Patent ID: 12259502

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made to exemplary embodiments of the disclosure, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. Moreover, the features explained in context of a specific embodiment, for example that one ofFIG.1, also apply to any one of the other embodiments, when appropriate, unless differently described.

FIG.1shows an exemplary embodiment of a method according to embodiments of the present disclosure. The method may be carried out by means of a system1, more in particular by an ultrasound system20. An example of an ultrasound system is described in context ofFIG.2.

The method may be an ultrasound method carried out by an ultrasound system. Possible ultrasound methods comprise B-mode imaging, shear wave elastography imaging (such as ShearWave® mode developed by the applicant, Doppler imaging, M mode imaging, CEUS imagine, Ultrafast™ Doppler imaging or angio mode named under Angio P.L.U.S™ ultrasound imaging or any other ultrasound imaging mode. Accordingly, different acquisition modes may be used to obtain signal data based in which the beamformed data may be determined. The method may be part of any of the above-mentioned methods or may be combined with any of these methods.

However, the method according to the present disclosure may also be applied to other technical fields than ultrasound examination. In particular, any technical field is possible which uses a plurality of transducer elements to acquire data/signals of an examined medium or environment and/or which may use a beamforming technique based on the collected data/signals. Examples comprise methods using a radar system, sonar system, seismology system, wireless communications system, radio astronomy system, acoustics system, Non-Destructive Testing (NDT) system and biomedicine system or any other technique in the field of active imaging. The principle of active imaging, i.e. of emitting pulses into a medium via one or several elements (sources) and receiving response pulses via one or several elements (receiver) and to estimate and/or compensate a clutter is similar to the functionalities of an ultrasound transducer.

Accordingly, the method according to the present disclosure may in each of these cases achieve the same positive technical effects as described above, for example of compensating undesired clutter at beamformed data. However, for mere illustration purposes of the present disclosure, in the following it is referred to the example of an ultrasound method.

The method may be for example a method for compensating clutter in beamformed data of a medium, and more in general for processing beamformed data.

In an optional operation (a) at least one pulse is transmitted into a medium. For example, the transmission step may comprise insonification of the medium with a cylindrical wave that focuses on a given point and/or plane waves of different angles. More in particular, in the transmission step a plurality of ultrasonic waves may be transmitted into an imaged region.

Generally, in the present disclosure a pulse may correspond to an acoustic or electrical signal emitted by a transducer element. The pulse may for example be defined by at least one of: the pulse duration, the frequency of the resulting wave, the number of cycles at the given frequency, the polarity of the pulse, etc. A wave may correspond to the wavefront generated by one or several transducer elements (i.e. by respectively emitted pulses). The wave may be controlled by means of emission delay between the different used transducer elements. Examples comprise a plane wave, a focused wave and a divergent wave. A beam may correspond to the physical area insonified by the wave (for example in the medium). Hence, the beam may be related to the wave but may have less or no temporal notion. For example, it may be referred to a beam when the depth of field of a focused beam is of interest.

In an optional operation (b), a response sequence is received from the medium by the set of transducer element(s). The response sequence may comprise backscattered echoes of the insonification of operation (a). The response sequence may also be referred to as signal data, in particular ultrasound signal data and/or RF and/or IQ signal data. The signal data may be in the time domain, more in particular in a spatio-temporal domain, as for example described in more detail below. In one example, the response sequence may be processed by bandpass filtering, in order to keep only one or several frequency ranges.

In an optional operation (c), the response sequence is processed to obtain beamformed data. Beamformed data may be data in the spatial domain, in particular in a two- or three-dimensional spatial domain, to represent characteristics of the medium. For example, in the case of B-mode imaging, the beamformed data is an estimation of the medium reflectivity. In one example, in case a plurality of beamformed data collections are obtained for a respective plurality of frequency ranges (as explained above), the beamformed data may be defined as a function of frequency.

It is noted that operations (a) to (c) are optional, as they may also be carried out by any other system than the system used for operations (d) to (f) or at another time. Data may also be provided by other functionalities such as simulation devices, insonification on a phantom, etc. It is also possible that the beamformed data are pre-stored, and for example provided by/read on a data storage, a communication interface, etc.

