DE102004063300A1 - Method and device for evaluating a function recorded by detection of a physical quantity - Google Patents

Abstract

The invention provides a method of judging a selected range of a function E (n) acquired by detecting the progression of a physical quantity E over the abscissa n and which may include aleatory and / or deterministic components, the aleatory component being unknown and the deterministic components are at least partially unknown. According to the invention, all possibly known deterministic components are first removed from the function E (n), and an auxiliary function G (n) is calculated from the resulting function F (n), which is the running sum of the function values of F (n) along the selected range represents anb. By comparing the two functions F (n) and G (n), a judgment value W is determined which reflects the degree of similarity of both functions and thus is a measure of the relative proportion of the aleatory component of the function F (n) within the selected one Range of this function. The subject matter of the invention is also an assessment device (10) which functions according to this principle.

Description

The The invention relates to a method and a device for judging a function that can be detected by detecting the course of a physical Size over one Abscissa is recorded, according to the preamble of patent claim 1 or claim 15. Preferred, but not exclusive Field of application of the invention is the processing of recorded Image data, in particular in magnetic resonance imaging (MRI = Magnetic Resonance Imaging).

background the invention

One primary Process in both metrology and data transmission technology is the detection of a physical quantity E (which is also can be the output voltage of a data source) and the Providing a continuous or discrete function E (n), which the course of the size E over a Abscissa represents n. With "gradient" here is the amplitude distribution E (x) the size E along of any coordinate x. This coordinate can be a time coordinate, a space coordinate or a co-ordinate in any other Dimension, e.g. a temperature coordinate. The abscissa n of the provided "mapped" function E (n) must not the same dimension as the course coordinate x of the detected Have size E. If e.g. a spatial Course of a size through time sequential scanning of the size at different points the spatial coordinate is detected, then the course is in a time function transformed. In similar Thus, a time function is obtained when e.g. the temperature dependence a size through Observation of the size in itself changing over time Temperature is detected. Conversely, a space function is obtained if the values of the history in the spatially-spaced memory cells of a Data storage are stored. With parallel reading of the memory cells the function remains a room function, in case of serial reading they are again provided as a time function.

The Whole of all elements involved in the delivery of the function E (n) are involved, hereinafter referred to as "channel". This channel transforms the course E (x) of size E in the functions).

The Measurement of physical quantities and also the further processing of the measurement results for the provision a continuous or discrete function, ie the "channel", form in theirs Entirety a stochastic process. This process does not flow only the actual measurand as a "determinate" component, but also a complex of random phenomena, the "aleatoric" part of the stochastic Process forms. The obtained function thus contains a determinate one Component D (n), which is usually the actual object of the observation is thus the requested "information" represents, and an aleatorische Component A (n), which is common flat rate also as "noise" is called. This component can be unique depending on its strength the requested information more or less difficult or even impossible do.

It Methods are known for the strength of aleatoric influence of a channel. On In the field of communications engineering, "channel tests" are common, about quality a channel for transmission an information signal in the form of a time-varying To serve tension, to judge. This is done in a test mode at the entrance of the channel a test voltage with a known course is created, e.g. a constant voltage, and the output checks to what extent the voltage appearing there differs from that of the course, in the ideal case, so without aleatorischen influence in the channel, too would be expected.

is the test voltage is a constant DC voltage, then the said exam e.g. simply consist of the AC power in the output signal to eat. The measurement result gives directly the strength of the aleatorischen component of the channel influence again. At more complicated Method is known as test voltage information signal with a known and recognizable information content, and at the output becomes checked, whether the information received there is recognized without error, and if desired, how high the error rate is. However, these methods are not suitable, the strength an aleatoric component in a signal to recognize the additionally contains an unknown deterministic component.

However, it is also known to determine the channel quality on the basis of an output signal in which a deterministic component with unknown information content exists. However, this assumes that the information in the deterministic component is redundantly encoded by means of an error-detecting code. A decoder on the output side of the channel can determine the error rate (so-called Bit error rate BER in the case of digitally coded information). This error rate is usually higher, the stronger the aleatoric component introduced in the channel relative to the deterministic component (the intensity ratio of the deterministic component to the aleatoric component is usually referred to as "signal-to-noise ratio" S / N). In practice, this technique is used to switch the information transfer to another channel as soon as the determined bit error rate becomes unacceptably high.

One Another known method for detecting the relative content on aleatory and deterministic components in a function E (n) is the frequency analysis by means of mathematical Fourier transformation. In this case, the amplitudes of the function E (n) investigated in the examined function calculated frequency components. It is believed that the aleatoric component A (n) has an equal value for all frequency components shows (so-called "white noise"), so a flat "flat" spectrum has, without significant rashes (Peaks). If in the spectrum of the total function E (n) any Peaks may occur, their amplitude and frequency may be indicative the presence and intensity of a deterministic component give. However, you can such peaks also be caused by certain functional relationships between Frequency and amplitude, ie the frequency response of the channel, if this does not have ideal all-pass characteristics, which usually is to be expected. The influence of the frequency response of the channel is in Basically a deterministic component, but is not correlated with the actual information. To the relationship between the aleatoric Component and the really interesting information correctly estimate have to so the "frequency response peaks" are ignored, which requires a prior knowledge of the channel frequency response. Another Disadvantage is the considerable computational complexity of the Fourier analysis.

In summary let yourself say that the previously known assessment methods have significant disadvantages either because they have previous knowledge of certain properties of the Information or about presuppose the frequency response of the channel or because they are an error-detecting Encoding the information of interest in the deterministic one Require component. by the way the misdetection also has certain knowledge about the deterministic component, namely the knowledge of the error-detecting Codes.

