Method and system for obtaining a motion surrogate signal

Abstract

A method for obtaining a motion surrogate signal in medical imaging, the method comprising the steps of: receiving 102 a projection stack comprising a plurality of two-dimensional projections of a patient volume; selecting a plurality 104 of sub-volumes of the projection stack; extracting 106 a candidate motion surrogate signal from projection data contained within each sub-volume of the projection stack to create a plurality of candidate motion surrogate signals; and combining 108 the plurality of candidate motion surrogate signals into a single final motion surrogate signal. The final surrogate may be an average of the candidate set or their weighted sum, the weights possibly being noise-dependent. The method may be implemented iteratively. A reference signal, possibly a sinusoid may be compared to the candidate surrogates. Differences between sub-stacks may be computed. High or low-frequency variations may be removed from the signals.

Description

Field of the Invention Embodiments of the present invention described herein relate to methods and systems for obtaining a motion surrogate signal. More specifically, the present invention relates to a computer-implemented method for obtaining a motion surrogate signal, and data processing apparatuses, computer programs, and non-transitory computer-readable storage mediums configured to execute methods of obtaining a motion surrogate signal. Background of the Invention Radiotherapy (RT) is one of the cornerstones of cancer treatment, using ionizing radiation to eradicate tumor cells. A total radiation dose for a patient is typically divided into 3-30 daily fractions to optimize its effect. As the surrounding normal tissue is also sensitive to radiation, highly accurate delivery is a key part of effective RT. Image guided RT (IGRT) is a technique to capture the anatomy of the patient at the time of dose fraction delivery, using in-room imaging in order to align the treatment beam with the tumor location. Cone Beam Computed Tomography (CBCT) is the most widely used imaging modality for IGRT. In CBCT imaging, a motion surrogate refers to a measure or signal that indirectly represents the motion of anatomical structures or the patient during image acquisition. This motion is typically due to involuntary movements such as breathing, cardiac motion, or other physiological factors. The need for motion surrogates arises because capturing high-quality CBCT images requires the patient to remain as still as possible during the scan. However, involuntary motion, such as breathing, can lead to motion artifacts in the images, reducing their quality and diagnostic value. Motion surrogates help in managing this challenge by providing a means to monitor and compensate for such motion during image acquisition. In particular, respiratory motion surrogates track the motion of the patient's respiratory cycle. Types of respiratory motion surrogates include: external surrogates where external markers or sensors are placed on the patient's chest or abdomen to monitor the movement associated with breathing; and internal surrogates where internal structures such as the diaphragm or lung are directly monitored using imaging modalities. Examples of internal surrogate methods include the Amsterdam Shroud method (Zijp, Lambert &Sonke, JJ &Herk, M. (2004). Extraction of the Respiratory Signal from Sequential Thorax Cone-Beam X-Ray Images. Proc. 14th ICCR.) and an intensity-based approach (Kavanagh, Anthony, etal. "Obtaining breathing patterns from any sequential thoracic x-ray image set." Physics in Medicine &Biology 54.16 (2009): 4879.). Disadvantages of external surrogate methods include the need for additional measurements or motion tracking components. Disadvantages of known internal surrogate methods include that they only work on restricted anatomy (the lung or the diaphragm) and / or that they require human intervention (e.g. identification of a region of interest). Once a motion surrogate is obtained, it is used to gate the CBCT acquisition or to sort acquired data into different motion phases. Gating involves triggering the CBCT acquisition based on specific phases of the motion cycle (e.g., end-expiration for respiratory gating), ensuring that images are acquired when motion is minimal. Sorting the data into different motion phases allows for retrospective sorting and analysis of the data based on different motion states, facilitating motion correction or compensation techniques. Motion surrogates play a crucial role in improving the quality and accuracy of CBCT images by enabling motion management strategies during image acquisition. They help mitigate motion artifacts and ensure that diagnostic information is preserved in the final images. In medical imaging, high image quality during radiation therapy is an important aid to accurately adjust, for instance, cancer treatments according to the current medical state of the patient. Summary of the Invention It is an aim of the present disclosure to at least partially address one or more of the challenges mentioned above. The invention is defined in the independent claims, to which reference should now be made. Further features are set out in the dependent claims. According to an aspect of the invention, there is provided a method of obtaining a motion surrogate signal. The method comprises receiving a projection stack comprising a plurality of two-dimensional (2D) projections of a patient volume. The projection stack may be acquired or received from external computational means, such as a data storage server, or directly from an imaging or treatment system. The projection stack comprises projections, which are representative of measured ray intensities corresponding to attenuated rays of radiation. Beams of rays are emitted from some radiation source, passed through the region of the patient, and subsequently detected at a detector. The detector and the radiation source may be configured on or in a gantry and may be rotated about an axis of the patient. Equivalently this rotation is about a radiation isocentre, which is the point (or centre of mass of a small bound region) in space through which rays intersect when the detector and the radiation source are rotated during beam-on. The techniques herein are equally applicable to static detectors and static radiation sources, arranged circumferentially about an axis of the patient. Similarly, the techniques herein are equally applicable to a combination of a static detector and rotating radiation sources, or a rotating detector and static radiation sources. The method further comprises selecting a plurality of sub-volumes of the projection stack. A sub-volume of the projection stack may refer to a subset (or all) of the acquired 2D projections that cover a fixed sub-region of the detector. For example, a sub-volume may be created by taking the same rectangular sub-region of every projection. The method further comprises extracting a candidate motion surrogate signal from projection data contained within each sub-volume of the projection stack to create a plurality of candidate motion surrogate signals; and combining the plurality of candidate motion surrogate signals into a single final motion surrogate signal. Several advantages are obtained from embodiments according to the above-described aspect. The method extracts and combines multiple noisy (and easy to obtain) motion surrogates into a single clean motion surrogate. Unlike previous methods for obtaining motion surrogates, this method does not require specific anatomy to be imaged, nor a specific field of view (FOV). In some embodiments, the combining step comprises averaging the plurality of candidate motion surrogate signals to produce the single final motion surrogate signal. This averaging may involve using a weighted average. In some embodiments, each candidate motion surrogate signal is assigned a weight, and the plurality of candidate motion surrogate signals are combined into the single final motion surrogate signal using a weighted sum of the plurality of candidate motion surrogate signals. Any suitable weighting scheme may be used. High weights should be assigned to signals for which motion (e.g. breathing motion) contributes significantly to the signal variation, and low weights are assigned to the surrogates which contain only very little or no relationship to the breathing motion. In other words, high weights may be assigned to signals with strong and approximately cyclic (e.g. sinusoidal) components and low levels of noise relative to this underlying cycle. In some embodiments, candidate motion surrogate signals with greater