In optional operation (d) a first set of beamformed data associated with a first spatial region of the medium is selected. It is also possible to select a second set of beamformed data associated with a second spatial region of the medium in an optional operation (d′). Said selection may be controlled by a predefined selection algorithm, as for example described in more detail below.

In optional operation (e) (in particular following operation (d)) a second set of beamformed data associated with a second spatial region of the medium is determined. Said second region is located such that it may cause clutter at the first set, or in other words, such that the first set is susceptible for clutter generated at the second spatial region. Accordingly, based on the location of the first and second spatial region, it may be determined, in operation (e), whether the (second) region would generally be able to cause clutter at the first set or not. In case operation (d) is replaced by operation (d′), it is further possible in an optional operation (e′) to determine a first set of beamformed data associated with a first spatial region of the medium. The further features of the method may be adapted, respectively.

Optionally, operations (d) and (e) or both of them may be carried out in advance. In other words, these operations may be carried out once for a given transducer device, a given acquisition sequence and a given beamforming process and may then be valid for any medium. This is possible, since these operations does not depend on characteristics of a specific medium. Therefore, the calculations of these operations may be stored for the specific transducer device, acquisition sequence and beamforming process. Once the method is applied to specific medium, the calculations of these operations (d) and (e) may be read from a data storage. It is also possible to store respective calculations for different types of transducer devices.

In one example, for each first region the respectively (pre-)determined second regions may be stored in a look-up table or other form of mapping. The look-up table may be usable right after determination or in the future, locally or remotely.

In operation (f) the clutter caused by the second spatial region at the first set is estimated. Accordingly, in this operation, it is estimated, whether the second spatial regions actually cause clutter or not, and optionally also to which extent (i.e. amplitude or/and amount of clutter).

As stated above, for a given first spatial region and speed of sound model used for the beamforming process, there may be multiple second spatial regions that are susceptible to cause clutter at the first set for a given emission and a given received transducer. In some beamforming process, signals generated by multiple emitted waves and measured by multiple transducers are used to generate the first set of beamformed data. In this case, clutter contribution arises from multiple second spatial regions may be estimated for each emitted waves and received transducer used to beamform the first set.

According to a first option, the operations (e) and (f) may be repeated via loop L1over the spatial second regions for a given emitted waves and received transducer and may hence be carried out for several iterations. In each iteration a different second spatial region may be determined in operation (e) and a respective clutter contribution of said second region may be estimated in operation (f). Accordingly, in one example, a total or summed clutter at the first set may be estimated by a linear combination of the plurality of clutter contributions.

According to a second option, the operations (e) and (f) may be repeated via a further loop L2over the receiving transducer elements and may hence be carried out for several iterations. In each iteration, an ensemble of second spatial regions may be determined for a given (different, receiving) transducer element of the transducer device used for determining the first set of beamformed data. A respective clutter may be estimated for said transducer element in operations (e) and (f). As shown inFIG.2, the method may namely be applied to a single transducer element. The method may hence be repeated to consider a plurality of transducer elements. Said plurality of transducer elements may comprise all transducer elements of the transducer device or only those transducer elements whose signal data are used for determining the first set of beamformed data. The loop L2may comprise the loop L1. In other words, in each iteration of loop L2, the iterations according to loop L1may be included.

According to a third option, the operations (e) and (f) may be repeated via loop L3over emitted waves and may hence be carried out for several iterations, for example in case of synthetic beamforming. In each iteration, another emitted wave may be considered. Hence, the operations (e) and (f) may be iterated over the number of transmitted waves used to beamform the first set. A wave may be generated by one or several transducer elements. For example, the transducer device may generate planar emission waves with different predefined emission angles. A beam may also be referred to as the area through which the sound energy emitted from the transducer device travels. The loop L3may comprise at least one of or all of the loops L1and L2. In other words, in each iteration of loop L3, the iterations according to loops L1and L2may be included.

Note that loop L1, L2, L3may be processed in various order and combined in order to estimate a total clutter at the first set that arises from the combination of clutter contributions generated by each one of the second spatial regions determined by the loop L1, L2and L3.

It is also possible that at least one of loops L1to L3comprises an iteration from operation (e) to operation (g) (or alternatively (g′)), instead of from operation (e) to operation (f). Accordingly, in each iteration, the estimated clutter may be compensated and/or removed in operation (g),(g′).