Task of Invention and solution principle

The Object of the present invention is technically feasible activities indicate the content of aleatorischer components relative to the informative share in a function are estimated can, without any previous knowledge about the information or frequency response of the function providing the function Channels are required. This object is achieved by the method characterized in claim 1 solved.

object Accordingly, the invention is a method for judging a selected range a ≤ n ≤ b of a function E (n) obtained by detecting the course of a physical quantity E over the Abscissa is recorded n and the aleatory and / or determinate Components may contain, with the aleatorische component unknown and the deterministic components are at least partially unknown. According to the invention from the function E (n) first removes any known deterministic components, and from the resulting function F (n) becomes an auxiliary function G (n) calculates the running sum of the function values of F (n) along the chosen one Range a ≤ n ≤ b represents. By comparative examination of the two functions F (n) and G (n), a judgment value W is determined, which is the measure of similarity reflects both functions and thus is a measure of the relative share of aleatoric component of the function F (n) within the selected range this function.

The invention is based on the insight that the essential difference between an aleatory function A (n) and a determinate function D (n) is also revealed in how the function in question differs from a running sum of the values of this function. The essence of a purely aleatory function A (n) is that successive values of the function are statistically independent of the preceding values. Thus, the sum SA (n) of the successive values of the function A (n), which starts at a starting point n = a, is likewise a purely aleatoric function. The amplitude changes of the sum function SA (n) are in the range from the starting point a with increasing abscissa n always closer to the amplitude changes of the original function A (n); the absolute difference remains only a constant amplitude difference which is equal to the value of the original function A (n) at the starting point a of the summation. This is because it belongs to the aleatory character of the original function A (n), that all Previous amplitude changes of this function in the course of the summation increasingly accurate.

Different is the matter with a determinate function D (n). Because here successive values of the function are not statistically independent of are the preceding values, it comes at formation of the current Sum not to a progressively more accurate evaluation of the previous amplitude changes the original function D (n). Thus, here is in terms of amplitude changes no adjustment of the sum function SD (n) to the original function to observe.

The above-described distinguishing feature between aleatoric and determined function is in the assessment method according to the invention exploited to the aleatorischen portion relative to the informative Estimate proportion in a function F (n). The more pronounced the Alignment of the amplitude changes the sum function to the amplitude changes of the original function F (n) is, the bigger it gets be the aleatorische share. The less the functions in In this respect, the greater the determinate becomes Share. Through a comparative study of the original function and the summation function may have a degree of alignment or similarity between the two functions, which is a measure of the relative Proportion of the aleatory component of the original function F (n). For this Different methods of investigation are suitable.

The validity of the assessment method according to the invention is best when the determinate component D (n) of the function F (n) contains only that deterministic component which represents the requested information, ie the "informative" component. Frequently, components detected in the detected physical variable E (n) are already involved in the detection and / or further transmission and transformation through the channel, the characteristics of which are known. Therefore, a first method step is to remove the sum D ₀ (n) of all these known components.

To the known deterministic components may e.g. a constant Belong to offset, or a known fault function such as a hum or a known temperature influence. One another example is damping mechanisms, which accompany the course of the function F (n) and often in one Waste of the detected function over time demonstrate. This waste is usually due to an exponential Waste of the physical quantity E (n) mathematically described as time progresses. So in the first Process step also such, as provided known damping behavior be removed. But it is also possible, a specific damping model, such as. the ideal damping, described by an individual exponentially described Signal drop, to adapt to the measured data, and this too remove. Deviations of reality from this given model are considered deterministic component in the function thus obtained remain; they are too an "informative" component of the function.

Special embodiments the invention and advantageous applications and the embodiments of Devices which function according to the principle of the invention, are characterized in further claims.

detailed explanation the invention

below the invention is based on embodiments closer by means of drawings explained.

1 shows an original function to be assessed by the method according to the invention, which contains determinate and aleatoric components;

2 shows an auxiliary function formed by summing up the original function;

3 shows the judgment value as a function of the relative strength of the aleatoric component in the original function;

4 shows the cross-correlation function of the original function and the auxiliary function;

5 shows the first derivative of the cross-correlation function;

6 shows a block diagram of a judging device according to the invention;

7 shows a first embodiment of the comparative analysis stage in the assessment device 6 ;

8th shows a second embodiment of the comparative analysis stage;

9 shows in block diagram the use of a judgment device according to the invention in a system for processing MR image information.

starting point of the evaluation method described below is the presence a set of values E that observed over a selected interval describes the course of a physical quantity as function E (n), where n is the scale or abscissa of the course direction. The physical Size can an electrical signal at the output of a "channel" connected to any measuring device or any other source of information and a lot of processing and transmission facilities may contain. In the way of the channel can be an analog or digital Storage medium containing the information source supplied information stores and the amount of values E on demand over reader provides, e.g. in analog form as continuously or discreetly sampled Voltage values or as discrete digital words.

As described above, the function E (n) may include, in addition to an unknown deterministic component D (n) representing the supplied information and a likewise unknown aleatoric component A (n), also known deterministic components D ₀ (n) but does not belong to the information supplied. Therefore, a first step of the method according to the invention is to subtract the known components D ₀ (n) from the function in order to obtain the "original function" to be assessed. F (n) = E (n) - D 0 (n) (Eq.1) to obtain.

In the 1 is a typical function F (n) within a selected observation window a ≤ n ≤ b, where the abscissa points n are scaled from a starting point a = 0 to an end point b = 99. The function F (n) contains the unknown aleatoric component A (n) and, as the deterministic component D (n), only the information. This "informative" component is in the 1 drawn as a dashed curve; Of course, in practice, it is unknown. For purposes of illustration, the in 1 represented function F (n) generated by a simulation, wherein a dashed drawn deterministic component D (n) was added to a generated by a random number generator noise function A (n).

gebildet werden, z.B. mittels einer analogen Integrierschaltung. Wenn F(n) als diskrete Funktion vorliegt, bestehend aus einer diskreten Folge analoger oder digital codierter Abtastwerte in gleichmäßigen Abständen entlang der Abszisse n, dann wird die laufende Summe als diskrete Funktion

gebildet durch schrittweises Aufsummieren der Abtastwerte. Die Funktion G(n) ist in der 2 graphisch dargestellt.As a second step, an auxiliary function G (n) is formed from the function F (n), which represents the running sum of the values of the function F (n) over the abscissa n. If F (n) is a continuous function, the running sum can be considered integral

be formed, for example by means of an analog integrated circuit. If F (n) is a discrete function consisting of a discrete sequence of analog or digitally coded samples at regular intervals along the abscissa, then the running sum becomes a discrete function

formed by stepwise accumulating the samples. The function G (n) is in the 2 shown graphically.

