = 1;
% bandwidths used for image formation
f_c = mean( f_bounds );
fractional_bandwidths = [ 1, 0.75, 0.5, 0.25 ];
%--------------------------------------------------------------------------
% 1.) compute images
%--------------------------------------------------------------------------
% specify cell array for results
images = cell( 1, numel( fractional_bandwidths ) );
% iterate fractional bandwidths
for index_bandwidth = 1:numel( fractional_bandwidths )
% current frequency bounds
f_bounds_act = f_c * ( 1 + [ -1, 1 ] * fractional_bandwidths( index_bandwidth ) / 2 );
% call Fourier-domain beamformer
images{ index_bandwidth } = das_pw( positions_x, positions_z, data_RF( :, :, index_angle ), f_s, steering_angles_rad( index_angle ), element_width, element_pitch, c_avg, f_bounds_act, index_t0 );
end
%--------------------------------------------------------------------------
% 2.) show results
%--------------------------------------------------------------------------
c_limits = [ -dynamic_range_dB, 0 ];
figure( 6 );
for index_bandwidth = 1:numel( fractional_bandwidths )
subplot( 2, numel( fractional_bandwidths ), index_bandwidth );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ index_bandwidth } ) / max( abs( images{ index_bandwidth }( : ) ) ) ), c_limits );
title( sprintf( 'Fractional bandwidth: %d %%', fractional_bandwidths( index_bandwidth ) * 1e2 ) );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
colormap gray;
if index_bandwidth > 1
subplot( 2, numel( fractional_bandwidths ), index_bandwidth + numel( fractional_bandwidths ) );
imagesc( positions_x * 1e3, positions_z * 1e3, 20 * log10( abs( images{ 1 } - images{ index_bandwidth } ) / max( abs( images{ 1 }( : ) ) ) ), c_limits );
title( 'Difference' );
xlabel( 'Lateral position (mm)' );
ylabel( 'Axial position (mm)' );
end
end