# Patent

## Title
Filtering of image sequences

## Abstract

Method of image processing, the method comprises providing a sequence (2) of images (F) which have contrast modulation (100) along said sequence (2); providing a reference frequency (fm, 10) related to said contrast modulations (100) along said sequence (2); and filtering said sequence of images depending on said reference frequency (fm, 10). According to an embodiment, a windowed harmonic filtering is applied to the sequence of input images to extract fundamental in-phase (122) and quadrature (124) components at a heart beat frequency (fm). The resultant time-signal phase is displayed (34) as image sequence.

## Background
FIELD OF THE INVENTION
The invention relates to the field of image processing and more specifically to the filtering of image sequences acquired with X-Ray scanner. In particular, the invention relates to a method and apparatus for blood flow visualization in a vessel of a body.
BACKGROUND OF THE INVENTION
U.S. Pat. No. 6,196,973 discloses a method for determining a blood flow velocity in a patient's blood vessel, into which a contrast agent has been introduced. Reflectors such as microbubbles introduced into a blood vessel of a patient are destroyed by focused ultrasound at a modulation point, thereby creating gaps in the flowing contrast agent that are sensed downstream sensing point. The pattern of gaps is then matched in time with the input modulation sequence to determine a transit time for the gaps, which is also the flow velocity of the blood.
SUMMARY OF THE INVENTION
It would be advantageous to achieve a method or an apparatus which provides a good visualization of a flow process.
To better address this concern, in a first aspect of the invention a method of image processing is presented, the method comprising providing a sequence of images, wherein the images have temporal contrast modulations along the sequence. The method further comprises providing a reference time frequency related to the contrast modulations along the sequence. Still further, the method comprises time filtering the sequence of images depending on the reference frequency.
According to an embodiment of the invention, a method is presented, wherein the images in the sequence are images of an object under consideration taken at different times. Hence in this embodiment, the sequence of images shows a time evolution of the object under consideration.
According to an embodiment of the invention, a method is presented, wherein the images of the sequence of images are images taken by dynamic X-ray angiography, e.g. dynamic X-ray angiography of the brain or dynamic coronay angiography.
According to still another embodiment of the invention, a method is presented which further comprises providing a filtered output, e.g. in the form of a sequence of output images.
According to still another embodiment of the invention, a method is presented wherein the sequence of images show a blood vessel of a vessel system. For example, the vessel system may be the vessel system of a human body or of an animal body.
According to still another embodiment of the invention, a method is presented which further comprises generating the contrast modulations along the sequence of images by injecting a contrast agent at a steady rate into the vessel system at an injection region. In this way, the contrast modulations in a sequence of images is generated by modulations of a blood velocity at the injection region due to a heart beat and the resulting pulsed arterial pressure. This is a natural way of generating a contrast modulation in a sequence of images due to a concentration modulation of a contrast agent in a blood vessel.
According to still another embodiment of the invention, a method is presented wherein providing the reference frequency comprises extracting the reference frequency from an electrocardiogram (ECG) signal. Since an electrocardiogram can be easily taken during image generation and is often taken as a routine measure, extracting the reference frequency from an ECG signal is a well suited and easy way to provide the reference signal.
According to still another embodiment of the invention, a method is presented wherein providing the reference frequency comprises extracting the reference frequency from a time dependence of contrast along the sequence of images. This has the advantage that this embodiment can be performed irrespective of the relation of the reference frequency to the heart beat. For example, if the contrast modulation is not related to the heart beat, e.g. because it is induced externally, this embodiment provides an easy and save way to obtain the required reference frequency.
According to still another embodiment of the invention, a method is presented wherein filtering the sequence of images includes filtering the sequence of images in pass-band around the reference frequency. For example, according to still another embodiment of the invention, a method is presented, wherein the filtering the sequence of images is performed according to the well-known operating principle of lock-in amplifiers.
According to still another embodiment of the invention, a method is presented wherein filtering the sequence of images includes extracting a phase information from the sequence of images.
According to still another embodiment of the invention, a method is presented wherein the reference frequency is a harmonic frequency of the contrast modulations along the image sequence. Further, in this embodiment, filtering the sequence of images comprises extracting a harmonic frequency component from the images at the reference frequency. The harmonic frequency component obtained thereby can be used to advantage since it may enhance e.g. the visualization of blood flow. According to still another embodiment, the harmonic frequency is a first harmonic frequency of the contrast modulations along the sequence. According to still another embodiment, a method is presented further comprising providing at least one of an in-phase component of the images and an out-of-phase component of the images. For example, output images which are generated by performing the method may comprise the in-phase component and/or the out-of-phase component. According to another embodiment, output images may comprise the in-phase component and/or the out-of-phase component. For example, the output images may show the amplitude of the respective component.