levels of noise are given lower weights and candidate motion surrogate signals with lower levels of noise are given higher weights. In some embodiments, the method further comprises generating a spatial saliency map showing where motion occurred within the projection stack (which may be used to infer the location of motion in the patient volume) based on the assigned weights of the candidate motion surrogate signals. A spatial saliency map indicates which regions were most valuable for the construction of the motion surrogate. The spatial saliency map may be created by calculating the average weight for each pixel / region of the projection. In some embodiments, selecting a plurality of sub-volumes of the projection stack comprises: selecting a region of the two-dimensional projections and extracting this region over at least a subset of the projection stack (in some embodiments, this may be the whole of the projection stack) to obtain a sub-volume of the projection stack; and repeating the above step at least once to obtain a plurality of sub-volumes. In some embodiments, the final motion surrogate signal is a respiratory motion surrogate signal or a cardiac motion surrogate signal. In some embodiments, the method further comprises using the single final motion surrogate signal in a reconstruction process to reconstruct a volumetric image from the projection stack. For example, this may involve using the motion surrogate to inform binning of the projections for binned 4D reconstruction or using the motion surrogate to create a motion compensated reconstruction. In some embodiments, the method may be used for binning projection data of the projection stack into a plurality of bins for image reconstruction, each bin corresponding to a portion of the respiratory / cardiac cycle, each bin having a reference motion surrogate value for the portion of the respiratory / cardiac cycle relating to that bin, wherein the projection data is binned based on a similarity of its motion surrogate signal value to the reference motion surrogate value. The motion surrogate signal value being the value of the single final motion surrogate signal at that projection. Each projection will have an associated motion surrogate signal value. In some embodiments, the method further comprises, prior to combining the plurality of candidate motion surrogate signals: for each candidate motion surrogate signal, determining a similarity of the signal to a reference signal; and discarding the candidate motion surrogate signals which are below a predetermined similarity threshold (and thus not using the discarded signals in the final combining step); or selecting the candidate motion surrogate signals which are above a predetermined similarity threshold (and thus using only the selected signals in the final combining step). This is advantageous because this removes candidate signals which do not provide useful information for the motion surrogate (they may be too noisy or may not have information regarding respiratory motion, if for example, the candidate signal was taken from anatomy not affected by respiratory motion). Generally, the reference signal can be created to check the candidate motion signals meet some expected criteria (e.g. the signal is sufficiently regular, sufficiently smooth, or has an expected frequency range). In some embodiments, the reference signal is a sinusoidal signal. For example, for each candidate motion surrogate signal, the method may determine effectively how “sinusoidal” the candidate signal is (i.e. how much does the signal resemble a sine wave). In this example, those signals which looked sinusoidal would meet the predetermined similarity threshold and be used in the final step of combining the plurality of candidate motion surrogate signals into the single final motion surrogate signal. This is advantageous as respiratory motion is approximately sinusoidal. In some embodiments, after receiving the projection stack, the method further comprises computing differences between consecutive projections to create a difference projection stack and selecting the plurality of sub-volumes from the difference projection stack. This is advantageous as it makes it easier to extract the candidate signals from the projections stack. Subtracting one projection from the following projection leaves only the "change" between the projections, which comprises: a) the change caused by slightly rotating between the two projections and b) the change caused by anatomy moving. Once the change caused by rotation is removed, an approximate motion surrogate is left. In some embodiments, extracting a candidate motion surrogate signal for each sub-volume comprises taking a mean value of each projection in the sub-volume to obtain the candidate motion surrogate signal. In some embodiments, the method further comprises, prior to combining the plurality of candidate motion signals, removing low frequency variation from the plurality of candidate motion surrogate signals. This is advantageous as this removes the slow variation caused by the rotation of the gantry during the scan where the projections are obtained. This is done before combining the candidate signals because the way in which rotation influences the signal may vary between the candidate signals. In some embodiments, the method further comprises, prior to combining the plurality of candidate motion signals, removing high frequency variation from the plurality of candidate motion surrogate signals. This is advantageous as this denoises the candidate surrogate signals. This may be done using any suitable smoothing approach. In some embodiments, the method further comprises removing high frequency variation from the single final motion surrogate. This is advantageous as this denoises the final motion surrogate signal. This may be done using any suitable smoothing approach. In some embodiments, the method further comprises estimating a confidence value of the motion surrogate signal for each two-dimensional projection based on calculating a variance between candidate motion surrogate values at that projection. In some embodiments, the projection stack serves for cone-beam computed tomography, CBCT, reconstruction. In some embodiments, the method may be applied in adaptive radiotherapy, which enables a patient’s treatment to be changed or adapted to respond to a signal that additional information is known about the patient or that the patient has changed from the original state at the time of planning. Embodiments of another aspect include a data processing apparatus comprising a memory storing computer-readable instructions and a processor. The processor (or controller circuitry) is configured to execute the instructions to carry out the method. Embodiments of another aspect include a computer program comprising instructions, which, when executed by computer, causes the computer to execute the method. Embodiments of another aspect include a non-transitory computer-readable storage medium comprising instructions, which, when executed by a computer, cause the computer to execute the method. Other features of the disclosure are described below and recited in the appended claims. The invention may be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. The invention may be implemented as a computer program or a computer program product, i.e., a computer program tangibly embodied in a non-transitory information carrier, e.g., in a machine-readable storage device or in a propagated signal, for execution by, or to control the operation of, one or more hardware modules. A computer program may be in the form of a stand-alone program, a computer program portion, or more than one computer program, and may be written in any form of programming language, including compiled or interpreted languages, and it may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a data processing environment. The invention is described in terms of particular embodiments. Other embodiments are within the scope of the following claims. For example, the steps of the invention may be performed in a different order and still achieve desirable results. Elements of the invention have been described using the terms “processor”, “input device” etc. The skilled person will appreciate that such functional terms and their equivalents may refer to parts of the system that are spatially separate but combine to serve the function defined. Equally, the same physical parts of the system may provide two or more of the functions defined. For example, separately defined means may be implemented using the same memory and / or processor as appropriate. Brief Description of the Drawings Embodiments of the invention