In an optional operation (g) the estimated clutter is compensated at the beamformed data. In particular, in an optional operation (g′) the clutter may be removed at the beamformed data. It is however also possible that the clutter is compensated only in part.

According to a fourth option, the operations (d) to (g) (or alternatively (g′)) may be repeated via loop L4and may hence be carried out for several iterations. In each iteration a different first set associated with a respectively different first spatial region may be selected in operation (d). A respective clutter caused by a determined second spatial region may be estimated in operation (f) and compensated and/or removed in operation (g), (g′). For example, a predefined selection algorithm may select different first regions on a coordinate system of the beamformed data, for example in a stepwise manner. In this way, clutter may be estimated across a spatial region of interest in the beamformed data or across the complete spatial extension of the beamformed data. The loop L4may comprise at least one of or all of the loops L1to L3. In other words, in each iteration of loop L4, the iterations according to loops L1to L3may be included.

It is also possible that loop L4comprises an iteration from operation (e) to operation (f), instead of from operation (e) to operation (g),(g′). Accordingly, in each iteration of loop L4, the estimated clutter may be merely estimated in operation (f). Once the clutter has been estimated for the plurality of first sets (for example for the entirety of beamformed data), the clutter may be compensated and/or removed respectively for the plurality of first sets in operation (g),(g′).

It is further possible that the iterations of at least one of loops L1to L4are parallelly processed.

In case operations (d) and (e) are replaced by operations (d′) and (e′), the iterations of loops L1to L4may be adapted by respectively exchanging the first set by the second set and the second set by the first set.

In an optional operation (h) processed beamformed data may be obtained. This may in particular be the case, once the iterations of (at least one of or all of) loops L1to L4are terminated. As a result, the entirety of beamformed data may be processed. For example, the processed beamformed data may be displayed (for instance to a user of the system described in context ofFIG.2) and/or may be further processed. For example, the processed beamformed data may be provided to another system or module, for instance an algorithm or AI-based model.

According to a fifth option, the operations (d) to (h) may be repeated via loop L5and may hence be carried out for several iterations. In each iteration processing of the beamformed data according to operations (d) and (h) may be repeated. Accordingly, the loop L5may comprise at least one of or all of the loops L1to L4. In other words, in each iteration of loop L5, the iterations according to loops L1to L4may be included. At each iteration, modified beamformed data may be obtained by processing the beamformed data obtained in a previous iteration. In other words, the modified beamformed data obtained in a first iteration may be used in a subsequent second iteration. Accordingly, with each iteration, the clutter may be more accurately estimated and compensated.

The method may also be carried out using any combination of loops L1to L5.

FIG.2shows a system carrying out a method according to an exemplary embodiment of the present disclosure.

The system100may for example be configured to obtain and process beamformed data of a medium11, or for instance for the purpose of imaging an area in a medium11.

The medium11is for instance a living body and in particular human or animal bodies, or can be any other biological or physic-chemical medium (e.g. in vitro medium). The medium may comprise variations in its physical properties. For example, the medium may comprise a liver, breast, muscles (muscle fibers), and in particular any interfaces in the medium (e.g. walls of organs). Such interfaces can namely have an increased reflectivity which might in return lead to clutter at other regions.

The system100may include a probe12comprising at least a transducer device, for example an ultrasound transducer device. Said transducer device may comprise one or a plurality of transducer elements20, for example in the form of a transducer array arranged along an x-axis. Each transducer element20may be adapted to transform a signal into an ultrasound wave (emit) and/or to transform an ultrasound wave into a signal (receive).

The system100may further include an electronic processing unit13. Said unit may optionally control the transducers in the probe in any mode (receive and/or emit) in the case the same probe is used for emission/reception. Different probes may also be used, either for emission/reception or for appropriate adaptation to scanned medium. Emit and receive transducer elements may be the same, or different ones, located on one single probe or on different probes.

Furthermore, the unit13may process ultrasound signal data, and determine characteristics of the medium and/or images of said characteristics.

The probe12may comprise a curved transducer so as to perform an ultrasound focusing to a predetermined position in front of the probe into a direction of a z axis. The probe12may also comprise a linear array of transducer. Moreover, the probe12may comprise few tens of transducer elements up to several thousand (for instance 128, 256, or 8 to 2064) juxtaposed along an x axis so as to perform ultrasound focusing into a bi-dimensional (2D) plane. The probe12may comprise a bi-dimensional array so as to perform ultrasound focusing into a tri-dimensional (3D) volume. Moreover, the probe may also comprise several transducer devices, for example at least one for emission and at least one for reception. In another example, the probe12may comprise a single transducer element. In another example, the probe12may comprise a transducer device in a matrix form (comprising in this case for example up to several thousand transducer elements).