According to still another embodiment of the invention, a method is presented wherein extracting a harmonic frequency component at the reference frequency comprises applying a windowed harmonic filtering to each pixel of the first image. The windowed filtering is performed by taking into account images within a temporal window of images around a reference image and a number of images within the window of images corresponds to a time period corresponding to the reference frequency.
According to still another embodiment of the invention, a method is presented which further comprises removing the harmonic frequency component from the images to thereby provide a sequence of modified images. Further according to this embodiment, the method comprises providing a higher harmonic frequency of the contrast modulations along the image sequence and filtering the sequence of modified images depending on the higher harmonic frequency of the contrast modulations. By taking higher harmonic frequency components into account, a space and/or time resolution of output images may be increased.
According to other embodiments of the invention, a method is presented, wherein the reference frequency does not match the respective harmonic frequency of the contrast modulations but is only close to the respective harmonic frequency of the contrast modulations. In experiments it has been found, that a deviations of the reference frequency by 30% from the respective harmonic frequency is acceptable. For example, the deviations can be between 0% to 30%, or between 0% and 25%, or between 0% and 20%, or between 0% and 15% or between 5% and 15% or between 10 % and 20%.
According to still another embodiment of the invention, a method is presented which further comprises detecting contrast regions having a predetermined contrast of interest in the images and spatially low pass filtering each of images in the contrast regions. In this way, the image quality may be enhanced. According to still another embodiment of the invention, contrast regions having a predetermined contrast of interest may be regions having a contrast higher than a predetermined contrast value. For example, a spatial low pass filtering mask may be provided for spatially low pass filtering the image regions within the mask.
According to still another embodiment of the invention, a method is presented which further comprises extracting from the images a low frequency component along the sequence of images and removing the low frequency component from the images before performing the filtering of the sequence of images. An advantage of this embodiment is that a slowly varying background signal which might influence the subsequent filtering is removed. Thereby, the image quality of an output image may be enhanced.
According to a second aspect of the invention, a computer program is presented which enables a processor to carry out a method according to the first aspect of the invention or any embodiment thereof.
According to a third aspect of the invention, a electronic circuit is presented which can be operated to carry out the method according to the first aspect of the invention or any embodiment thereof.
According to a third aspect of the invention, an apparatus for processing an image sequence is presented, the apparatus comprising a reference frequency providing unit for providing a reference frequency which is related to a modulation of a contrast along the image sequence, and a filter unit for filtering the sequence of images depending on the reference frequency.
According to an embodiment of the invention, an apparatus is presented wherein the filter unit provides a filtered output, for example a sequence of output images.
According to still another embodiment of the invention, an apparatus is presented wherein the filter unit comprises an extractor unit for extracting a harmonic frequency component from the images at the frequency of contrast modulations and providing at least one of an in-phase component of the images and an out-of-phase component of the images. According to still another embodiment of the invention, an apparatus is presented which further comprises providing a sequence of output images, wherein the output images of the sequence of output images comprise the in-phase and/or the out-of-phase component.
According to a fourth aspect of the invention, a system for generating an image is presented, the system comprising an apparatus for processing an image sequence according to the third aspect of the invention and a display unit for displaying an a signal indicative of an output of the filter unit.
In summary, one basic idea used by at least an embodiment of the invention is to extract information from contrast modulations along the sequence of images, wherein the contrast modulations may be induced by the heart beat. Another basic idea used by at least an embodiment of the invention is to modulate an image contrast at a frequency fm and detect in a pass-band around fin. Another basic idea used by at least an embodiment of the invention is to provide a phase information of the contrast modulation. This phase information may be provided in the form of a sequence of output images depicting the phase information. According to one aspect of the invention, a method of image processing is presented, the method comprises providing a sequence of images which have contrast modulation along the sequence; providing a reference frequency related to the contrast modulations along the sequence; and filtering the sequence of images depending on the reference frequency. According to an embodiment, a windowed harmonic filtering is applied to the sequence of images to extract fundamental in-phase and quadrature components at a heart beat frequency. The resultant time-signal phase is displayed as image sequence.
These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.