will now be further described by way of example only and with reference to the accompanying drawings, wherein like reference numerals refer to like parts, and wherein: Figure 1 is a flow chart of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 2 is a flow chart of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 3 is a flow chart of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 4 is a flow chart of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 5 illustrates a step of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 6 illustrates a step of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 7 illustrates a step of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 8 illustrates a step of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 9 shows example results of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 10 shows example agreement between a method for obtaining a motion surrogate signal, according to an embodiment, and the known Amsterdam shroud method on chest data; Figure 11 shows a reconstructed abdominal scan using the result of a method for obtaining a motion surrogate signal, according to an embodiment; Figure 12 shows an example of a saliency map that may be produced as an additional output from a method for obtaining a motion surrogate signal, according to an embodiment; Figure 13 is a diagram of the geometric arrangement for cone beam projection scanning and reconstruction; Figure 14 is a diagram of a cone beam CT scanner suitable for obtaining a projection stack for use in a method for obtaining a motion surrogate signal, according to an embodiment; and Figure 15 is a radiotherapy system, suitable for using motion surrogate signals, according to embodiments. Detailed Description Overview Motion surrogates provide a means to monitor and compensate for respiratory or cardiac motion during image acquisition, for example, CBCT imaging. This reduces motion artifacts in CBCT images, and thus improves image quality and diagnostic value. This disclosure provides a method of obtaining a motion surrogate (a signal closely correlated with the patient’s breathing or cardiac motion over the course of a scan - also referred to herein as a “motion surrogate signal”) from CBCT projection data by using different (but potentially overlapping) regions (also referred to herein as sub-volumes) of the data to obtain multiple (inherently noisy) candidate surrogate signals. A sub-volume of a projection stack may refer to a subset (or all) of the acquired 2D projection images that cover a fixed sub-region of the detector. Alternatively, the sub-region may not be fixed and may vary between projections. These candidate surrogates contain various levels of information about the breathing or cardiac motion, and various degrees of noise. These candidate signals are then advantageously combined into a single (clean) final surrogate signal. The combination may be achieved using a weighted sum of the candidates. The weight may be calculated using a heuristic which assigns higher weights to less noisy and more regular candidates. Zero weight may be assigned to candidates deemed too poor by these metrics, to avoid these degrading the final surrogate. Fundamentally, the invention may be thought of as a method to extract and combine multiple noisy (and easy to obtain) motion surrogates into a single clean motion surrogate. Unlike previous methods, this method does not require specific anatomy to be imaged, nor a specific FOV. A CT image may be reconstructed from multiple projections that are acquired as an X-ray source rotates around the object (a patient). The acquisition geometry may be defined by the acquisition FOV, which may be determined by the beam angle, and may determine the maximum possible size of reconstructed image. Various aspects and details of these principal concepts will be described below with reference to Figures 1 to 15. Figure 1 shows a general method 100 for obtaining a motion surrogate. At step 102, a projection stack comprising a plurality of 2D projections of a patient volume is received. At step 104, a plurality of sub-volumes of the projection stack are selected. This may comprise selecting a region of the 2D projections and extracting this region over at least a subset of the projection stack (this could be over the whole projection stack) to obtain a sub-volume of the projection stack. This step may then be repeated at least once to obtain a plurality of subvolumes. As the projections are taken over the time of the scan, each projection is taken at a different instance of time. Thus, extracting the region over at least a subset of the projection stack involves extracting the region over projections taken at different instances of time. The 2D projection has dimensions of height and width. Thus, the projection stack may be visualised as having three dimensions, height, width and time. The plurality of sub-volumes are volumes within this 3D projection stack volume. At step 106, a candidate surrogate signal is extracted from projection data contained within each sub-volume to create a plurality of candidate surrogate signals. Extracting a candidate motion surrogate signal for each sub-volume may comprise taking a mean value of each projection in the sub-volume to obtain the candidate motion surrogate signal. At step 108, the plurality of candidate surrogate signals is combined into a single final surrogate signal. The combining step may comprise averaging the plurality of candidate motion surrogate signals (preferably using a weighted average) to produce the single final motion surrogate signal. If using a weighted average, each candidate motion surrogate signal may be assigned a weight, and the plurality of candidate motion surrogate signals may be combined into the single final motion surrogate signal using a weighted sum of the plurality of candidate motion surrogate signals. Candidate motion surrogate signals with greater levels of noise may be given lower weights (and thus have less of an impact on the final motion surrogate signal) and candidate motion surrogate signals with lower levels of noise may be given higher weights (and thus have more of an impact on the final motion surrogate signal). Figure 2 shows an example method 200 for obtaining a motion surrogate signal. Example method 200 is similar to method 100 described immediately above, but with additional optional steps 202 and / or 204. In method 200, between steps 106 and 108, the method 200 comprises removing low frequency variation from the plurality of candidate surrogate signals (step 202). This removes the slow variation caused by the rotation of the gantry during the scan where the projections are obtained. This is done before combining the candidate signals because the way in which rotation influences the signal may vary between the candidate signals. At this stage (i.e. between steps 106 and 108) the method may optionally comprise removing high frequency variation from the plurality of candidate motion surrogate signals. This denoises the candidate signals. After step 108, method 200 comprises removing high frequency variation from the single final surrogate signal (step 204). This denoises the final motion surrogate signal. Removing high frequency variation may be achieved by using any suitable smoothing approach. Figure 300 shows an example method 300 for obtaining a motion surrogate signal. Method 300 is similar to method 200 described immediately above, but with additional optional steps 302 and 304. In method 300, between steps 202 and 108, the method 300 comprises steps 302 and 304. At step 302, for each candidate surrogate signal, a similarity of the signal to a reference signal (e.g. a sinusoidal signal) is determined. At step 304, candidate surrogate signals which are above a predetermined similarity threshold are selected. It is then these selected candidate surrogate signals which are combined into the single final surrogate signal at step 108. It should be noted that optional steps 302 and 304 may equally be applied to method 100 and do not require the presence of steps 202 and / or 204. Figure 400 shows an example method 400 for obtaining a motion surrogate signal. Method 400 is similar to method 300 described immediately above, but with additional optional step 402. Between steps 102 and 104, method 400 comprises step 402. At step 402, differences between consecutive projections are computed to create a stack of difference images. It is then this stack of difference images from which the plurality of sub-volumes are selected from at step 104. It should be noted that optional step 402 may equally be applied to methods 100 or 200 and does not require the