The above processing unit13and the probe12may be configured to send an emitted sequence ES of ultrasound waves We into the medium11, using for example one transducer elements20or a predefined group of transducer element20. The above processing unit13and the probe12may further be configured to receive a received sequence RS of ultrasound waves (i.e. ultrasound signal data) from the medium, using for example one transducer element20or a predefined group of transducer elements20(the same or another than that one used for emission).

The ultrasound waves We, Wr toward and from the location may be a focused wave (beam) or a non-focused beam. In this context, a pre-defined beamforming method may be used, for example: The emitted ultrasound wave We may be generated by a plurality of transducers signals that are delayed and transmitted to each transducer of a transducer array. The received ultrasound wave Wr may be composed of a plurality of transducer signals that are combined by delay and summation to produce a received sequence RS.

In a possible embodiment of the method ofFIG.1specific transducer element20amay be considered. A clutter caused by a second spatial region r2at a first set of beamformed data associated with a first spatial region r1may be estimated.

As shown inFIG.2, for a given emission wave (or the respective acoustic beam) the echo signal from both regions r1and r2may have the same round trip propagation time for the received transducer element20a. Accordingly, the signal data received from the first region r1may be isochronous to signal data received from second region r2. Hence, since the signals associated with the respective first and second set have the same propagation time for the transducer element20a, the signals associated with the second set can potentially cause clutter at the first set. In a simplified manner, it may be said that region r2is isochronous to region r1for a given transducer element and a given emission wave.

Due to this isochronous characteristic, the second set of beamformed data associated with the second spatial region r2is located such that the first set is susceptible for clutter generated at the second spatial region r2. In other words, an area (or location) may be determined on which any second regions are located which can generate clutter at the first set. In one example, said area may have the form of a parabola p1(for example in case of a planar emission wave). However, the area may also have any other form, for example of an ellipse. Generally, the area may be determined as a function of at least one of the selected first set, the considered transducer element, the geometry of the transducer device (or more in particular its transducer array), the emission wave (or the respective acoustic beam), and a predetermined propagation speed model of the medium.

In one example, the propagation speed c may be assumed to be constant in the medium. In another example, the propagation speed c may be determined by a propagation speed model. If for example the medium is known, speed values may be attributed to different areas of the medium, for instance to muscles, etc.

It may be assumed in the present disclosure that the size of the transducer element may be relatively small in comparison to the wavelength of the emitted waves and/or their spatial pulse length. The spatial pulse length of an emitted wave may also determine the width of the above-mentioned area, i.e. of the exemplary parabola p1on which second regions are located.

In order to estimate the clutter (in particular to evaluate whether there exist really clutter caused by r2), the second set of beamformed data associated with r2may be taken into account, in particular the amplitude (or energy level) of said second set. In other words, the clutter may be estimated as a function of the second set and/or the amplitude of the second set. It is further possible to take the position of the r1and r2into account. For example, the closer they are located to each other and/or the closer the second region r2is to a point directly ahead of the considered transducer element (in the direction z), the more the clutter contribution of said second region r2may be weighted. Furthermore, in case the amplitude of the second set does not exceed a predefined threshold, r2may be completely disregarded in the estimation operation. Generally, characteristics of r1and r2(for example their respective amplitude or location) may be determined in the associated beamformed data, i.e. in the first and second set of beamformed data.

A corresponding exemplary scenario is shown for transducer element20bin view of spatial regions r1and r3being located on a parabola p2relevant for the transducer element20b. Accordingly, for transducer element20bthe clutter caused by the third spatial region r3may be estimated at the first set. In other words, in order to estimate the clutter at the first set, a plurality of transducer elements20a,20bmay be considered. Said plurality of transducer elements may comprise all transducer elements of the transducer device or only those transducer elements whose signal data are used for determining the first set of beamformed data (cf. also the iteration over loop L2, as explained above).