BRIEF DESCRIPTION OF THE DRAWINGS
In the following detailed description, reference is made to the drawings in which
FIG. 1 shows a schematic view of an embodiment of an image sequence according to the invention;
FIG. 2 shows a flow chart illustrating an embodiment of a method of image processing according to the invention;
FIG. 3 shows a schematic view of an embodiment of a X-ray imaging system according to the invention;
FIG. 4 illustrates a first step of an embodiment of an image processing method according to the invention;
FIG. 5 illustrates a further step of the image processing method illustrated in FIG. 4;
FIG. 6 illustrates schematically an embodiment of an image processing method according to the invention;
FIG. 7 illustrates schematically details of an embodiment of an image processing method according to the invention;
FIG. 8 shows a overview over embodiments of several aspects of the invention.



DETAILED DESCRIPTION OF EMBODIMENTS
With reference to the drawings, illustrative embodiments of the present invention will now be described in more detail. Throughout the detailed description of the embodiments, an exemplary example for the images under consideration are X-ray images and in particular images taken by dynamic X-ray angiography. Although the invention provides means that may assist a physician in reaching a diagnosis or treating a patient, it is to be understood that the invention is not about to provide a diagnosis or about treating patients, but rather about a technical invention that may improve visualization of dynamic processes in a patients body.
FIG. 1 schematically shows a sequence 2 of input images suitable for illustrating the principles of the invention. The sequence 2 of input images comprises a plurality of individual input images F(k), F(k+1), F(k+2), F(k+3) which show a specific object under consideration, e.g. a part of a human body. The input images F(k), F(k+1), F(k+2), F(k+3) are taken at different times. Hence the sequence of input images shows the time evolution of the object under consideration. This is indicated in FIG. 1 by the arrow 6. The input images have a contrast modulation along the sequence, i.e. the images have in a certain region a contrast which is modulated in time, thereby forming the contrast modulation along the sequence. Accordingly, each individual pixel 8 in a region showing the contrast modulation exhibits a contrast modulation along the sequence.
In order to extract information from contrast modulations along the sequence of input images, a reference frequency 10 is provided, the reference frequency being related to the contrast modulations along the image sequence. For example, the reference frequency may be equal to or close to a harmonic frequency, e.g. the fundamental harmonic frequency of the contrast modulations along the image sequence. This is schematically shown in FIG. 2. Using the input image sequence 2 and the reference frequency 10, a filtering 12 of the input image sequence 2 is then performed, wherein the filtering 12 depends on the reference frequency 10. In the embodiment shown in FIG. 2, the filtered output is provided as output image sequence 14.
In the following, having regard to FIG. 3 to FIG. 8, an embodiment of the invention is described in greater detail. The embodiment relates to the field of estimating and assessing blood flow from x-ray densitometry. One relevant information to extract is the blood velocity in the different vessel and its time dependence, in particular its variation within a heart cycle. This is particularly useful to help in assessing vessel pathologies (stenoses, aneurysms) and in planning interventional procedures such as stent-placement in coronary network. Of particular interest when assessing brain aneurysms is the occurrence of blood jets impinging on the aneurysm wall that may provide evidence for high rupture risk. It would be of advantage to enhance visualization of such flow patterns and also of turbulent flows.
State of the art flow assessment techniques are based on analysing time-intensity-curves at different vessel location or distance-intensity-curves at different instants of time following the injection of a contrast agent bolus, wherein ideally, the image contrast increases as a step-function at the injection point. In practice however, due to several factors, the bolus front gets progressively blurred away from the injection point an this introduce considerable measurement uncertainty in particular in realistic conditions in which considerable noise (random or structural) is present.
An embodiment of the invention proposes a technique to extract useful information even in a noisy or cluttered environment using a principle similar to that of lock-in amplifiers or stroboscopic imaging. A principle which is used by the illustrated embodiment is to modulate an image contrast at a frequency fin and detect in a pass-band around fm. Embodiments of the invention allow enhancing the visualization of turbulent flow and flow occurring in narrow streams as occurs in aneurysms.
The illustrated embodiment of the invention makes use of the natural time modulation in contrast agent density, which occurs when injecting a contrast agent at a steady rate while performing dynamic X-ray imaging, e.g. dynamic X-ray angiography of brain vessels or cardiac vessels. The time modulation is due to the fact that the blood velocity greatly varies during a heart cycle so that the contrast agent dilution varies with time according to heartbeat periodicity.
Features of the illustrated embodiment comprise at least one of the following:
1. A synchronizing reference (quasi-) periodic signal capturing the heartbeat periodicity is extracted either from the ECG or from the image contrast within a region of interest around the contrast agent injection point.
2. A windowed temporal harmonic filtering is applied to each pixel of the image where the blood contrast is liable to be observable to extract the fundamental in-phase and quadrature components of the fundamental frequency (theartbeat frequency) and, according to a further embodiment, at a few harmonics, e.g. up to the third harmonic. Here the term fundamental frequency and the first harmonic frequency are used synonymously. The time window length is typically on heart beat length, or close hereto.
3. Space low-pass filtering is combined with the time filtering to improve the signal to noise ratio.
4. The resulting time-signal phase is displayed as image-sequences for each time-frame to visually enhance the flow and are used to extract velocity maps at different time instants.
The illustrated embodiment has the following advantages:

    
    
        The average blood flow pattern within a heartbeat cycle is greatly enhanced when displaying the phase corresponding to the fundamental frequency. Improved visualization in difficult situations is obtained (blood jets, flow turbulence).
        A good assessment of blood velocity is thus obtained using robust optical flow.
        A qualitative assessment of blood pulsatility, i.e. the range of velocity variation with a heart cycle, is obtained when including harmonic components and in particular higher harmonic components.
    
    