A comparison of the functions F (n) and G (n) shows that they are very different from each other. In the example shown here, the dynamic range of G (n) is much larger due to the summation than for the function F (n), as can be seen on the scale of the ordinate. In the absence of a deterministic component, the dynamic range of F (n) and G (n) would be approximately equal. In this case, the only observable difference would be only a constant amplitude shift equal to the value of the function F (n) at the abscissa point n = a equivalent.

Of the Difference in dynamic range, however, will be less noticeable if the deterministic component D (n) in rapid succession and relative regularly between positive and negative values changes. Nevertheless, said distinguishing feature in many practical cases be revealing, such as when such rapid changes in D (n) are not expected. By means of a comparative examination can the feature is quantified to an assessment score W to determine which is a measure for the relative proportion of the deterministic versus the aleatoric component the function F (n) within the selected range this function.

oder, bei diskreten Funktionen F(n) und G(n),

One possible method for the comparative analysis of the two functions F (n) and G (n) is to determine the judgment value W as the ratio of the determined integral of the absolute value of the function F (n) versus the particular integral of the magnitude (Absolute values) of the function G (n), in each case over the entire range from a to b, according to the formula

or, for discrete functions F (n) and G (n),

The 3 FIG. 14 is a graph showing how the thus-obtained judgment value W changes when the relative proportion of the aleatoric component A (n) to that in FIG 1 the deterministic component D (n) shown in dashed lines increases.

oder, bei diskreten Funktionen F(n) und G(n),

der beiden Funktionen gebildet. Der Parameter τ ist das in diskreten Schritten einer Schrittweite Δ geänderte Maß der gegenseitigen Verschiebung der beiden Funktionen bei der Berechnung der diskreten Kreuzkorrelationsfunktion. Somit ist die Funktion K(τ) eine diskrete Funktion. Der Parameter k ist ein beliebig wählbarer Maßstabsfaktor.Another method for the comparative study of the two functions F (n) and G (n) used in an advantageous embodiment of the invention involves a cross-correlation. This is done by the cross-correlation function

or, for discrete functions F (n) and G (n),

formed of the two functions. The parameter τ is the degree of mutual displacement of the two functions in the calculation of the discrete cross-correlation function which is changed in discrete steps of a step width Δ. Thus, the function K (τ) is a discrete function. The parameter k is a freely selectable scale factor.

In In words The formation of the cross-correlation function K (τ) is general as follows: The functions of F (n) and G (n) are progressively different Multiples of the step size Δ along the abscissa n in a negative and / or positive direction to each other postponed. After each step, a product function is formed, the for each abscissa point n the product of the two shifted to each other Functions represents. The values of each product function within a chosen one The area of the abscissa n is added up (integration of the product function or adding their discrete value sequence), and the results will be over one Abscissa τ shown, whose scale the respective measure of Displacement represents as a corresponding multiple of the step size Δ. If F (n) and / or G (n) is a discrete function, ie a discrete one Sequence of samples along the n-coordinate, then this one Step size Δ preferably equal to the step from one sample to the next sample.

When choosing the range of the abscissa n, over which the product formation of the two mutually shifted functions F (n) and G (n) and the summation of the products, takes place, the following should be noted: The above-mentioned observation window, ie the range a ≤ n ≤ b of the two functions, comes in the shift out of coverage. If τ _{max1 is} the amount of the maximum shift in the negative direction and τ _{max2 is} the amount of the maximum shift in the positive direction, then only the range from n = a + τ _max1 to n = b - τ _{max2 remains} within the observation _window maximum shift still overlapped. Only over this range should the product formation of the two mutually shifted functions F (n) and G (n) and the summation of the products take place. Of course, the larger this range, the more accurate the calculated values of the cross-correlation function.

The function values of the cross correlation function K (τ) are in 4 is shown as a bar graph over the abscissa τ, over a relatively wide range of τ values. It has been found that by analyzing the first derivative K '(τ) of the function K (τ) one can obtain a measure W which is representative of the relative proportion of the aleatoric component to the determinant component of the function F (n). Specifically, it has been found that the values of the derivative K '(τ) at the abscissa point τ = 0 form a peak over the adjacent values, which becomes more prominent over the values of adjacent points the stronger the relative proportion of the aleatory component in the function F (n) is.

For illustration is in the 5 the first derivative K '(τ) of the 4 shown cross-correlation function K (τ) shown. Since K (τ) is a discrete function, the first derivative K '(τ) is obtained by stepwise subtraction, according to the equation K '(τ) = [K (τ) - K (τ - Δ), (Eq.8) where Δ, as already defined above, the increment of the shifts in the formation of the cross-correlation function K (τ). In the 5 clearly shows the mentioned peak at the point τ = 0.

In order to determine a measure W for the relative height of this peak, at least two values of the derivative K '(τ) must be determined. As the first value W ₀ , the value of the function K '(τ) for the zero point τ = 0 is determined. A second value W _R is determined as a "reference value" from at least one function value in the neighborhood of the point τ = 0, generally speaking a set of function values K '(τ) for a set of points τ ≠ 0 within a selected environment area u ≤ τ ≤ v of the zero point. From the function values of the selected set of environmental points, a reference value W _R can be determined which can be compared with W ₀ to obtain the dimension W of the relative height of the peak.

To determine a suitable reference value W _R , it may be sufficient to select only one surrounding point, wherein preferably one of the immediately adjacent points τ = 0 - Δ or τ = 0 + Δ is selected. Since the difference between the value of the function K (τ) at this point and the value at the immediately preceding point must be formed at one point in order to calculate the derivative K '(τ), one needs only three points for this case beforehand τ = 0 - 2Δ, τ = 0 - Δ, τ = 0 (or τ = 0, τ = 0 + Δ, τ = 0 + 2Δ) of the correlation function K (τ). The reference value W _R can then be the function value K '(τ) _0-Δ or the function value K' (τ) _{0 + Δ} .