FIG.3shows an example of RF signal data of a medium composed by three reflectors. The RF signals have been measured in this example by a linear array and results from the insonification of this medium with a plane wave of incident angle equal to 0 with regards to the ultrasound array. In this example the RF signal data are in the form of a two-dimensional matrix. The signal data may be in the time domain or more in particular in a space-time domain. The signal data may have hence two dimensions wherein one dimension (inFIG.3the vertical axis) reflects the acquisition time and the other dimension (inFIG.3the horizontal axis) reflects the spatial axis of the transducer array of the used transducer device (i.e. inFIG.2the X-axis). Said signal data ofFIG.3may be acquired by a transducer device, as for example shown inFIG.2.

The example ofFIG.3shows signal data received from a medium with three point reflectors leading to three arched signal responses31a,31b,31c.

FIG.4shows the beamformed data of the RF signal data of theFIG.3. Said beamformed data are in the spatial domain. The beamformed data may have two dimensions wherein one dimension (inFIG.4the vertical axis) reflects the depth direction of the medium (i.e. inFIG.2the Z-axis) and the other dimension (inFIG.4the horizontal axis) corresponds to the axis of the transducer array of the used transducer device (i.e. inFIG.2the X-axis).

The beamformed data may be obtained by a Delay And Sum (DAS) beamformer, as shown in equation (2):

o⁡(x,z)=∑n=0N-1⁢αn⁢sn(t-τn)∑n=0N-1⁢αn2(2)where:τnis the estimated round-trip propagation time for the incident wave to travel to point (x,z) and to back-propagates toward the transducer element n, andαnis the apodization coefficient linked to (x,z) and transducer element n

An example of an optimum result of the beamformed data is shown inFIG.4which illustrates the three beamformed pixels40a,40b,40c(each one highlighted by a circle), which represent the reflectors in the medium.

However, the DAS beamformer is optimal in case of a single point reflector only. Therefore, in the example ofFIG.3, the multiple (i.e. inFIG.3three) point reflectors result in clutter blurring images and degrading contrast. This may be in particular due to the overlapping sections30of the arch signals31a,31b,31c. As a consequence, the beamformed data ofFIG.4would in reality be deteriorated by clutter.

FIG.5shows the principles of a first example of a method for compensating clutter. In particular,FIG.5shows four stages of an exemplary Expectation-Maximization (E-M) method for compensating clutter. The used E-M algorithm may enable to separate the not-tractable problem of likelihood maximization into parallel easy likelihood maximizations.

In stage S1beamformed data are shown (obtained for example in operation (c) of the method ofFIG.1) which may comprise undesired clutter.

In stage S2the beamformed data may be transformed back into RF signal data. Accordingly, the pixels of the beamformed data matrix may be back-projected to the RF data matrix, i.e. to inverse the beamforming process.

In stage S3, for a plurality of different spatial regions or for each spatial region of the medium, modified RF signal data may be built by removing the contribution of other (or all other) spatial regions. Said operation may be referred to as the E (estimation) step. In the example ofFIG.5, the contribution of the reflectors associated with pixels40a,40c, i.e. arches31a,31care “removed”.

In stage S4the modified RF signal data is beamformed, to obtain the beamformed data of isolated pixel40b. A regular DAS beamformer may be used in for this purpose. Said operation may also be referred to as the M (Mximisation) step.

The E-step and the M-step may be repeatedly performed in a plurality of iterations. As starting point in the first iteration the first E-step may use conventional beamformed data (cf. stage S1), and the subsequent E-step may be based on the beamformed data obtained in the preceding M-step (cf. stage S4). Every iteration of the method may result in a modified RF data matrix building step (cf. stage S3), based on the current image estimate followed by a regular DAS beamforming (cf. stage S4) operated on the modified RF data matrix.

The method ofFIG.5may decouple the complicated multiparameter optimization problem of image beamforming while taking into account off-axis signals into N separate maximum likelihood optimizations, with N being the total number of spatial regions. However, the method ofFIG.5iterates back and forth between beamformed data (i.e. parameter estimates) and RF signal data (i.e. observed data), which is computationally expensive.

FIG.6shows the principles of a second enhanced exemplary embodiment of a method for compensating clutter according to the present disclosure.

