Passive acoustic mapping using compressive sensing

1 . A near field passive compression wave imaging system for locating cavitation bubbles, the system comprising a plurality of sensor elements arranged in an array and each arranged to produce an output signal representing detected compression waves, and a processor configured to:

define a sample period, and a sample space over which the signal can be sampled at each of a plurality of sample points in the sample space;

define a grid of candidate cavitation bubble positions;

define a random projection identifying a respective different group of the sample points for each of the output signals;

sample each of the output signals at the group of sample points defined by the random projection to generate sample data;

define a dictionary which defines sample values that would be obtained for the signal of each of the respective group of sensor elements at each of the sample points for the sample period for a cavitation bubble at each of the candidate cavitation bubble positions;

define a vector, the vector having a plurality of elements each having a value, wherein the values of the elements identify at which of the candidate cavitation bubble positions a cavitation bubble is located;

perform a minimization operation to derive the vector element values, and hence the cavitation bubble positions, from the sample data, the dictionary and the random projection.

2 . The system according to claim 1 wherein the sample space is time and the processor is further configured to define a sample rate that defines the sample points as a plurality of sample times within the sample period at which samples can be taken.

3 . The system according to claim 1 wherein the sample space is frequency.

4 . The system according to claim 3 wherein the processor is further configured to define the sample points as a plurality of sample frequencies at which samples can be taken.

5 . The system according to claim 3 wherein the processor is configured to separate out an analogue component of the sensor output signals at each of the frequency sample points, and to sample each of the components for the sample period.

6 . The system according to claim 2 wherein the processor is configured to sample each of the sensor output signals, and to determine frequency component samples for each of the output signals from the time sample space.

7 . The system according to claim 1 wherein the processor is configured to form linear combinations of the sample data from the sensors thereby to form virtual sensor data corresponding to a plurality of virtual sensors.

8 . The system according to claim 1 wherein the random projection is defined by at least one matrix.

9 . The system according to claim 1 wherein the processor is configured to identify one of the sensor elements as a reference sensor element, to sample the output signal from the reference sensor element at each of the sample points to generate reference data, to define a delay time for each combination of one of the candidate cavitation bubble positions and one of the senor elements, and to determine the dictionary from the reference data and the delay times.

10 . A method of near field passive compression wave imaging of cavitation bubbles, the method comprising:

receiving a plurality of output signals representing detected compression waves each from a respective sensor element in an array of sensor elements;

defining a sample period, and a plurality of sample points over a sample space;

defining a grid of candidate cavitation bubble positions;

defining a random projection identifying a respective different group of the sample points for each of the output signals;

sampling each of the output signals at the group of sample points defined by the random projection to generate sample data;

defining a dictionary which defines sample values that would be obtained for a signal of each of the sensor elements at each of the respective group of sample points for the sample period for a cavitation bubble at each of the candidate cavitation bubble positions;

defining a vector, the vector having a plurality of elements each having a value, wherein the values of the elements identify at which of the candidate cavitation bubble positions a cavitation bubble is located; and

performing a minimization operation to derive the vector element values, and hence the cavitation bubble positions, from the sample data, the dictionary and the random projection.

11 . The method according to claim 10 wherein the sample space is time, the method further comprising defining a sample rate that defines the sample points as a plurality of sample times within the sample period at which samples can be taken.

12 . The method according to claim 10 wherein the sample space is frequency.

13 . The method according to claim 12 further comprising defining the sample points as a plurality of sample frequencies at which samples can be taken.

14 . The method according to claim 12 further comprising separating out an analogue component of the sensor output signals at each of the frequency sample points, and sampling each of the components for the sample period.

15 . The method according to claim 11 further comprising sampling each of the sensor output signals, and determining frequency component samples for each of the output signals from the time sample space.

16 . The method according to claim 10 further comprising forming linear combinations of the sample data from the sensors thereby to form virtual sensor data corresponding to a plurality of virtual sensors.

17 . The method according to claim 10 wherein the random projection is defined by at least one matrix.

18 . The method according to claim 10 further comprising identifying one of the sensor elements as a reference sensor element, sampling the output signal from the reference sensor element at each of the sample points to generate reference data, defining a delay time for each combination of one of the candidate cavitation bubble positions and one of the senor elements, and determining the dictionary from the reference data and the delay times.

19 . A near field passive compression wave imaging system for locating cavitation bubbles, the system comprising a plurality of sensor elements arranged in an array and each arranged to produce an output signal representing detected compression waves, and a processor configured to:

define a sample period, and a sample space over which the signal can be sampled at each of a plurality of sample points in the sample space;

define a grid of candidate cavitation bubble positions;

define a random projection identifying a respective different group of the sample points for each of the output signals;

sample each of the output signals at the group of sample points defined by the random projection to generate sample data;

define a dictionary which defines sample values that would be obtained for the signal of each of the respective group of sensor elements at each of the sample points for the sample period for a cavitation bubble at each of the candidate cavitation bubble positions;

define, for each of the sensor elements, a vector, the vector having a plurality of vector elements each having a value, wherein the values of the vector elements identify at which of the candidate cavitation bubble positions a cavitation bubble is located; and

perform a minimization operation to derive the vector element values, and hence the cavitation bubble positions, from the sample data, the dictionary, and the random projection.

20 . A method of near field passive compression wave imaging of cavitation bubbles, the method comprising:

receiving a plurality of output signals representing detected compression waves each from a respective sensor element in an array of sensor elements;

defining a sample period, and a plurality of sample points over a sample space;

defining a grid of candidate cavitation bubble positions;

defining a random projection identifying a respective different group of the sample points for each of the output signals;

sampling each of the output signals at the group of sample points defined by the random projection to generate sample data;

defining a dictionary which defines sample values that would be obtained for a signal of each of the sensor elements at each of the respective group of sample points for the sample period for a cavitation bubble at each of the candidate cavitation bubble positions;

defining, for each of the sensor elements, a vector, the vector having a plurality of vector elements each having a value, wherein the values of the vector elements identify at which of the candidate cavitation bubble positions a cavitation bubble is located; and

performing a minimization operation to derive the vector element values, and hence the cavitation bubble positions, from the sample data, the dictionary and the random projection.