However, it may be advantageous to choose as the reference value W _R for the height W of the peak not exactly an immediately adjacent point, but rather any mean value over several points τ ≠ 0 within a region including these points u ≦ τ ≦ v. The mean may be the arithmetic mean, the root mean or a different weighted average.

In general, therefore, it suffices to calculate the cross-correlation function K (τ) according to the above equation Eq. 6 or Eq. 7 only over the range u ≦ τ ≦ v. This means that τ _max1 can be chosen equal to u and τ _max2 can be chosen equal to v. The smaller this range is, the lower the computational effort and thus the computing time. In addition, as already mentioned above, the smaller the area, the larger the accuracy of the values of the cross-correlation function K (τ) calculated for this area.

oder als Absolutwert des verschobenen Quotienten:

wobei w ein beliebig gewählter Maßstabsfaktor ist.As a measure W for the relative height of the mentioned peak in the derivative K '(τ) and thus as a judgment value for the relative proportion of the aleatoric component against the determinant component of the function F (n), a value can be determined which has a relation between W ₀ and W _R indicates, for example, the difference or the quotient. Preferably, the judgment value W is calculated as the absolute value of the difference: W = w · | W 0 - W R |, (Eq.9) or as the absolute value of the quotient:

or as the absolute value of the shifted quotient:

where w is an arbitrarily chosen scale factor.

If desired, you can classify the rating value by adding a number graded thresholds that give different quality classes be assigned. The judgment value W becomes with these thresholds and the quality class that is displayed is displayed highest the exceeded Thresholds (or the lowest of the undershot thresholds) assigned. In many applications, it may suffice to provide a single threshold to provide quality information "useful" or "unusable". suitable Thresholds can for a System in which the method according to the invention is realized, be found empirically.

The steps of the above-described evaluation method are described in U.S.P. 6 shown in the form of a block diagram. This diagram applies equally to the structure of a rating device which operates on the principle according to the invention. The individual blocks in this case represent the stages of an arithmetic processing device, which in total with 10 is designated. The block 11 is a subtractor stage having a first input for receiving the function E (n) and a second input for receiving the function D ₀ (n), which is the sum of the known deterministic components, to obtain the function F (n) according to equation Eq To form .1. The block 12 is an integrating stage, which from the function F (n) forms the auxiliary function G (n) according to the above equation Eq. 2 or Eq. The block 13 is an analyzing stage which, by a comparative examination of the two functions F (n) and G (n), determines a judgment value W which is a measure of the relative proportion of the aleatory component of the function F (n) within the selected range a ≤ n ≤ b.

The analysis stage 13 may be formed in any suitable manner. In the 7 a first embodiment is shown which operates with the formation of the cross-correlation function. A correlator 14 forms the discrete cross-correlation function K (τ) according to equation Gl.6 or Eq.7 above. A differentiation level 15 calculates the derivative K '(τ) according to Equation Eq. 8 above, and a comparison stage 16 calculated from adjacent values K '(τ = 0) and K (τ ≠ 0) of the derivative K' (τ), the judgment value W according to the above equation Eq.9 or Eq.10 or Eq.11.

The 8th shows as a second example an embodiment of the analyzing stage 13 , which works according to the above described principle of magnitude integration and quotient formation. These are two absolute value formers 17a and 17b for the functions F (n) and G (n), each of which has an integrating stage 18a respectively. 18b is downstream. The output signals of the two integration stages 18a and 18b become a divisional level 19 to calculate the judgment value W according to the above equation Eq. 4 or Eq.

In the 6 is also a block 20 which is a threshold comparator which derives the quality judgment Q from the judgment value W by comparison with a threshold value S. The in the 6 to 8th shown stages can be realized as electrical circuits or, at least partially, be realized as a computer program.

In the above-described judging method, some inaccuracy may occur due to the fact that, in the calculation of the auxiliary function G (n), the initial value of the summation (that is, the value of the function F (n) at the starting point n = a) is a constant appears. This initial value F (n) _a is composed of the initial value A (n) _{a of} the aleatory component and the initial value D (n) _{a of} the deterministic component. Although the initial value A (n) _{a is} itself aleatory, it acts as a constant deterministic component over all calculations. In the end, this leads to the calculated evaluation value W having a certain error rate. That is, there may be some likelihood that the quality information will be "usable", although the quality would actually be deemed "unusable," and vice versa.

This error rate can be ignored in some applications. But there are also ways to reduce this error rate. One way is to repeat the recording of the function E (n) one or more times and to average the evaluation values obtained in each case. Another possibility is to calculate the quality information twice in succession in two passes, with the addition of the function F (n) in opposite directions. That is, in one of the passes, the auxiliary function G _a (n) is generated by integrating or summing the function F (n) from the point n = a in the "forward" direction to b, as shown in FIG 2 and in the comparative analysis the functions G _a (n) and F (n) are considered. The other pass is "mirror inverted", ie, the auxiliary function G _b (n) is generated by integrating or summing the function F (n) from the point n = b in the "backward" direction to a, and in the comparative analysis Function G _b (n) and the corresponding mirrored version of the function F (n) considered. Only if both passes provide the quality information "usable" will the final judgment be given "usable". This can actually reduce the probability of error: If, for example, the error probability for the sole use of one or the other auxiliary function G _a (n) or G _b (n) equals 50%, the result for the final judgment is an error probability of only 25%.

The Inventive assessment method can be used with advantage in various fields of technology be to the quality a measuring or data transmission system to judge. The procedure can be supplemented by further steps, which particular consequences from the determined assessment value W or continue to process this value.

So can be about in a data transmission system the judgment "usable" or "unusable" derived from the appraisal value W is used; in the "unusable" case the data transmitter to redo his broadcast or the system too induce the same shipment and / or subsequent shipments via a to transfer another channel. Another application is e.g. the examination of Devices, e.g. the final exam of measuring equipment at the manufacturer. This may cause a "useless" ruling the device in question weed.

