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k-Wave Toolbox


Compute k-Wave input plane from measured time-varying data.


source_estimate = calculateMassSource(measured_data, dx, dt, c0, source_offset)
source_estimate = calculateMassSource(measured_data, dx, dt, c0, source_offset, grid_expansion)
[source_estimate, output] = calculateMassSource(measured_data, dx, dt, c0, source_offset, grid_expansion)
[source_estimate, output] = calculateMassSource(measured_data, dx, dt, c0, source_offset, grid_expansion, ...)


calculateMassSource takes a measured 2D plane of time-varying pressure signals (e.g., measured using a hydrophone in a scanning tank) and calculates an equivalent time-varying additive pressure source positioned a given distance away that recreates the measured data when used as an input to k-Wave (i.e., by assigning the equivalent source to source.p with source.p_mode = 'additive').

The equivalent source is calculated using an iterative optimisation based on gradient descent, where functional gradients are calculated using the adjoint. Both the forward and adjoint operators are computed using kspaceFirstOrder3D. The calculation assumes the propagation is linear and the medium is lossless. The algorithm and approach are described in detail in [1].

If the source is larger than the measured input plane, for example, if measuring a focused bowl transducer, a suitable value should be specified for the value of grid_expansion. Note, the value of source_offset does not need to match the position of the real source in the experiment.

An alternative approach to project measured data using k-Wave is to directly use the measured data as a pressure source with a Dirichlet boundary condition (i.e., by assigning the measured data to source.p and setting source.p_mode = 'dirichlet'). However, this approach leads to errors in the imposed spatial gradient, which manifests as errors in the projected field. Thus, for accurate holographic projections using k-Wave, it is recommended to use calculateMassSource to first calculate the input data (see [1] for a comparison).

[1] Treeby, B., Lucka, F., Martin, E., & Cox, B. T. (2018). Equivalent-Source Acoustic Holography for Projecting Measured Ultrasound Fields Through Complex Media. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 65(10), 1857-1864.


measured_data 3D matrix containing the time varying pressure over a 2D input plane indexed as (x, y, t) [Pa].
dx Spatial step between grid points in the input plane [m].
dt Temporal step between time points in the input plane [s].
c0 Speed of sound in the medium [m/s].
source_offset Offset between the measured input plane and the source plane [grid points]. For example, if source_offset = 1, the input plane and source plane are on adjacent grid points.
grid_expansion Number of grid points used to expand the size of the estimated source plane in each lateral dimension relative to the measured input plane (set to 0 if not defined).

Optional Inputs

Optional 'string', value pairs that may be used to modify the default computational settings.

Input Valid Settings Default Description
'NumSteps' (integer) 20 Number of gradient descent steps.
'StepSize' (numeric scalar) 0.5 Starting size of gradient descent step.
'StepSizeIncrement' (numeric scalar) 1.1 Multiplicative factor used to increase the step size when the error is reduced.
'StepSizeDecrement' (numeric scalar) 0.5 Multiplicative factor used to decrease the step size when the error is increased.
'Plot' (Boolean scalar) true Boolean controlling whether the update steps are displayed.
'ReturnIterations' (Boolean scalar) false Boolean controlling whether the source estimate at each gradient descent step is returned. If set to true, the source_estimate output is given as a 4D matrix, each x-y plane corresponds to the source estimate at each step.
'UseCpp' 0: MATLAB code
1: C++ CPU code
2: C++ GPU code
0 Integer controlling whether the simulations are run using the C++ or CUDA implementations of kspaceFirstOrder3D.


source_estimate If 'ReturnIterations' is false (the default), source_estimate is given as a 3D matrix of pressure [Pa] indexed as (x, y, t). If 'ReturnIterations' is true, source_estimate is given as a 4D matrix containing the source estimate after each iteration, indexed as (x, y, t, iteration).
output Structure containing details of the optimisation with the following fields:

See Also

calculateMassSourceCW, kspaceFirstOrder3D