FIG. 3 shows a schematic view of a X-ray imaging system 16 having a X-ray source 18 and a X-ray detector 20. A central unit 22 is communicating with the X-ray source 18 and the X-ray detector 20 via communication signals 24, 26, respectively. The central unit 22 comprises a control unit for controlling the X-ray source 18 and the X-ray detector 20. The X-ray source 18 is capable of emitting X-ray radiation 28 in response to a respective communication signal 24. At least part of the X-ray radiation 28 passes through the object 30 of interest, i.e. a patient and is received by the X-ray detector 20. The central unit further comprises an image generating unit 32 for generating a sequence of images from detector signals which are generated by the detector in response to detected X-ray radiation. A display device 34 is provided for displaying e.g. images and/or control settings in response to display signals 36 provided by the central unit 22.
Further depicted in FIG. 3 is a reference frequency providing unit 38 comprising a ECG sensor 40 a signal line 42 and heartbeat frequency extractor 44 which extracts a heartbeat frequency from the ECG signal provided by the ECG sensor 40 over the signal line 42. The heartbeat frequency extractor 44 may be part of the central unit 22, as shown in FIG. 3. Further, the ECG sensor 40, signal line 42 and heartbeat frequency extractor 44 may be part of a conventional laboratory equipment.
It should be understood that the X-ray imaging system 16 depicted in FIG. 3 is provided only for illustrative purposes and can be replaced by any system that is capable of generating a sequence of images of an object of interest. Any parts of the central unit 22 may be formed of an individual system, module or device. The X-ray source 18 and the X-ray detector 20 may be stationary or may be movable. E.g. the X-ray source 18 and the X-ray detector 20 may be part of a computer tomography system and may be rotatable around the object of interest to provide three-dimensional images of the object under consideration.
The sequence of images provided by the central unit may be a sequence 2 of images as depicted in FIG. 1. A first step of an embodiment of an image processing method is illustrated in FIG. 4, where a low frequency component is removed from the input image sequence 2. Graph 4a shows the time dependence (time evolution) of the contrast, i.e. the intensity I of a single pixel over the respective frame number F, i.e. the contrast of this pixel along the input image sequence 2. In other words, graph 4a (as well as graph 4b and graph 4c) shows a time-intensity curve. In the following the intensity (contrast) of a pixel along the image sequence 2 is denoted as pixel sequence. The pixel sequence 101 in graph 4a shows peaks 100 which are related to the heart beat and a underlying low frequency component 102 which, according to an embodiment of the invention, is removed from the pixel sequence.
From the pixel sequence 101 of graph 4a, the low frequency component 102 is extracted by low frequency component extraction 104. A graph 4b shows the extracted low frequency component, i.e. the low frequency component of the intensity of the pixel over the frame number F. The low frequency component extraction can be performed by any appropriate method which filters or smoothes the peaks 100 due to the heart beat. For example, the low frequency component extraction from a pixel sequence, e.g. the pixel sequence 101 shown in graph 4a, may be performed by averaging the respective pixel sequence over an averaging window of appropriate length. For example, the length of the averaging window may be equal to the period associated with the respective harmonic frequency which is intended to be extracted after the low frequency component extraction and removal.
After extraction, the low frequency component 102 is removed from the input pixel sequence 101 shown in graph 4a by low frequency component removal 106. The remaining pixel sequence 108 after the low frequency component removal is shown in graph 4c. It should be understood that the above described procedure is performed for every pixel 8 in the input images F(k), F(k+1), F(k+2), F(k+3). In this way, removing a low frequency component from the input image sequence 2 is performed by removing a low frequency component separately for every pixel in the image sequence.
FIG. 5 illustrates the filtering of an input image sequence shown in graph 5a according to an embodiment of the invention. In the illustrated embodiment, the image sequence which is used for filtering is an image sequence which is obtained by removing a low frequency component from an initial input image sequence 2. Therefore, the pixel sequence of graph 5a corresponds to the remaining time-intensity curve 108 of graph 4c. Accordingly, graph 5a shows the time dependence of the intensity I (contrast) of a single pixel over the respective frame number F, i.e. the contrast of this pixel along the image sequence.
The illustrated filtering method comprises extracting a harmonic frequency component from the input images F(k), F(k+1), F(k+2), F(k+3) at the reference frequency fm, 10. In other embodiments, the filtering method comprises extracting a harmonic frequency component from the input images at the reference frequency and in a pass-band around the reference frequency fm. Reference number 123 denotes a harmonic frequency component extraction. A graph 5b shows the real part 122, i.e. the in-phase response, and the imaginary part 124, i.e. the out-of-phase response, of an extracted first harmonic frequency component 126 of the pixel sequence 108 shown in graph 5a over the frame number F and hence, over time.
According to the illustrated embodiment, a phase image is provided as an output of the method of image processing. For example, the phase φ may be determined from the real part of the intensity of the harmonic frequency component according to

Re(I(p,t)/abs(I(p,t)))=cos(φ(p,t)) wherein

    
    
        “Re” denotes the real part, I(p,t) denotes the intensity of the harmonic frequency component at the pixel identified by the vector p at time t, “abs(I(p,t))” denotes the absolute value of I(p,t), and φ(p,t) denotes the phase at the pixel identified by the vector p at time t.
    
    