presence of steps 202, 204, 302 and / or 304. At step 106, a candidate surrogate signal is extracted from projection data contained within each sub-volume to create a plurality of candidate surrogate signals. Extracting a candidate motion surrogate signal for each sub-volume may comprise taking a mean value of each difference image in the stack to obtain the candidate motion surrogate signal. Some embodiments may comprise additional steps such as estimating a value of the motion surrogate signal for each 2D projection based on calculating a variance between candidate motion surrogate values at that projection, and / or generating a spatial saliency map showing where motion occurred in the patient volume based on the assigned weights of the candidate motion surrogate signals. Embodiments of the invention described herein may be used to obtain respiratory motion surrogate signals or cardiac motion surrogate signals as both respiratory motion and cyclic motion are cyclic. Respiratory motion is generally larger than cardiac motion, and thus if embodiments of the invention are used to obtain cardiac motion surrogate signals, there may be additional steps and / or considerations in order to measure the smaller cardiac motion instead of the larger respiratory motion. One option is for the projection data to be free from breathing (e.g. the patient should hold their breath over enough time to see cardiac motion). As such, the only cyclic cycle present in the projection data will be the cardiac motion. Another option is to restrict the projections to focus only on the heart region as a pre-processing step. The dominant cyclic signal from the heart region will be from cardiac motion. Another option is to extract the two most prominent signals from the same projection stack (e.g. running the same surrogate extraction twice, and in the second run strongly reducing the weights of the individual surrogates that are similar to the first extracted 'final surrogate'). Another option is to obtain an approximate cycle rate for the patient’s cardiac signal (e.g. 70 bpm) and choose a reference signal which captures motion with a similar cycle rate (e.g. has a similar frequency). Embodiments of the invention described herein are for obtaining motion surrogates. The motion surrogate may be used in a reconstruction process to reconstruct a volumetric image from the projection stack. For example, motion surrogates may be used for separating projections into bins for binned 4D reconstruction. Other uses of motion surrogates include using the surrogate to create a motion compensated reconstruction (in which all projections are used, but a motion-state dependent deformation field is used during the reconstruction). This may be done either using a known motion model (which may be extracted from a previous 4D CT scan, for example), or directly from the surrogate. Any of the methods 100, 200, 300, 400 described above may be used for binning projection data. For example, the motion surrogate obtained using any of methods 100, 200, 300, 400 may be used for binning projection data of the projection stack into a plurality of bins for image reconstruction, each bin corresponding to a portion of the respiratory / cardiac cycle. Each bin may have a reference motion surrogate value for the portion of the respiratory / cardiac cycle relating to that bin. The reference value for each bin may be a predicted value for what the motion surrogate of the projection data would be if the projection data was acquired during the portion of the respiratory / cardiac cycle corresponding to that bin. Projection data may be binned based on a similarity of its motion surrogate value to the reference motion surrogate value, wherein its motion surrogate value is a value of the motion surrogate signal at said projection data (obtained using any of methods 100, 200, 300, 400). The projection data may be binned at a projection level (i.e. whole projections are allocated to bins), the projection data may be binned at a pixel level (i.e. each pixel is binned individually), or anywhere in between, for example, regions of projections may be binned. The binning of the projection data may be weighted based on the similarity. 08 05 24 The use of the motion surrogate signal in binning projection data may improve upon known binning processes for 4D reconstruction. Instead of binning projections purely based on the time at which they were acquired (i.e. temporal binning), this approach may bin projections (or parts of projections) based on their similarity to a prediction of what the projection (or the part 5 of the projection) should look like if it were acquired at a certain point in the motion cycle. This is a weaker requirement than temporal binning, and thus allows more projection data to contribute to each bin. Further, the contribution of each projection (or part of a projection) to the reconstruction can be weighted based on their determined similarity. Further detail of this approach may be found in Elekta Limited’s co-filed application titled “Method and System for 10 Projection Binning for Image Reconstruction” with Agent Reference P149886GB00 and Application No. GB2406441.2. At a high level, embodiments of the present invention take input projection data comprising T sequential projection images (step 102), and output a vector of length T (the single final 15 surrogate signal), with one value corresponding to each projection, such that projections acquired at the same point in the breathing cycle have the same value, and projections acquired at similar points in the breathing cycle have similar values. One example of the method is detailed below. 20 Detailed Example 1. Extract candidate surrogates With reference to Figure 5, the projection data (obtained at step 102) comprises an ordered 25 series of T projection images (each of size HxW): [pi, p2,..., Pt], also referred to as a “projection stack”. This projection stack can be visualized as a 3D volume 502. The differences between sequential / consecutive projections are computed (step 402), d, = p, - P(i+i), resulting in a volume of T-1 difference images 504 each still of size HxW: [di, d2, ..., dj-i]. Each candidate surrogate is then produced by: 30 1. Choosing a spatial sub-region of the HxW image area (step 104), also referred to as a “sub-volume” (for example, the top left 8x8 pixels in the projection). As shown in Figure 6, a region 602 may be selected on the face of the difference volume 504, for example a rectangular region of height y and width x. This region can then be extracted over all 35 projections, resulting in a sub-volume of T-1 difference images each of size y by x. 2. Taking the mean of that sub-region independently in each of the T-1 difference images, resulting in a vector of length T-1. This is then the surrogate associated with that spatial sub-region (i.e. step 106). As shown in the example of Figure 6, the mean is taken over the height and width (y and x) dimensions to create a 1D signal 606 (with T-1 values) corresponding to the originally selected region. In this way any region selected on the face of the difference volume yields 1D signal. By changing the sub-region selected, different candidate surrogate signals are produced (step 106). This is shown in Figure 7 which shows different sub-regions 602, 702, 704, 706 and their corresponding candidate surrogate signal 606, 712, 714, 716, e.g. region 602 has corresponding candidate surrogate signal 606. By selecting multiple regions from the difference volume many 1D signals can be produced. These will then be combined at step 108 to produce a single final surrogate. Sub-regions can be of any size of shape, but as an example consider the case where projection images are 512x512 pixels, and the set of sub-regions are all rectangles with height and width each an integer multiple of 8, and with x and y pixel coordinates of the top left corner each being an integer multiple of 16 and taking only those rectangles that fit fully within the 512x512 image size. After this stage there are K candidate surrogate signals, each of which is a vector of length T-1. 