In the embodiment ofFIG.6the method does not need to iterate back and forth between beamformed data (i.e. parameter estimates) and RF signal data (i.e. observed data) and can therefore be computationally less expensive (for example in view of the required time, resources, memory, power, etc.). In particular, the method may process merely beamformed data, i.e. operate merely with beamformed data.

It is possible to avoid iterating back and forth between beamformed data and RF signal data, since beamforming is a linear process. Therefore, removing a linear combination of signals from beamformed data is equivalent to removing a specific signal from RF data. Moreover, for predetermined or known characteristics of a transducer device (e.g. the geometry of the transducer array, the type of wave etc.) it is possible to predict which reflectors are going to impact a specific pixel, or in general terms, which second special region can cause clutter in a first set of beamformed data associated with a first region.

The improvement of the embodiment ofFIG.6may consist in implementing the E-M method ofFIG.5on beamformed data. The E step may remove a linear combination of second spatial regions (for example pixels) that are located so that they can generate clutter on a first spatial region (for example a pixel of interest). Accordingly, the M step is combined with the E step such that the computationally expensive back and forth processing of beamforming and inverse beamforming can be avoided.

Accordingly, the embodiment ofFIG.6may save a significant amount of computation operations because it implies no need to back-project the pixels from the image to the RF data matrix, i.e. to inverse the beamforming process.

FIG.6schematically illustrates two transducer elements20c,20dand respective isochronous reception areas (schematically indicated by exemplary parabolas60a,60b). As further shown, pixel40aassociated with a respective region in the medium lies on parabola60a, pixel40cassociated with a respective region in the medium lies on parabola60b, and pixel40bassociated with a respective region in the medium lies on the overlapping section of parabolas60aand60b. The principles of estimating clutter may correspond to those described above in context ofFIG.2. However, in context ofFIG.6it is referred to the beamformed data, i.e. to a first and a second set of beamformed data according to the present disclosure. In the example ofFIG.6, these first and second sets may be respective pixel40a,40b

The signal data received from for example a first region associated with the first pixel40amay be isochronous to signal data received from a second region associated with the second pixel40b. Hence, since the signals associated with the respective first and second beamformed pixel may have the same propagation time at the transducer element20c, the signals associated with the second pixel may cause clutter at the first beamformed pixel.

More generally, any pixel located on the parabola60amay imply isochronous signal data for the (selected) first pixel40a. Hence, these pixels may be determined as being associated with second spatial regions of the medium that are located such that they can cause clutter at the first pixel40a.

For each of these pixels the clutter contribution may be estimated as a function of the amplitude or intensity of the determined pixels on the parabola60a.

In a further option, in order to reduce computational power, only such pixels located on the parabola60amay be considered for estimating the clutter, whose amplitude exceeds a predefined threshold. This may simplify the method and advantageously reduce computational costs.

Furthermore, in order to reduce further the clutter, the compensation method may be carried out in a plurality of iterations.

Instead of single pixels also groups or clusters of pixels may be considered as a set of beamformed data in the method.

A corresponding exemplary scenario is shown for transducer element20din view of pixels40aand40cbeing located on a parabola60brelevant for the transducer element20d. Accordingly, for transducer element20bthe clutter caused by a third region associated with pixel40cmay be estimated at pixel40a. In other words, in order to estimate the clutter at pixel40a, a plurality of transducer elements20c,20dmay be considered. Said plurality of transducer elements may comprise all transducer elements of the transducer device or only those transducer elements whose signal data are used for determining pixel40a(cf. also the iteration over loop L2, as explained above).

The embodiment ofFIG.6may correspond to the method described in context ofFIGS.1and2and may comprise any of the features described in the context ofFIGS.1and2.

The second spatial regions may also be determined according to the following example. In said example, a medium is insonified by means of a linear array that generates successive plane waves with varying incident angle. Furthermore, the response sequence of the medium received by the linear transducer array is processed to obtain two-dimensional beamformed data. In other words, the beamformed may be in the form of pixels in two-dimensional matrix. Each pixel may correspond to a set of beamformed data according to present disclosure (for example an in-phase and a quadrature phase, IQ, value).

M(x0,z0) may be a first spatial region associated with a first beamformed IQ data set according to the present disclosure. M(x0,z0) then refer to the pixel associated to this first spatial region. Then, the location of the second spatial regions that may cause clutter at the first. N(x,z) refer to such second spatial regions. By construction, N and M share the same propagation time for a given transmitted angled plane wave θinand a given receive transducer element Pout(xout,zout=0). In the following, the medium speed of sound is assumed constant and equal to c. The following demonstration aims at computed the coordinates (x,z) of point N that validate the above conditions.