The spatial and time resolution of the output phase sequence can be increased by taking higher harmonics of the first harmonic frequency into account. To this end, the extracted harmonic frequency component 126 is stored in a storage device (not shown in FIG. 5). Then the harmonic frequency component 126 is removed from the pixel sequence 108, e.g. by subtracting the harmonic frequency component from the pixel sequence 108, thereby providing a remaining time-intensity curve 128 which is shown in graph 5c. The harmonic frequency component removal is denoted by the reference number 123. The pixel sequence of the time intensity curve 128 and the corresponding image sequence can be subjected to a filtering depending on a higher harmonic of the first harmonic frequency.
The same method as described for extracting the first harmonic frequency component can be used with the higher harmonic frequency as reference frequency. For example, if the first harmonic frequency corresponds to a number of N images, the period of the second harmonic comprises N/2 images. FIG. 6 shows in a schematic way the subsequent extraction 123 and removal 130 of the first harmonic frequency component 126 and the extraction and removal 132 of a second harmonic frequency component. In FIG. 6, HFCE&R is short for Harmonic Frequency Component Extraction and Removal. Higher harmonic frequency components may be extracted and removed up to the extraction and removal 134 of the p-th frequency component. According to one embodiment of the invention, only the first and the second harmonic frequency component are extracted. According to other embodiments of the invention, higher harmonics up to the third harmonic frequency or up to the fourth harmonic frequency are extracted. As exemplarily illustrated in FIG. 6, the first harmonic frequency may corresponding to a filter window of N images, the second harmonic frequency may correspond to a filter window of N/2 images and the p-th harmonic frequency may correspond to a filter window of N/p images, as indicated in brackets in FIG. 6. In the above description of FIG. 6, the reference numbers introduced in FIG. 4 and FIG. 5, which relate to an exemplary pixel sequence have been used. However, it is to be understood that the method illustrated in FIG. 6 is performed at least for all relevant pixel sequences of the image sequence 2, for example for all pixel sequences of the image sequence 2.
Further illustrated in FIG. 6 is a removal of a low frequency component. In FIG. 6, LFCR is short for Low Frequency Component Removal. An exemplary low frequency component removal has been illustrated in FIG. 4. The low frequency component extraction 104 and removal 106 may be performed before each individual extraction and removal of the respective harmonic frequency component, as shown in FIG. 6. In other embodiments the low frequency component extraction and removal may be performed only before the first harmonic frequency component extraction and removal. Generally the low frequency component extraction and removal serves to improve the quality of the subsequent harmonic frequency component extractions. Accordingly, the averaging window for the low frequency component extraction may be selected appropriately depending on the input images. For example, the averaging window may be set to the same width as the filtering window which is used for extracting the respective harmonic frequency component, as indicated in FIG. 6.
Hence, in the embodiment illustrated in FIG. 6, before extracting from an image sequence 2 a harmonic frequency component at a first harmonic frequency that corresponds to a period of N images, a first low frequency component is extracted and removed from the image sequence 2, thereby generating a first remaining image sequence 138 without low frequency component. Extraction and removal of the first low frequency component is denoted with the reference number 136. Herein, the extraction of the first low frequency component is performed by averaging the input image sequence 2 over an averaging window of N images. Thereafter, the first harmonic frequency component is extracted from the first remaining image sequence 138 at the first harmonic frequency. Removing the extracted first harmonic frequency component from the first remaining image sequence provides the second remaining image sequence 140 including the pixel sequence 108. Extraction and removal of the first harmonic frequency component from the first remaining image sequence 138 is denoted with the reference number 142. Before extracting from the second remaining image sequence 140 a second harmonic frequency component at a second harmonic frequency that corresponds to a period of N/2 images, a second low frequency component is extracted and removed from the second remaining image sequence 140, wherein the extraction of the second low frequency component is performed by averaging the second remaining image sequence over a averaging window of N/2 images. Extraction and removal of the second low frequency component is denoted with the reference numeral 144 in FIG. 6. Removal of the second low frequency component from the second remaining image sequence 140 provides a third remaining image sequence 146. Thereafter, the second harmonic frequency is extracted from the third remaining image sequence 146 at the second harmonic frequency. Extraction and removal of the second harmonic frequency component is denoted with the reference number 132.
In the same way, higher harmonic frequency components can be extracted up to the p-th harmonic frequency. Herein, before extracting from the respective remaining image sequence 148 a p-th harmonic frequency component at a p-th harmonic frequency that corresponds to a period of N/p images, a p-th low frequency component is extracted and removed from the respective remaining image sequence 148, wherein the extraction of the p-th low frequency component is performed by averaging the respective remaining image sequence 148 over a averaging window of N/p images. Extraction and removal of the p-th low frequency component is denoted with the reference numeral 150. Removal of the p-th low frequency component from the respective remaining image sequence 148 provides a further remaining image sequence 152. Thereafter, the p-th harmonic frequency component may be extracted from the further remaining image sequence 152 at the p-th harmonic frequency. Extraction and removal of the p-th harmonic frequency component is denoted with the reference number 134. It should be noted that after extracting the highest harmonic frequency component of interest, the removal of this harmonic frequency component is not necessary for further processing the extracted harmonic frequency components and can be omitted.
For providing the harmonic frequency components after the subsequent extraction and removal steps, storage devices 154, 156, 158 are provided for storing 160, 162, 164 the respective harmonic frequency component.
According to still another embodiment of the invention before performing the low frequency component removal, contrast regions having a predetermined contrast of interest are detected in the images and each of the images is spatially low pass filtered in the contrast regions. The contrast regions may be regions having a contrast higher than a predetermined contrast value, e.g. imaged blood vessels containing blood with a contrast agent. For example, a low pass filtering mask, which may correspond to the image of the blood vessel, may be provided for low pass filtering the image regions within the mask. Further, a similar low pass filtering may be employed for space regularization of complex images.
In the following, having regard to FIG. 7, an exemplary method for performing the low frequency component extraction and removal and an exemplary method for performing the harmonic frequency component extraction and removal is presented.
The low frequency component extraction can be performed by any appropriate method which filters or smoothes the peaks 100 due to the heart beat. For example, each pixel value of the low frequency component 102 can be obtained as the mean value of a part of the input pixel sequence 101 within a time window that is equal to or greater than a period corresponding to the reference frequency, e.g. equal to or greater than a period corresponding to the heartbeat frequency in the illustrated embodiment. An efficient embodiment of a of a low frequency component extraction method is the following:
The sequence of images 2 provided by the X-ray imaging system 16 is fed to a low frequency component extraction and removal block 200 having a first delayer 201, which outputs an input image after N further input images of the sequence 2 have been fed to the first delayer 201. In FIG. 7, “dly. N” is short for “delay N” and “dly N/2” is short for “delay N/2”. The first delayer 201 may comprise an appropriate storage (not shown) for storing N of the input images (frames) F. The number of delayed images, N, is chosen to correspond to the reference frequency fm, 10. At a startup of the image processing method according to the embodiment illustrated in FIG. 7, it takes a waiting time of N images until the first image is output of the first delayer 201. The output of the delayer 201 is then null during this waiting time. The input images F(k+N/2) and the output of the delayer 201 are fed to the first subtracting device 202. During the waiting time, the output of the subtracting device are the images dF(k)=F(k−N/2) and after the waiting time, this output is dF(k+N/2)=F(k+N/2)−F(k−N/2). The resulting difference image dF(k+N/2) is fed to an integrator 204 which accumulates difference images provided by the first subtracter and provides a respective sum 210. During the waiting time, the integrator accumulates the N first images of the sequence. After the waiting time, the integrator adds to the previous accumulation the new image difference. In this way, the sample F(k−N/2) is removed from the previous sum and the sample F(k+N/2) is added, which performs a sliding windowed accumulation. In the illustrated embodiment, the integrator 204 comprises an adder 206 and a memory 208 which stores the sum of the last N images dFc′(k−1) and feeds it back to the adder 206 for the next sample. The adder 206 adds the temporally first, actual difference image dF(k+N/2) to the sum dFc′(k−1) of the last N images, thereby producing the sum 210 over N subsequent images [F(k+1−N/2, F(k+N/2]. around the image F(k)This embodiment has the advantage it is time efficient since the respective sum over N subsequent images F(k) can be performed with very few operations. The sum 210 over N subsequent images F(k) is then normalized by a normalizer 212, wherein the sum 210 is divided by the respective number of summed difference images, N. The result 214, i.e. normalized sum of N images, may thus be obtained for each individual pixel sequence according to the following equation