2. Optionally: remove low variation from rotation, and denoise As an optional step (step 202), the slow variation caused by gantry rotation is removed from each of the candidate surrogates. Note that this step is performed before combining the candidate signals because the way in which rotation influences the signal may vary between candidates. Specifically, a highly smoothed version of the signal is subtracted from the original signal. In the smoothed signal any local fluctuations caused by breathing motion are smoothed away, leaving only the large-scale variation resulting from rotation. Thus, subtracting this smoothed signal should remove the change resulting from rotation from the surrogate, but leave the variations resulting from the breathing cycle. Any suitable smoothing approach can be used here, for example, a SavitzkyGolay filter with a large filter scale. Resulting candidate surrogates may be referred to as the “rotation corrected candidate surrogates”. Note this step also has the effect of making the mean value of the rotation-corrected candidate surrogates approximately zero. Next, an optional denoising step may be performed to try and remove noise from the rotation-corrected candidate surrogates. Specifically, very high frequency variation is removed from the signal by smoothing. Again, any suitable smoothing approach is possible, for example, a Savitzky-Golay filter with a small filter scale. The resulting signals may be referred to as the “cleaned candidate surrogates”. 3. Combining the candidate signals At this stage there is a set of K cleaned candidate surrogates (each of length T-1). To combine them into a single surrogate signal, a weight may be assigned to each surrogate and then a weighted sum may be calculated. Any suitable weighting scheme could be used here. High weights are assigned to signals for which breathing motion contributes significantly to the signal variation, and low weights are assigned to the surrogates which contain only very little or no relationship to the breathing motion. In other words, signals with strong and approximately regular cyclic (e.g., sinusoidal) components and low levels of noise relative to this underlying cycle are weighted highly and thus will have a greater impact on the final surrogate signal. This is shown in Figure 8 where a plurality of candidate surrogate signals 606, 712, 714, 716 are combined to produce a final surrogate signal 802. To combine the surrogates 606, 712, 714, 716, each surrogate is assigned a weight. In this example, candidate 606 is assigned a weight of 0.5, candidate 712 is assigned a weight of 0.3, candidate 714 is assigned a weight of 0, and candidate 716 is assigned a weight of 0.2. Note that some surrogates may be given a weight of 0 meaning that they will not contribute to the final surrogate signal. In the example, candidate 714 is very noisy which is why it is given a weight of 0. Finally, a weighted sum of the surrogates is taken to produce a single surrogate 802 (step 108), which then may undergo smoothing and cleaning before being given as the final output. In one example, the weight for a surrogate is calculated as follows. As the surrogate signals are centred on zero (from step 2 above) a binary version of each surrogate is created, which is 0 when for values less than 0 and 1 otherwise. The ‘run lengths’ for this binary signal are calculated, which is the length of each sequential run of 1s (or 0s). For example, the binary string 0011101000011 has runs of length 2,3,1,1,4, and 2. The standard deviation (std) of this set of run lengths is then calculated. If the std is low, then the signal is dominated by a regular cyclic component, whereas if the std is high the signal is likely either highly noisy or lacking a consistent cyclic component. Thus, the negative std is taken as the weight for each surrogate (offset by the highest std seen across all candidates, such that all weights are >=0). The surrogates with lower std values (i.e. the signals with cyclic components) are the signals which should be weighted more highly. The weight may be defined as w = k - std, where w is the resulting weight and k is a fixed value set as the largest std seen across all surrogates (to ensure w is never negative). This is one example of how to convert std values into weights such that high weights are given to low std values, and low weights are given to high std values. Many other ways to do such a conversion are possible. Finally, a weighted sum of the candidate surrogates is taken. Currently almost all candidates very likely have a weight >0, and thus would contribute to the final surrogate. However, in practice many of these surrogates may contain considerable noise and essentially no useful breathing motion signal, and thus will degrade the final surrogate if included in the weighted sum (even with a low weight). Thus, all candidates in the bottom X% (e.g., 50%, 60%, 70%, 80%, 90%, etc.) of signal weights may optionally be discarded, and the remaining (100-X)% (e.g., 50%, 40%, 30%, 20%, 10%, etc.) of weights may be linearly adjusted to lie between 0 and 1. X may be chosen depending on factors such as the number of candidates available or the quality of the candidate signals. The weighted sum of these X% is calculated to produce the final surrogate, which is now a single vector of length T-1 which may be referred to as the “combined surrogate”. This thresholding may be performed as described in steps 302 and 304, i.e. determining the similarity of the signal to a reference signal (e.g. a sinusoidal signal) may involve assigning a weight to the signal based on its similarity. The candidate motion surrogate signals which are below the predetermined similarity threshold (e.g. in the bottom X% of signal weights) may be discarded. Equally, the candidate motion surrogate signals which are above the predetermined similarity threshold (e.g. in the top X% of signal weights) may be selected and combined to form the single final surrogate signal (step 108). 3.a) Optional: per-projection surrogate confidence estimate A confidence estimate for the surrogate value at each frame can be produced by calculating the variance between the candidate surrogates (or just a top percentile of candidates) at that frame. A more refined approach can also be used, such as normalizing all signals before taking the variance, or similar. 3.b) Optional: spatial saliency map It is also possible to produce a saliency map over the projection image, indicating which regions were most valuable for the construction of the surrogate (in other words, a map showing where in the projection the motion visibly occurs). As each candidate surrogate comes from a known region in the projection image and also has an assigned weight, a saliency map can be created by calculating the average weight for each pixel in the projection image (with a range of specific implementations being possible, for example the average weight over all surrogates a pixel contributed to, or instead a weighted average with the weight being based on what percentage of the contributing region the pixel accounted for, etc). Smoothing this saliency map can also beneficially remove the artifacts resulting from the shape / spacings of the particular regions selected. 4. Optional: final signal cleaning Final correction on the combined surrogate may now be performed. First, the combined signal may be denoised (step 204), which can be done again as in the second step of stage 2 above. Secondly, the amplitude of the surrogate over the course of the scan can vary, and the rotation correction step in stage 2 only corrects for the slow variation in mean value. Thus, to produce a surrogate that is of a similar amplitude over all frames, the surrogate may be divided by a smoothed version of the absolute value of the surrogate (i.e. the signal may be divided by its approximate local amplitude). This amplitude corrected combined surrogate is now the final surrogate estimate. However, in this example, the surrogate is T-1 values (corresponding to the points exactly between each frame) due to the initial use of the difference images to calculate the candidate surrogates. Thus, this signal is resampled to T values, one for each frame, interpolating and extrapolating as necessary. Figure 9 shows example results on a 344 projection pelvis scan. A slice of the projection volume is shown, overlayed with the result from the surrogate extraction algorithm (i.e. the final motion surrogate signal). Note that here the x-axis values for the surrogate signals have been scaled and offset to create the overlay. Figure 9 shows the motion surrogate signal 906 resulting from embodiments of the present invention. This surrogate 906 is overlaid on a sinogram-view slice of the projection data 910 so that the agreement between the surrogate 906 and the structure visible in the projection data 910 can be observed. The extracted surrogate signal 906 is a continuously varying signal with no strictly enforced structure. However, for some use cases this signal needs to be converted into a more rigidly structured format, such as a signal that linearly increase and decreases between fixed minimum and maximum values over the cycle. One surrogate post-processing approach is shown where pulses 902 