A special development of the assessment method according to the invention concerns the application in MRI, more specifically the application in the processing of image data obtained by acquisition of magnetic resonance data from a body by means of an MR device been recorded. The image data are after the recording as a record in a memory before and consist of a variety of values, each one pixel (pixel) within a to be reproduced image. Each of these pixel values has a defined memory address, which indicates the coordinates of the respective Indicates pixels in a multidimensional coordinate system. This Coordinate system, also referred to as "image grid", usually has two or three "space coordinates" for the pixel position in a two- or three-dimensional picture. For a record for the Representation of a moving picture, ie a sequence of individual pictures, there is another coordinate in the direction of the image sequence. This coordinate is referred to here as a "temporal" coordinate.

The Playback of an image is done by scanning the stored one Record along the coordinates. This is the record read out by scanning the addresses of the spatial coordinates. in the In the case of a motion picture, all spatial coordinates of the scanned the first frame of the sequence, and then follows the same Procedure for the following pictures, whereby from picture to picture a forwarding along the temporal coordinate.

Motion pictures are generated at the MRI to observe a temporal process in the body to depict, e.g. the flow of blood in the living human or animal body. There are several known MRI recording methods, pixels, which gained from volume areas (voxels) of flowing matter in the body be, opposite Pixels from other parts of the body emphasized. Such a "flow weighting" of the recording provides e.g. the so-called phase contrast measurement, in which suitable from one recorded record both a moving picture, the structure of the Object reproduces (the so-called amount image), as well Motion picture is generated, which reflects the flow velocity, which can be assigned to each pixel (the so-called phase image). Another technique is the perfusion measurement (blood circulation determination) with First-Pass, which uses a contrast agent in the flowing blood and the dynamics of the flow of this contrast agent observed in certain vessels and tissues becomes.

A detailed description of these and other suitable methods for flow weighting can be omitted here, it is referred to the relevant literature. For the technique of phase-contrast measurement see eg: Hombach V, Grebe O, Botnar R. "Cardiovascular Magnetic Resonance Tomography" Schattauer Publisher, Stuttgart, 2005; Morneburg H. "Imaging Systems for Medical Diagnostics" Wiley VCH Verlag, 1995; Stahlberg F., Sondergaard L., Thomson C. "MR flow quantification with cardiovascular applications: a short overview", Acta Paediatr Suppl., 1995 Aug. 410: 49-56. For the technique of perfusion measurement see eg: Hombach loc. Cit. Nail E, Al-Saadi N, spot E. "Cardiovascular magnetic resonance: myocardial perfusion" heart 2000; Edleman RR "Contrast-enhanced MR Imaging of the Heart: Overview of the Literature" Radiology 2004.

Moving images of flow-weighted MRI scans can give a viewer valuable insight into blood flow. They are thus a good diagnostic tool, for example, testing for disturbances in blood flow or heart valve leaks, or examining the effects of an infarct. Aleatoric components in the image data of motion pictures are particularly disturbing, because these components appear differently from image to image during image reproduction, thus simulating a movement even where there is in fact no movement whatsoever. Especially in recordings in which the movement itself is the actual object of the observation, so also in the mentioned river-weighted recordings, the image noise caused by the aleatorischen components is highly irritating. The assessment method of the present invention provides a surprisingly successful means of eliminating these irritations. A concrete embodiment of this will be described below with reference to the 9 described:
Using an MRI Scanner (Magnetic Resonance Tomography MRI) 41 are location-coded MR signals obtained from a volume range of an object to be examined and in an image reconstruction computer 42 is processed to generate pixel values which for each of the sampled elements (voxels) of the volume region respectively indicate the intensity of the obtained MR signal. In the example described here, the location coding in the MRI scanner 41 controlled so that the same volume range is scanned N times in succession. Let this volume range be a two-dimensional array of voxels that defines a flat layer within the object under investigation. The excitation and detection of magnetic resonance in the MRI scanner 41 is done so that the intensity of the MR signals is flow-weighted. The image reconstruction computer 42 Thus, for each of the N scanning cycles, the pixel values supplied in each case describe a two-dimensional image which, as a contrast, maps the intensity distribution of flow phenomena within the scanned layer of the object. The pixel values of all N consecutive "flow contrast images" are stored as a motion picture data set in an associated image memory 44 transfer.

The in the image memory 44 stored data set to be processed using the assessment method according to the invention. This is done in an image processing device whose components in 9 within the dashed frame 50 are drawn.

The image processing device 50 contains a processing memory 51 into which the data set contained in the flow contrast image memory is copied. This process, like all other image processing operations, is controlled by a controller 52 controlled. The control device supplies inter alia write commands WR, read commands RD and address signals ADR for writing and reading to individual memories, furthermore selection commands SEL for selecting the relevant memories and switching signals for controlling various data path switches. The said copying is done by: setting a data path switch 53 in the upper position, leaving a data path from the data output of the memory 44 for data input 51e of the processing memory 51 is set up; Selection commands SEL to the memory 44 and 51 ; Read command RD with addresses ADR to the memory 44 ; Write command WR with addresses ADR to the memory 51 ,

The organization of the copied record is in the 9 through a three-dimensional grid inside the block 51 illustrated. This raster contains a plurality of planes along an n-coordinate, and each plane forms a two-dimensional matrix of points whose position within the matrix is defined by an x-coordinate and a y-coordinate. All points of an xy matrix correspond to the pixels of a two-dimensional frame of the stored motion picture data set. The n-coordinate indicates the current frame number (ordinal number) of the respective frame within the sequence of frames. Each pixel P _{x, y, n of} the raster, that is to say each pixel of the motion picture sequence, is selectively addressable in the memory by its x-address, its y-address and its n-address. For clarity, the image grid in the 9 shown with a very low resolution of 13 by 13 pixels per frame. In practice, of course, the resolution is many times higher, for example in the range of 128 by 256 pixels to 512 by 512 pixels per frame and with 20 to 40 frames along the n-coordinate, which document, for example, the blood flow in humans via a heartbeat.

The object of the image processing in the example described here are those functions p _{i, j} (n) which each have the successive pixel values of a certain point P, which has the position x = i and y = j within the two-dimensional matrix, as it progresses along the n-axis. Describe coordinate. Each such function p _{i, j} (n) is a discrete sequence of values which is judged by the method according to the invention and modified or not depending on the result of the judgment. For this purpose, the data output 51a of the processing memory 51 with a judging device according to the invention 10 connectable. This connection is made by a data path switch 54 is set to its lower position at the data output.