Ic(k)=(Ic(k−1)+I(k+N/2)−I(k−N/2))/N, 

wherein Ic(k−1) is the sum of the intensity of N pixels along the pixel sequence and around the respective pixel of image F(k−1) and Ic(k) is the sum of the intensity of N pixels along the pixel sequence and around the respective pixel of image dF(k). The normalized sum 214 of N difference images is then fed to a second subtracter 216. The low frequency component extraction and removal block 200 further comprises a second delayer 218, which delays the incoming images of the sequence 2 by N/2. Hence, the output image F(k) of the second delayer 218 is an image in the middle of the window defined by the image F(k+N/2) which is about to be fed to the first delayer 201 and the image F(k−N/2) which is output by the delayer 201. The second subtracter 216 provides the difference image Fn(k) of the normalized sum 214 of the N difference images around the difference image dF(k) and the output image F(k) of the second delayer 218. Thus, the sequence of images provided by the second subtracter 216 corresponds to the remaining image sequence 138 (see also FIG. 6), a pixel sequence thereof is shown in graph 4c of FIG. 4 and graph 5a of FIG. 5.
An efficient embodiment of a of a harmonic frequency component extraction method is the following:
The image sequence 138 of which the low frequency component has been removed, is fed to a harmonic frequency component extraction and removal block 230 having a first delayer 231, which outputs an input image after N further images of the remaining sequence 138 have been fed to the first delayer 231. The first delayer 231 may be identically configured as the first delayer 201 of the low frequency component extraction and removal block 200. The number of delayed images, N, is chosen to correspond to the reference frequency fm, 10. As for the previous low frequency processing, the association of delay, subtracting device and adder allows to integrate data in a sliding window of N samples. Between each accumulation step, data are multiplied by the complex factor exp(i2π/N), representing the time variation related to the harmonic frequency considered. At a startup of the harmonic frequency component extraction and removal method according to the illustrated embodiment, it takes a waiting time of N images until the first image is output of the first delayer 231. The output of the delayer 231 is then null during this waiting time. The input images F(k+N/2) and the output of the delayer 201 are fed to the first subtracting device 232. During the waiting time, the output of the subtracting device are the images dF(k)=F(k−N/2) and after the waiting time, this output is dF(k+N/2)=F(k+N/2)−F(k−N/2). In a multiplicator 234, the difference image dFn(k) is multiplied by the factor exp(i2π/N), wherein “exp( . . . )” is the exponential function and “i” is the imaginary unit. The resulting complex images cF(k), i.e. complex image data, are fed to an adder 236, wherein the double lines in Fig. indicate real part and imaginary part of the complex images. A back-feeder 238 stores and feeds back the sum of the last N complex images cFc(k−1). A multiplicator 239 multiplies the sum cFc′(k−1) of the last N complex images by the factor exp(i2π/N) and supplies the result cFf (k−1) to the adder 236, the adder 236 adding the temporally first, actual complex image cF(k+N/2) of the actual window to the sum cFf′(k−1) of the last N-images, thereby producing the sum 240 over N subsequent complex images around the complex image cF(k). This embodiment has the advantage it is time efficient since the respective sum over N subsequent complex images dF can be performed with very few operations. The sum 240 over N subsequent complex images is then normalized by a normalizer 242, wherein the sum 240 is divided by the respective number of summed complex images, N. The result 244, i.e. normalized sum of N complex images, may thus be obtained for each individual pixel sequence according to the following equation

