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This example demonstrates the use of k-Wave for the time-reversal reconstruction of a two-dimensional photoacoustic wave-field recorded over a circular sensor array. The sensor data is simulated and then time-reversed using kspaceFirstOrder2D
. It builds on the 2D Time Reversal Reconstruction For A Line Sensor Example.
The sensor data is simulated using kspaceFirstOrder2D
with an external image map for the initial pressure distribution in the same way as the Loading External Image Maps Example (this time the image is representative of vasculature). A plot of the initial pressure distribution (scaled to 256 by 256 pixels) and the Cartesian sensor mask used to record the pressure field (70 sensor points over a 270 degree measurement angle) is shown below.
To avoid the inverse crime (in which computations are run forwards and backwards using the same parameters and discretisation thereby possibly disguising any underlying errors), in this example the time-reversal reconstruction is computed using measurement data with added noise and a different computational grid. The use of a different reconstruction grid size is straightforward for a Cartesian sensor mask; in the forward simulation the pressure time-series at the Cartesian points are computed using interpolation and can thus be transposed to a grid of any size. The time-reversal reconstruction using a 300 by 300 pixel k-space grid is shown below.
In the reconstruction shown above, because the boundary condition is only enforced at a small number of points, the edges of the reconstructed image are considerably blurred. This effect can be reduced by interpolating the sensor data onto a continuous sensor surface. This can be achieved using interpCartData
and a binary sensor mask of a continuous arc that is spatially equivalent to the original Cartesian measurement surface. This function calculates the equivalent time-series at the sensor positions on the binary sensor mask from those on the Cartesian sensor mask via interpolation (nearest neighbour is used by default).
% create a binary sensor mask of an equivalent continuous circle pixel_radius = round(sensor_radius/kgrid_recon.dx); binary_sensor_mask = makeCircle(kgrid_recon.Nx, kgrid_recon.Nz, kgrid_recon.Nx/2, kgrid_recon.Nz/2, pixel_radius, sensor_angle); % interpolate data to remove the gaps [binary_sensor_data] = interpCartData(kgrid_recon, sensor_data, sensor_mask, binary_sensor_mask);
Details of the interpolation are printed to the command line.
Interpolating Cartesian sensor data... interpolation mode: nearest number of Cartesian sensor points: 70 number of binary sensor points: 574 computation completed in 0.018583s
The reconstructed image and a profile through z = -0.5 are shown below. The interpolation has considerably sharpened the edges of the reconstruction and the magnitude has also been improved through correction for the limited view problem.
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2D Time Reversal Reconstruction For A Line Sensor | 3D Time Reversal Reconstruction For A Planar Sensor | ![]() |
© 2009 Bradley Treeby and Ben Cox.