The image processing first requires a large number of successive identical reading and evaluating cycles, but in each case a different point position x _i , y _j within the xy coordinate system is selected from cycle to cycle. Each cycle begins with a read operation on the memory 51 in which a sequence of address words is applied, in which only the n-address changes progressively, while the x-address and the y-address remain the same (corresponding to the selected point position x _i and y _j , the set of the points thus addressed is in the 9 drawn for the example x _i = 5 and y _j = 1). The addressing leads to the reading of the above-mentioned value sequence p _{i, j} (n) at the data output 51a , the assessment body 10 is supplied as input function E (n) and processed there, as described above in connection with the 1 to 8th has been described in order to generate the assessment value W, which indicates the relative proportion of the aleatory component, ie the "noise component" in the value sequence p _{i, j} (n). This processing takes a certain amount of time. The computation time for the total number of cycles in a typical phase-contrast motion picture recording is less than one second on a modern personal computer.

The function D ₀ (n), which represents the known deterministic signal components to be subtracted, is in 9 (as well as in 6 ) as a second input of the judging means 10 shown. The subtraction of some or all of these deterministic components can also be done elsewhere, eg before or in or after the image reconstruction computer 42 and before writing the image data into the processing memory 51 ,

The judgment value W from the output of the judging means 10 will be in a threshold comparator 20 compared with a selected threshold value S in order to deliver the quality judgment "unusable" when the threshold value is exceeded, and otherwise the quality judgment "usable". The thus-obtained quality judgment for the selected value sequence p _{i, j} (n) is stored in a log memory 55 entered. This completes the cycle for the selected point position x _i , y _j .

The log store 55 For example, it may contain a list of all possible xy address combinations that can be individually tagged to indicate whether the "useable" quality rating has been provided for that particular xy address combination.

Once in the manner described p the value sequences _{i, j} (n) x _i for all possible point positions, y _j are (that is, for all possible combinations of x- and y-coordinate values) evaluated and the quality judgments have been logged, followed by the actual Image editing based on the protocol. For this purpose, the control device causes 52 a write operation to the processing memory 51 , where it first the data path switch 53 in the lower position sets to the data input 51e the processing memory with a fixed value source 56 connect to. Then the controller addresses 52 successively all those points P _{x, y, n} for whose xy address part the quality judgment "unusable" has been logged, and causes the pixel values of these points to be replaced by a fixed value E _f .

The The result of this processing is a flow contrast motion picture in which every point of the xy image matrix that is not in any of the consecutive Frames represent a recognizable flow information, throughout is displayed with the fixed value. Points, however, that in at least represent any recognizable flow information to any frame, be in the course of the image sequence according to their modulation by the MR signal is shown. That is, all those parts of the Scanned volume range in which during the entire recording time no flow has occurred, appear in a rendition of the processed flow contrast image smoothly, without any modulation. In the usual Image rendering, ie without inventive image editing, appears in the "flowless" parts one by noise caused modulation, which manifests itself as sparkling and flow phenomena pretends or at least perceived as an unpleasant and irritating disorder becomes.

Said fixed value E _f may be selected to represent a particular color and / or brightness that contrasts with the color or brightness scale used to represent the MR signal intensity. In a particular embodiment, a value is chosen that makes the respective pixels "transparent" pixels. This is advantageous if the flow contrast moving picture is superimposed on a second moving picture, which images physical structures of the scanned volume area.

If the flux-weighted image is obtained with the above-mentioned phase-contrast measurement, such a "structure" image as well as the flow-contrast image may be processed by the image reconstruction computer 42 be derived from the same MR signals. In the phase contrast measurement, the measured data are recorded as complex value pairs, in which one value represents the magnitude and the other value represents the phase of the MR signal. The image obtained from the magnitude values contrasts physical structures such as biological tissue. The computer 42 directs the magnitude values into a structure image memory 45 and the phase values in the flow contrast frame buffer 44 ,

If, however, the flow weighting is carried out using another MR recording technique, from which no structural contrast can be derived, then before or after the flow-weighted recording, a separate structural recording must take place in order to generate the structure motion picture and into the memory 45 to give. If, for example, the flow contrast image should represent the blood flow of a person in the cardiovascular system, then the relevant volume region of the body is scanned cyclically N times over the duration of a heartbeat by means of the flow-weighting MR sequence. The structure-scan image is obtained by cyclically scanning this volume area N times over the duration of a heartbeat using an MR sequence that contrasts biological tissue.

The flow contrast moving image processed in the above-described manner is under the control of the controller 52 , from the editing memory 51 and the read-out pixel values become a first input of a superimposition device 46 supplied (data path switch 54 in the upper position). Synchronous with this readout is the structure image memory 45 read out, and the pixel values read there are a second input of the superposition device 46 fed. At the exit of the overlay device 46 For example, those pixels that are "transparent" in the flow contrast motion picture (that is, do not render a flow) contain only the information of the texture image. All other pixels appear with the information of the flow contrast image. The result of the overlay is as a combination image in a memory 47 written. The image data from the memory 47 can then be fed to a suitable output device, such as a display or printer, to visualize the combination motion picture.

In an advantageous embodiment, the pixels of the flow contrast moving picture are given color information in order to emphasize them in the reproduced picture more clearly with respect to the tint of the structure moving picture. Such a "coloring" can be done according to a color grading scale, which converts the intensity levels of the recorded MR signal in color levels. This reaction is preferably carried out by means of a suitable color coder 57 in the way between the processing memory 51 and the overlay device 46 , A color representation of the flow information implemented in this manner may give the combination motion picture a similar appearance to that used in imaging sonographic Doppler flow measurements.

In the 9 shown system components 42 to 57 may be implemented as discrete electrical circuits or implemented, at least in part, by use of hardware and software in a computer.

