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2D Time Reversal Reconstruction For A Line Sensor Example

Overview

This example demonstrates the use of k-Wave for the time-reversal reconstruction of a two-dimensional photoacoustic wave-field recorded over a linear sensor array. The sensor data is simulated and then time-reversed using kspaceFirstOrder2D. It builds on the 2D FFT Reconstruction For A Line Sensor Example.

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Performing the time-reversal reconstruction

The first-order k-space functions already used for the simulation of photoacoustic wave propagation can also be used for photoacoustic image reconstruction by setting the optional input parameter 'TimeRev' to true. Instead of the initial pressure distribution, the time varying pressure recorded over the sensor array is given as p0. This pressure is then enforced over the given sensor mask as a time-varying Dirichlet boundary condition. By passing the sensor_data returned from a k-space simulation directly to kspaceFirstOrder2D with 'TimeRev' set to true, it is straightforward to compute a time-reversal reconstruction via the inverse crime.

% run the simulation
sensor_data = kspaceFirstOrder2D(p0, kgrid, c, rho, t_array, sensor_mask, input_args{:});
    
% add time-reversal flag to the input options
input_args = [input_args, {'TimeRev', true}];

% run the time-reversal reconstruction
p0_recon = kspaceFirstOrder2D(sensor_data, kgrid, c, rho, t_array, sensor_mask, input_args{:});

The initial photoacoustic pressure distribution used in the simulation, and the reconstructed initial pressure distribution using time-reversal are shown below.

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Comparison with the FFT reconstruction

It is useful to compare the performance of the time-reversal and FFT reconstruction algorithms. The command line output of the two functions are given below. It is clear that the time-reversal reconstruction takes significantly longer to compute; more than an order of magnitude for this example, even using the slower '*cubic' interpolation and a non 2^N grid size for the FFT comparison. However, in contrast to the one-step FFT reconstruction, time-reversal can account for a heterogeneous propagation medium and a sensor mask of arbitrary shape.

Running k-space time reversal...
  dt: 20ns, t_end: 15.54us, time steps: 778
  input grid size: 216 by 88 pixels (21.6 by 8.8mm)
  expanding computational grid...
  computation grid size: 256 by 128 pixels
  precomputation completed in 0.26306s
  starting time loop...
  computation completed in 11.7251s
Running k-space line reconstruction...
  grid size: 216 by 778 pixels
  interpolation mode: *cubic
  applying positivity condition...
  computation completed in 0.5837s

The time-reversed initial pressure distribution with a positivity condition is shown below. A profile through the larger disc, including a comparison with the analogous FFT reconstruction, is also given. The time-reversal reconstruction has a slightly improved signal to noise ratio, although, it is important to note that the inverse crime has been commited.

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© 2009 Bradley Treeby and Ben Cox.