If(k)=(If(k−1)+I(k+N/2)−I(k−N/2))*exp(i2π/N)/N 

wherein If(k−1) is the sum of the intensity of N pixels along the pixel sequence of a pixel in the image sequence 240, wherein the sum is performed within a window [k−N/2−1; k+N/2−1] around the pixel in the image cF(k−1); and If(k) is the sum of the intensity of N pixels along the pixel sequence of a pixel in the image sequence 240, wherein the sum is performed within a window [k−N/2; k+N/2] around the pixel in the image cF(k). The normalized sum 244 of N complex images is then fed to a storage device 154 (see also FIG. 6) which stores the normalized sum 244. Further, the normalized sum 244 of N complex images is then fed second subtracter 246. The harmonic frequency component extraction and removal block 230 further comprises a second delayer 248, which delays the incoming images of the sequence 222 by N/2, i.e. the output image Fn(k) of the second delayer 248 is an image in the middle of the window defined by the image Fn(k+N/2) which is about to be fed to the first delayer 231 and the image Fn(k−N/2) which is output by the first delayer 231. The second subtracter 246 provides the difference image of the normalized sum 244 of the N complex images around the complex image cF(k), and the output image F(k) of the second delayer 218. Thus, the sequence of images provided by the second subtracter 246 corresponds to the remaining image sequence 140 (see also FIG. 6), a pixel sequence thereof is shown in graph 5c. 
It should be noted that the normalized sum 244 of index k, cFf(k)/N is comparable to a discrete Fourier transform of the input image sequence within the window [k−N/2; k+N/2]. However, any other method for providing a discrete Fourier transform may be used to determine a quantity which provides in-phase and out-of-phase harmonic frequency components.
Having regard to FIG. 6, the low frequency component extraction and removal 144, 150 which is performed in advance to the respective higher harmonic frequency extraction and removal 132, 134 can be performed in the same way as described with regard to the low frequency component removal block 200 except that the value of N has to be set to the respective value corresponding to the higher harmonic frequency of consideration, e.g. the value of N has to be set to N/2 for the second low frequency component extraction and removal and for the second harmonic frequency component extraction and removal.
The low frequency component extraction and removal block 200 and the harmonic frequency extraction and removal block can be realized in software or in hardware. That is, a respective computer program product may be provided which enables a processor to carrying out the methods described above. In particular the elements of the low frequency component extraction and removal block 200 and the harmonic frequency extraction and removal block can be realized as respective software modules. For example, the low frequency component extraction and removal block 200 and the harmonic frequency extraction and removal block 230 form a filter unit for filtering said input sequence of images depending on the reference frequency. The filtering unit 200, 230 may be implemented in the central unit of the X-ray imaging system 16 shown in FIG. 3. An output indicative of the harmonic frequency, e.g. the phase φ may be displayed by the display device 34 of the X-ray imaging system 16.
A software solution has the advantage that the respective computer program product or the respective software modules may be provided only once and the respective harmonic frequencies are assessed by adjusting the variable N. Further, as N corresponds to the heartbeat frequency in the illustrated embodiments, a change in heartbeat frequency can be easily taken into account within a software realization of the present invention. However, it can also be taken into account by an appropriate hardware realization. A software realization of the present invention may be carried out on available computers in an X-ray imaging system.
A hardware realization of the present invention may yield a higher image processing performance than a software solution.
FIG. 8 shows the co-operation of several aspects of the present invention of an exemplary embodiment of an X-ray imaging system. In FIG. 8 a contrast agent is introduced at a steady rate in an injection region 300 of a vessel 302 of a vessel system 303 resulting in a contrast modulation of images taken by X-ray imaging 304 of the vessel 302. At 306 a reference heartbeat signal having a frequency fm is detected either from ECG or from periodicity of image contrast. For X-ray imaging 304 of the vessel 302, an X-ray imaging system 308 is provided, the X-ray imaging system 308 having a high resolution and a high frame rate. At 310, a time-domain band-pass about the heartbeat frequency fm is applied to each pixel of a sequence of images provided by the X-ray imaging system 308. From applying a time-domain band pass about frequency fm quadrature filter pair outputs (α, β) may be derived. At 312, as a result of applying a time-domain band pass to the sequence of images, grey or color display of a phase map (φ) (fundamental or including harmonics) is provided. Optionally, at 314, the system may comprise computing a blood velocity from α, β maps and its time domain behaviour (Noise Robust Optical Flow).
In summary, an embodiment of the invention makes use of the natural of the natural modulation in contrast agent density at the injection point that results from the periodic variation of blood velocity at heartbeat frequency. It is particularly suited to dynamic X-ray angiography of the brain (Neuro). A reference quasi-periodic signal is derived either from the ECG or from direct extraction of the heartbeat related component of the image-contrast around the contrast product injection point. The intensity of every pixel in the angiographic image sequence is time filtered using a sliding window Fourier Transform to obtain, in particular, the fundamental in-phase and quadrature responses (at heartbeat frequency) as well as responses related to the first few harmonics. In particular, the phase of the fundamental component is displayed as a colour coded or grey-coded image sequence. The display of the phase image sequences strongly enhances the visualization of the flow process. The eye readily follows each constant phase front, which advance at a velocity related to the mean blood-velocity in a heartbeat cycle. The visualization of the blood jet that sometime impinges the aneurysm wall is also enhanced. The wide-band phase (including the 2nd and 3rd harmonic) gives furthermore a qualitative idea of the degree of pulsatility of blood velocity in the vessel.
While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclose embodiments.
For example, the invention is not limited to an X-ray imaging system. Rather, it is possible to use the filtering of a sequence of input images having contrast modulations along the sequence, the filtering depending on the reference frequency in other imaging systems.
Other variations to the discussed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfil the functions of one or several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does no indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.