It It has been found that the image processing technique described above is surprising gives good results and that the image reproduction achieved a far better quality and meaningfulness, as one has it from the conventional technology ago is. However, it can hardly be ruled out that it worked in the Pixel value sequences come to certain "outliers" by a as "useful" judged episode in Reality is "useless", and vice versa. Such outliers However, they are far apart and almost always "lonely", that is, it is highly unlikely that several misjudged pixel value sequences immediately adjacent are. Therefore, such errors are hardly recognizable in the rendered image.

If desired, one can obscure the mentioned lone outliers by making the quality assessment (eg, "unusable") of a pixel value sequence positioned in the xy coordinate system between two different (eg, "useable") sequences subsequently changed ( thus changed into "useless"). This correction can eg in the log memory 55 of in 9 shown system done. Based on the previous entries in the log memory, the xy coordinates of the outliers to be corrected can also be determined.

Particular attention must be paid to the choice of threshold S. As mentioned above, a suitable threshold can be found empirically. For this purpose, several tests can be made by the in the processing memory 51 stored motion picture is processed several times in succession, each time with a different threshold S, and after each processing the Kombinati ons motion picture is recorded. Such a series of tests may in turn be repeated one or more times, each based on a new scan of the same volume range. From the recorded motion pictures the best can be selected for a closer look.

Such Test series can also be used to adapt the processing system to specific types of applications to oak. The volume range used here can be a "standard" object for the respective Be kind of application, e.g. the heart area of a healthy subject, in which to estimate well leaves, what an ideal flow-picture rendering would look like. The threshold S, in which the observed picture comes closest to the ideal picture, can then be used as a fixed parameter for the relevant type of application is stored in the system. These Calibration can be done by the manufacturer of the system or by the user become.

Optimization of image processing thresholds can also be achieved through a special adaptation process:
In a first pass, the value sequences p _{i, j} (n) are evaluated for all possible point positions x _i , y _j (ie for all possible combinations of x and y coordinate values), as described above. Here, the same threshold value is used for all point positions. The log store 55 thus contains a corresponding marking for each point position judged as "usable". In a second pass, the threshold is set individually for each dot position, depending on how many adjacent dot positions have been marked on the first pass. Depending on the number of adjacent marked dot positions, the threshold is more or less increased. If the point position in question is already marked as "usable", it will remain. Margins to marked areas (ie dot positions with many neighbors marked as "usable") thus have a higher threshold, locally adapted.

These new threshold will be for the final Calculation used individually for each point position. This is beneficial because the effects that you see in the pictures want, at the edges usually become less and through a strict uniform choice of the Threshold may be discarded as "unusable" point positions would. With the individual threshold adjustment, this can be very efficient be avoided.

The above based on the 9 described application of the evaluation principle according to the invention for image processing is just one example. Of course, other types of application are possible. Instead, each of the pixel value sequences p _{i to} judge _j (n) in each case in a single cycle over its entire length, the assessment can also be partially done on individual sub-cycles, which each a portion of the n-coordinate covers.

The Invention is not limited on the evaluation and processing of pixel sequences along the "temporal" coordinate of a Moving image. In similar Way you can also pixel sequences along another coordinate of a picture grid are processed, e.g. successive pixels along the x-coordinate and / or along the y-coordinate of a two-dimensional still image. The independent Variable (abscissa) "n" of function E (n) would be then the horizontal pixel position x or the vertical pixel position y in a two-dimensional image grid. Such editing is e.g. advantageous if border areas of a still image no Information included. Furthermore, the image processing according to the invention not limited on MR images. So can images are processed using the invention, the by X-ray computed tomography (CT), positron emission tomography (PET), sonography or any other Image capture methods such as e.g. obtained direct optical photography have been.

It should be noted that the above on the basis of 4 and 5 described, working with cross-correlation evaluation principle also for the realization of a noise filter can be applied. As mentioned, the relative height W ₀ -W _{R of} the peak amplitude W ₀ at the point τ = 0 of the derivative K '(τ) of the cross-correlation function K (τ) over the reference value W _R formed from the neighboring values is a measure of the relative Proportion of the aleatory component in function F (n). By varying the function F (n), a function F _q (n) can be found in which the value W ₀ approximates or even equals the value W _R. In detail, this can be done according to a particular embodiment of the invention, the following:
From the function K (τ), a "target function" K _q (τ) is calculated in which the value of the derivative K _q '(τ), which is valid for τ = 0, is equal to the reference value W ₀ . Then, the function F (n) is varied by an adaptation routine until a function F _q (n) is found, at which the cross-correlation function (obtained by cross-correlating the varied function F (n) with the running total and the integral, respectively this function according to the above equation Eq. 6 or Eq. 7) is equal to the calculated target function K _q (τ). The proportion of the aleatory component used in the previously performed evaluation method in function F (n) was contained in the found function F _q (n) is no longer contained, the function is therefore noise filtered.

The above-described adaptation of the function F (n) to the noise-filtered version F _q (n) can be carried out by known optimization algorithms ("fit routines"), for example by a Levenberg-Marquard algorithm, by means of a computer.

Claims (26)

A method of judging a selected range a ≤ n ≤ b of a function E (n) obtained by detecting the course of a physical quantity E over the abscissa n and which may include aleatory and / or deterministic components, wherein the deterministic components are at least partially are unknown, characterized in that from the function E (n) a function F (n) = E (n) - D 0 (N) where D ₀ (n) is the sum of known deterministic components, and that from the selected range of function F (n) is a Hils function

or, with discrete function F (n),

where c equals a and / or b, and that by comparing the two functions F (n) and G (n) a judgment value W is determined which is a measure of the relative proportion of the aleatory component of the function F (n) within the selected range of this function. A method according to claim 1, characterized in that the comparative examination of the two functions F (n) and G (n) the formation of the discrete cross-correlation function