are used to estimate the peaks and troughs in the surrogate 906, and then, after some cleaning to remove unrealistically short pulses, these cleaned pulses 904 guide the extraction of a strict triangular wave signal 908 (i.e. a processed motion surrogate signal 908) from the original surrogate 906. This more standardized surrogate 908 format may then be used directly for projection binning. Figure 10 shows an example of the agreement between the method of the disclosure and the Amsterdam Shroud method on chest data. Note that here the sinusoidal surrogate has been ‘unwrapped’ to transition from 0 to 1 over a cycle, to match the format of the Amsterdam shroud output (rather than the surrogate increasing and then decreasing over a cycle, as in Figure 9). It can be seen that the Amsterdam Shroud method and the method of the disclosure have a strong agreement. Figure 11 shows a reconstructed abdominal scan using a binning approach using the motion surrogate signal obtained using the method of the disclosure. The binning approach used was to sort all the projections based on their surrogate value, then split that ordered list into 6 equally sized bins (+ / - 1 projection if the total number of projections was not devisable by 6). Thus, the first bin contains the 1 / 6th of the projections with the lowest surrogate values, and so on to the final bin, which contains the 1 / 6th of the projections with the highest surrogate values. Here we show three (of six) bins, with bin 0 and 2 approximately corresponding to maximum inhalation and maximum exhalation states respectively. As can be seen, the patient’s contour changes with the breathing motion, as does the shape and position of the internal gas bubble. Figure 12 shows an example of a saliency map that can be produced as an additional output from embodiments of the present invention. The leftmost image shows the mean projection from a CBCT chest scan, the central image shows the resulting saliency mask, with dark areas indicating regions that are more informative for the motion surrogate. The right image overlays a contour of the most salient region on the mean projection image, as can be seen the most informative region for predicting the motion surrogate is the diaphragm region, which aligns with expectation. Cone Beam Projection Acquisition Figure 13 illustrates the geometry of a typical cone beam projection acquisition setup 1300, as may be used to obtain projection data for use in embodiments. For simplicity, only the x-y plane is illustrated; the skilled reader will appreciate that the beam of rays extends also into the z-axis, orthogonal to the x-y plane. In this example, the acquisition setup captures projection data of object 1302. X-ray source 1304 generates and emits X-rays 1306 towards object 1302. In CBCT, X-rays may be considered as a beam of rays, emitted from a point source. Detector (or detectors) 1308 capture projections, which are sets of line integrals along paths that radiate from the source 1304. Multiple projections of the image may be acquired from different angles by rotating the source 1304 and detector 1308 around the centre of the image 1310. In the present example, the source 1304 and detector 1308 may be rotated arcuately along orbital path 1312. In this way, the x-y plane may be rotated counterclockwise around the point of origin (or centre of the image 1310) in a manner that keeps the mutual positional relationship between source 1304 and detector 1308 when passing through the orbital path 1312. Other configurations of imaging systems are, of course, feasible; for instance, the source may be configured to rotate and a complete ring of detectors may be configured to capture projections, or there may be multiple sources arranged circumferentially around a complete ring of detectors. Further, the imaging system may rotate the source along a helical path, so as to capture projection data along the axis of the object 1302 of interest (along the z-axis in the present example). The attenuation of the intensity of the rays that pass through the object 1302 may be measured by processing signals received from the detector 1308. By making projective measurements at a series of different projection angles through the object 1302, a sinogram may be constructed from the projection data, mapping the spatial dimension of the detector array to the projection angle dimension. The intensity attenuation resulting from a particular volume within the object will trace out a sine wave for the spatial dimension along the detector perpendicular to the rotation axis of the system. Volumes of the object farther from the centre of rotation correspond to sine waves with greater amplitudes than those corresponding to volumes nearer the centre of rotation. The phase of each sine wave in the sinogram corresponds to the relative angular positions with respect to the rotation axis. By performing an image reconstruction technique (such as an inverse Radon transform) on the projection data in the sinogram, one may reconstruct an image, where the reconstructed image corresponds to a cross-sectional slice of the object 1302. The detector 1308 may comprise underlying detector elements (such as pixels or bins of pixels), rather than a single active region. The measured ray intensities may then be taken as a function of underlying intensity signals acquired at detector elements of the detector. This is advantageous in that one reduces the impact of random noise, which may plague an intensity (particularly a low intensity) measured at a single detector element. For example, the measured ray intensities may be an average (mean, mode or median) of underlying single detector element intensities. Figure 14 illustrates the geometry of a cone beam projection acquisition setup, as incorporated into a medical CT scanner 1400. Radiation sources 1402 emit beams of X-ray radiation, which may pass through the patient supported on a couch within the CT scanner (not depicted). Detectors 1404 capture attenuated X-rays. The radiation sources 1402 and detectors 1404 may be configured to rotate within a gantry of the CT scanner, so as to acquire projective measurements at a series of different projection angles. As shown, the angular separation between measurement orientations need not be equal. Referring back to the method of the disclosure, the received projection stack may be acquired using the set up described above in relation to Figures 13 and 14. Radiotherapy System In medical imaging, motion surrogates are utilized to address challenges related to patient motion during imaging procedures. The motion surrogate signal obtained using the method of the disclosure may be used for respiratory or cardiac motion management. During imaging procedures such as MRI, CT scans, and PET scans, patient motion due to breathing can cause image artifacts and reduce image quality. Motion surrogates are used to monitor motion in realtime. By synchronizing image acquisition with the respiratory or cardiac cycle or employing motion-correction techniques, motion artifacts can be minimized, leading to clearer and more accurate images. The motion surrogate signal may be used in image registration techniques to align multiple images acquired at different time points or from different imaging modalities. By incorporating motion information from surrogates, algorithms can accurately register images despite patient motion, enabling the comparison and integration of imaging data for diagnosis and treatment planning. In particular, in adaptive radiotherapy, motion surrogates play a crucial role in tumor targeting and treatment delivery. The motion surrogate signal may be used when monitoring tumor motion during treatment sessions. This information is used to adjust the position and orientation of radiation beams in real-time, ensuring accurate delivery of radiation doses while minimizing damage to surrounding healthy tissues. Figure 15 is a block diagram of an implementation of a radiotherapy system 1500, suitable for executing methods according to embodiments. The example radiotherapy system 1500 comprises a computing system 1510 within which a set of instructions, for causing the computing system 1510 to perform the method (or steps thereof) discussed herein, may be executed. The computing system 1510 may implement an image reconstruction system. The image reconstruction system may use any conventional image reconstruction technique suitable for use with projection data. Examples of known suitable reconstruction techniques include a known Feldkamp, Davis, and Kress (FDK) reconstruction method, an iterative reconstruction method, an Al reconstruction method, a deep-learning based reconstruction