The transmit propagation time tinrequired for the plane wave of angle θinto reach the point M (x0,z0) can be expressed as, cf. equation (3):

tin(θin,x,z)=1c⁢(x0⁢sin⁡(θin)+z0⁢cos⁡(θin)),(3)

The receive propagation time toutrequired for echoes generated at point M(x0,z0) to reach the transducer P(uout,0) can be expressed as, cf. equation (4):

tout(xout,x,z)=1c⁢(x0-xout)2+z0.(4)

The round-trip time of flight t0of echoes generated at point M(x0,z0) and measured by transducer Pout(xout,zout=0) can then be expressed as, cf. equation (5):

t⁡(x0,y0,θin,xout)=1c⁢(x0⁢sin⁡(θin)+z0⁢cos⁡(θin)+(x0-xout)2+z02)=t0.(5)

By definition, N(x,z) generates clutter at the pixel M(x0,z0). Consequently, M and N are isochronous, meaning that they share the same round-trip propagation time for the given plane wave θinand received transducer Pout. As a result, the coordinates (x,z) are solution of the following equation (6):

t⁡(x,z,θin,xout)=1c⁢(x⁢sin⁡(θin)+z⁢cos⁡(θin)+(x-xout)2+z2)=t0.(6)

After development, (Eq. (6)) can be expressed as, cf. equation (7):

x2(1-sin⁡(θin)2)+z2(1-cos2(θin))+2⁢x⁡(ct0⁢sin⁡(θin)-xout)+2⁢zct0⁢cos⁡(θin)-2⁢xz⁢cos⁡(θin)⁢sin⁡(θin)+xout2-c2⁢t02=0.(7)

This equation corresponds to a quadratic curve. One may compute the determinant of the matrix of the quadratic J is null, cf. equation (8):

J=(1-sin⁡(θin)2)⁢(1-cos2(θin))-(-cos⁡(θin)⁢sin⁡(θin))2=0.(8)

This characteristic ensure that the quadratic curve is a parabola.

In a first exemplary case, where the angle θinof the plane wave is zero, (Eq. (7)) can be simplified and the z coordinate of the second region may be determined as a function the x coordinate through the following equation (9):

z=-x2+2⁢xxout-xout2+c2⁢t022⁢ct0.(9)
This equation corresponds to a parabola curve. Only point N(x,z) whose coordinates validate the above equation (9) should be considered as potential source of clutter at the first data set corresponding to the spatial region M(x0,z0).

In a second exemplary case, the general problem may be considered. First a change of coordinates may be performed. The coordinate system may be rotated by an angle θ and a new coordinate system (x′,z′) may be obtained which can be described by, cf. equation (10) and (11):

x=x′⁢cos⁡(θ)+z′⁢sin⁡(θ)(10)z=-x′⁢sin⁡(θ)+z′⁢cos⁡(θ)(11)
By using these new coordinates, (Eq. 7) can be simplified and z′ can be expressed as a function of x′, cf. equation (12):

zcl′=x′2(cos4(θ)+sin4(θ))-2⁢x′⁢xout⁢cos⁡(θ)+xout2-c2⁢t022⁢sin⁡(θ)⁢xout-ct0(12)

Once x′ and z′ have been determined, it may be reverted to x and z if necessary, by a rotation of the angle—θ.

Throughout the description, including the claims, the term “comprising a” should be understood as being synonymous with “comprising at least one” unless otherwise stated. In addition, any range set forth in the description, including the claims should be understood as including its end value(s) unless otherwise stated. Specific values for described elements should be understood to be within accepted manufacturing or industry tolerances known to one of skill in the art, and any use of the terms “substantially” and/or “approximately” and/or “generally” should be understood to mean falling within such accepted tolerances.

Although the present disclosure herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present disclosure.

It is intended that the specification and examples be considered as exemplary only, with a true scope of the disclosure being indicated by the following claims.

A reference herein to a patent document or any other matter identified as prior art, is not to be taken as an admission that the document or other matter was known or that the information it contains was part of the common general knowledge as at the priority date of any of the claims.