## Claims

1. A method for image processing, the method comprising:
providing a sequence of images having contrast modulations along said sequence;
extracting for each pixel of the sequence of images a first reference frequency related to said contrast modulations along said sequence, the first reference frequency being a harmonic frequency of said contrast modulations; and
filtering each pixel of said sequence of images depending on said first reference frequency by extracting a harmonic frequency component from the sequence of pixels at the first reference frequency, thereby providing a modified sequence;
extracting for each pixel of the sequence of images a second reference frequency being a higher harmonic frequency of the contrast modulations along the sequence;
filtering each pixel of the modified sequence of images by extracting a higher harmonic frequency component from the modified sequence of pixels at the second reference frequency, thereby providing an output sequence of images, and providing at least one of an in-phase component of the of the output images and an out-of-phase component of the output images; and
displaying the output sequence of images as a color coded or grey coded image; and
wherein the first and second reference frequencies deviate from the respective harmonic frequencies by up to 30%; and
wherein the extracting and filtering steps above are performed via a processor.

2. The method according to claim 1, wherein
said sequence of images show a blood vessel of a vessel system;

the method further comprising:
generating said contrast modulations along said sequence of images by injecting a contrast agent at a steady rate into said vessel system at an injection region; wherein
said contrast modulations being generated by modulations of a blood velocity at said injection region due to a heart beat.

3. The method according to claim 1, wherein providing said first reference frequency comprises extracting said reference frequency from an electrocardiogram signal.

4. The method according to claim 1, wherein providing said first reference frequency comprises extracting said reference frequency from a time dependence of contrast along said sequence of images.

5. The method according to claim 1, wherein extracting a harmonic frequency component from one of said images at said reference frequency comprises:
applying a windowed harmonic filtering to each pixel of said one of said images;
wherein said windowed filtering is performed by taking into account images within a window of images around said one of said images; and
a number of images within said window of images corresponds to a time period corresponding to said reference frequency.

6. The method according to claim 1 further comprising detecting contrast regions having a predetermined contrast of interest in said images and low pass filtering each of the images in said contrast regions.

7. The method according to claim 1, further comprising
extracting from said images a low frequency component along said sequence of images;
removing said low frequency component from said images before performing said filtering of said sequence of images.

8. An apparatus for processing an image sequence, the apparatus comprising:
a reference frequency processor for receiving a sequence of images having contrast modulations along said sequence and extracting for each pixel of the sequence of images a reference frequency related to said contrast modulations along said sequence, the reference frequency being a harmonic frequency of said contrast modulations, wherein the reference frequency deviates from the respective harmonic frequency by up to 30%;
a first filter for filtering each pixel of said sequence of images depending on said reference frequency by extracting a harmonic frequency component from the sequence of pixels at the reference frequency, thereby providing a modified sequence of images;
a second filter for filtering each pixel of the modified sequence of images by extracting a higher harmonic frequency component from the modified sequence of pixels at a different reference frequency, thereby providing an output sequence of images, and providing at least one of an in-phase component of the output images and an out-of-phase component of the output images; and
a display for displaying the output sequence of images as a color coded or grey coded image sequence.

9. A computer program product including non-transitory computer data stored on a tangible computer readable medium, the computer program product comprising program code instructions to perform the steps of:
providing a sequence of images having contrast modulations along said sequence;
extracting for each pixel of the sequence of images a first reference frequency related to said contrast modulations along said sequence, the first reference frequency being a harmonic frequency of said contrast modulations;
filtering each pixel of said sequence of images depending on said first reference frequency by extracting a harmonic frequency component from the sequence of pixels at the first reference frequency, thereby providing a modified sequence of images;
extracting for each pixel of the sequence of images a second reference frequency being a higher harmonic frequency of the contrast modulations along the sequence;
filtering each pixel of the modified sequence of images by extracting a higher harmonic frequency component from the modified sequence of pixels at the second reference frequency, thereby providing an output sequence of images, and providing at least one of an in-phase component of the output images and an out-of-phase component of the output images; and
displaying the output sequence of images as a color coded or grey coded image sequence;
wherein the first and second reference frequencies deviate from the respective harmonic frequencies by up to 30%.