method and a Polyquant reconstruction method. The computing system 1510 may also be referred to as a computer. In particular, the methods described herein may be implemented by a processor or controller circuitry 1511 of the computing system 1510. The computing system 1510 shall be taken to include any number or collection of machines, e.g., computing device(s), that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methods discussed herein. That is, hardware and / or software may be provided in a single computing device, or distributed across a plurality of computing devices in the computing system. In some implementations, one or more elements of the computing system may be connected (e.g., networked) to other machines, for example in a Local Area Network (LAN), an intranet, an extranet, or the Internet. One or more elements of the computing system may operate in the capacity of a server or a client machine in a client-server network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. One or more elements of the computing system may be a personal computer (PC), a tablet computer, a set-top box (STB), a Personal Digital Assistant (PDA), a cellular telephone, a web appliance, a server, a network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. The computing system 1510 includes controller circuitry 1511 and a memory 1513 (e.g., readonly memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM) or Rambus DRAM (RDRAM), etc.). The memory 1513 may comprise a static memory (e.g., flash memory, static random access memory (SRAM), etc.), and / or a secondary memory (e.g., a data storage device), which communicate with each other via a bus (not shown). Memory 1513 may be used to store or buffer projection data until required for image processing. Controller circuitry 1511 represents one or more general-purpose processors such as a microprocessor, central processing unit, accelerated processing units, or the like. More particularly, the controller circuitry 1511 may comprise a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, processor implementing other instruction sets, or processors implementing a combination of instruction sets. Controller circuitry 1511 may also include one or more special-purpose processing devices such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. One or more processors of the controller circuitry may have a multicore design. Controller circuitry 1511 is configured to execute the processing logic for performing the operations and steps discussed herein. The computing system 1510 may further include a network interface circuitry 1515. The computing system 1510 may be communicatively coupled to an input device 1520 and / or an output device 1530, via input / output circuitry 1516. In some implementations, the input device 1520 and / or the output device 1530 may be elements of the computing system 1510. The input device 1520 may include an alphanumeric input device (e.g., a keyboard or touchscreen), a cursor control device (e.g., a mouse or touchscreen), an audio device such as a microphone, and / or a haptic input device. The output device 1530 may include an audio device such as a speaker, a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), and / or a haptic output device. In some implementations, the input device 1520 and the output device 1530 may be provided as a single device, or as separate devices. In some implementations, the computing system 1510 may comprise image processing circuitry 1514. Image processing circuitry 1514 may be configured to process image data 1570 (e.g., images, imaging data, projections, projection data), such as medical images obtained from one or more imaging data sources, a treatment device 1550 and / or an image acquisition device 1540. Image processing circuitry 1514 may be configured to process, or pre-process, image data 1570. For example, image processing circuitry 1514 may convert received image data into a particular format, size, resolution or the like. Image processing circuitry 1514 may be configured to perform methods described herein for obtaining a motion surrogate signal. Image processing circuitry 1514 may be configured to perform image reconstruction. In some implementations, image processing circuitry 1514 may be combined with controller circuitry 1511. In some implementations, the radiotherapy system 1500 may further comprise an image acquisition device 1540 and / or a treatment device 1550. The image acquisition device 1540 and the treatment device 1550 may be provided as a single device. In some implementations, treatment device 1550 is configured to perform imaging, for example in addition to providing treatment and / or during treatment. Image acquisition device 1540 may be configured to perform positron emission tomography (PET), computed tomography (CT), magnetic resonance imaging (MRI), single positron emission computed tomography (SPECT), X-ray, and the like. Image acquisition device 1540 may be configured to output image data 1570, which may be accessed by computing system 1510. Treatment device 1550 may be configured to output treatment data 1560, which may be accessed by computing system 1510. Treatment data 1560 may be obtained from an internal data source (e.g., from memory 1513) or from an external data source, such as treatment device 1550 or an external database. The various methods described above may be implemented by a computer program. The computer program may include computer code (e.g., instructions) arranged to instruct a computer to perform the functions of one or more of the various methods described above. For example, the steps of the methods described in relation to any of Figures 1 to 12 may be performed by the computer code. The steps of the methods described above may be performed in any suitable order. The computer program and / or the code for performing such methods may be provided to an apparatus, such as a computer, on one or more computer readable media or, more generally, a computer program product. The computer readable media may be transitory or non-transitory. The one or more computer readable media could be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, or a propagation medium for data transmission, for example for downloading the code over the Internet. Alternatively, the one or more computer readable media could take the form of one or more physical computer readable media such as semiconductor or solid-state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disk, such as a CD-ROM, CD-R / W or DVD. The instructions may also reside, completely or at least partially, within the memory 1513 and / or within the controller circuitry 1511 during execution thereof by the computing system 1510, the memory 1513 and the controller circuitry 1511 also constituting computer-readable storage media. In an implementation, the modules, components and other features described herein may be implemented as discrete components or integrated in the functionality of hardware components such as ASICS, FPGAs, DSPs or similar devices. A “hardware component” is a tangible (e.g., non-transitory) physical component (e.g., a set of one or more processors) capable of performing certain operations and may be configured or arranged in a certain physical manner. A hardware component may include dedicated circuitry or logic that is permanently configured to perform certain operations. A hardware component may comprise a special-purpose processor, such as an FPGA or an ASIC. A hardware component may also include programmable logic or circuitry that is temporarily configured by software to perform certain operations. In addition, the modules and components may be implemented as firmware or functional circuitry within hardware devices. Further, the modules and components may be implemented in any combination of hardware devices and software components, or only in software (e.g., code stored or otherwise embodied in a machine-readable medium or in a transmission medium). 5 Unless specifically stated otherwise, as apparent from the following discussion, it is appreciated that throughout the description, discussions utilizing terms such as “receiving”, “determining”, “comparing ”, “enabling”, “maintaining”, “identifying”, “obtaining”, “accessing”, or the like, refer to the actions and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) 10 quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. While certain embodiments have been described, these embodiments have been presented 15 by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel methods and apparatuses described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of methods and apparatus described herein may be made.

Claims

1. A method for obtaining a motion surrogate signal, the method comprising:receiving a projection stack comprising a plurality of two-dimensional projections of a patient volume;selecting a plurality of sub-volumes of the projection stack;extracting a candidate motion surrogate signal from projection data contained within each sub-volume of the projection stack to create a plurality of candidate motion surrogate signals; andcombining the plurality of candidate motion surrogate signals into a single final motion surrogate signal.

2. The method of claim 1, wherein the combining step comprises averaging the plurality of candidate motion surrogate signals to produce the single final motion surrogate signal.

3. The method of claim 1 or 2, wherein each candidate motion surrogate signal is assigned a weight, and the plurality of candidate motion surrogate signals are combined into the single final motion surrogate signal using a weighted sum of the plurality of candidate motion surrogate signals.

4. The method of claim 3, wherein candidate motion surrogate signals with greater levels of noise are given lower weights and candidate motion surrogate signals with lower levels of noise are given higher weights.

5. The method of claim 3 or 4 wherein the method further comprises generating a spatial saliency map showing where motion occurred within the projection stack based on the assigned weights of the candidate motion surrogate signals.

6. The method of any of the preceding claims, wherein selecting a plurality of sub-volumes of the projection stack comprises:selecting a region of the two-dimensional projections and extracting this region over at least a subset of the projection stack to obtain a sub-volume of the projection stack; andrepeating the above step at least once to obtain a plurality of sub-volumes.

7. The method of any of the preceding claims, wherein the final motion surrogate signal is a respiratory motion surrogate signal or a cardiac motion surrogate signal.

8. The method of any of the preceding claims, further comprising using the single final motion surrogate signal in a reconstruction process to reconstruct a volumetric image from the projection stack.

9. The method of any of the preceding claims, further comprising, prior to combining the plurality of candidate motion surrogate signals:for each candidate motion surrogate signal, determining a similarity of the signal to a reference signal; anddiscarding the candidate motion surrogate signals which are below a predetermined similarity threshold; orselecting the candidate motion surrogate signals which are above a predetermined similarity threshold.

10. The method of claim 9, wherein the reference signal is a sinusoidal signal.

11. The method of any of the preceding claims, wherein, after receiving the projection stack, the method further comprises computing differences between consecutive projections to create a difference projection stack and selecting the plurality of sub-volumes from the difference projection stack.

12. The method of any of the preceding claims, wherein extracting a candidate motion surrogate signal for each sub-volume comprises taking a mean value of each projection in the sub-volume to obtain the candidate motion surrogate signal.

13. The method of any of the preceding claims, further comprising, prior to combining the plurality of candidate motion signals, removing low and / or high frequency variation from the plurality of candidate motion surrogate signals.

14. The method of any of the preceding claims, further comprising removing high frequency variation from the single final motion surrogate.

15. The method of any of the preceding claims, further comprising estimating a confidence value of the motion surrogate signal for each two-dimensional projection based on calculating a variance between candidate motion surrogate values at that projection.

16. The method of any of the preceding claims, wherein the projection stack serves for cone-beam computed tomography, CBCT, reconstruction.

17. The method of any of the preceding claims, for use in adaptive radiotherapy.

18. The method of any of the preceding claims, for use in binning projection data of the projection stack into a plurality of bins for image reconstruction, each bin corresponding to a portion of a respiratory or cardiac cycle, each bin having a reference motion surrogate value for the portion of the respiratory or cardiac cycle relating to that bin, wherein the projection data is binned based on a similarity of its motion surrogate signal value to the reference motion surrogate value, wherein its motion surrogate signal value is a value of the motion surrogate signal at said projection data.

19. A data processing apparatus comprising a memory storing computer-executable instructions, and a processor configured to execute the instructions to carry out the method of any of the preceding claims.

20. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any of claims 1 to 18.

21. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the method of any of claims 1 to 18.

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