or, for discrete functions F (n) and G (n),

for these two functions over a range u ≤ τ ≤ v, which contains the value τ = 0, where τ is the measure of the mutual displacement of the two functions in discrete steps with a step size Δ in the calculation of the discrete cross-correlation function and k is any arbitrary scale factor, and that within the range u ≤ τ ≤ v the derivative K '(τ) = [K (τ) - K (τ - Δ) is calculated, and that as a judgment value W, a value is generated which is a measure of the deviation of the value W _{0 of} the derivative K '(τ), which is valid for τ = 0, from a reference value W _R which is equal to one valid for τ ≠ 0 Value or equal to a mean value of several values of the derivative K '(τ) valid for τ ≠ 0. A method according to claim 2, characterized in that the assessment value W according to the formula W = w · | W 0 - W R | where w is an arbitrarily chosen scale factor. A method according to claim 2, characterized in that the assessment value W according to the formula

where w is an arbitrarily chosen scale factor. Method according to one of claims 1 to 4, characterized that the amount of the assessment value W with a selected threshold and that a quality judgment is "unusable" or "usable" dependent is generated by whether the amount of the value W exceeds the threshold or Not. A method according to claim 5, characterized in that it is performed twice for the same function F (n), wherein in the one implementation, the auxiliary function

or, with discrete function F (n),

is used in the other implementation and the auxiliary function

or, with discrete function F (n),

is used and that a final quality judgment is made "usable" only if the quality rating "usable" has been generated in both executions. A method according to claim 5 or 6, characterized in that the function E (n) is generated as a discrete function by sampling a sequence of values describing successive pixels of captured image information along a selected portion of a coordinate n of an image raster and all values of this sequence E (n) are set to a fixed value E _f if the evaluation value W determined for the sequence furnishes the quality judgment "unusable" Method according to claim 7, characterized in that that the captured image information is a sequence of individual images of a represents an observed process that takes place in an observed spatial area expires wherein the image grid of the captured image information two or three spatial coordinates for the definition of the spatial position of the pixels contains and a temporal coordinate for the position of the frame within the frame, and that the value sequence E (n) the longitudinal the temporal coordinate of successive pixels of the same spatial Position describes. Method according to claim 8, characterized in that that it is for every sequence of values is performed is, each successive pixels the same spatial Position longitudinally the tempo coordinate describes an edited version of the to provide recorded image information. Method according to claim 9, characterized in that the individual images of the processed image information are superimposed on the individual images of a second image information which describes a structure of the observed spatial region, a value being selected for the "unusable" value sequences in the processed image information as the fixed value E _f for the respective pixels in the superimposition makes transparent. Method according to one of claims 7 to 10, characterized that the or each value sequence E (n) discrete pixels of a Magnetic resonance imaging recorded image information describes. Method according to claims 10 and 11, characterized that the image information to be processed is representative of flow processes in the observed one space area and that the second image information is representative is for the structure of biological tissue in the observed space. A method according to claim 2, characterized in that subsequently from the function F (n) a freed from aleatorischen components version F _q (n) is determined by the following steps: from the function K (τ) a target function K _q (τ) is calculated in which the value of the derivative K _q '(τ), which is valid for τ = 0, is equal to the reference value W ₀ , the function F (n) is varied by an adaptation routine until a function F _q (n) is found in which the cross-correlation function is equal to the calculated objective function K _q (τ). Computer program product for implementing a method according to one of the claims 1 to 13. Means for judging a selected range a ≤ n ≤b of a function E (n) obtained by detecting the course of a physical quantity E over the abscissa n and which may include aleatory and / or deterministic components, wherein the deterministic components are at least partially are unknown, characterized by: a subtraction stage ( 11 ) having a first input for receiving the function E (n) and a second input for receiving a function D ₀ (n), which is the sum of the known deterministic components, for forming the function F (n) = E (n) - D 0 (N); an integrating stage ( 12 ) with an input for receiving the function F (n) to an auxiliary function

or, with discrete function F (n),

to calculate, where c is a and / or b; an analysis stage ( 13 ) which is adapted to determine, by a comparative examination of the two functions F (n) and G (n), a judgment value W which is a measure of the relative proportion of the aleatory component of the function F (n) within the selected range a ≤ n ≤ b. Device according to claim 15, characterized in that the analyzing stage ( 13 ) comprises: a correlation stage ( 14 ) to form the discrete cross-correlation function

or, for discrete functions F (n) and G (n),

over a range u ≤ τ ≤ v, which contains the value τ = 0 or τ = 0 - Δ, where τ in discrete steps with a step size Δ is a modified measure of the mutual displacement of the two functions in the calculation of the discrete cross-correlation function, and k is an arbitrarily selectable scale factor; a differentiation stage ( 15 ) to calculate the derivative K '(τ) = [K (τ) - K (τ - Δ)] within the range u ≤ τ ≤ v; a comparison stage ( 16 ) for calculating the assessment value W as a measure of the deviation of the value W _{0 of} the derivative K '(τ) ₀ , which is valid for τ = 0, from a reference value W _R which is equal to a value valid for τ ≠ 0 or a mean value of several τ ≠ 0 of valid values of the derivative K '(τ). Device according to claim 16, characterized in that the comparison stage ( 16 ) is configured to calculate the judgment value W according to the formula W = w · | W 0 - W R |, where w is an arbitrarily chosen scale factor. Device according to claim 16, characterized in that the comparison stage ( 16 ) is configured to calculate the judgment value W according to the formula

where w is an arbitrarily chosen scale factor. Device according to one of Claims 15 to 18, characterized by a threshold comparator ( 20 ), which receives the judgment value W and generates a quality judgment "unusable" or "usable" depending on whether or not the amount of the judged value W exceeds the selected threshold S. Combination of a rating device ( 10 . 20 ) according to claim 19 with an image processing system ( 42 - 57 ), in which the function E (n) is generated as a discrete function by sampling a sequence of values describing successive pixels of a captured image information along a selected portion of a coordinate n of an image raster. Combination according to claim 20, characterized by one with the assessment device ( 10 . 20 ) associated control device ( 52 ), which sets all values of this sequence E (n) to a fixed value E _f if the evaluation value W determined for the sequence furnishes the quality judgment "unusable" A combination according to claim 21 for processing a captured image information representing a sequence of frames of an observed process running in an observed spatial area, the image grid of the captured image information containing two or three spatial coordinates for defining the spatial position of the pixels, and a temporal coordinate for the position of the single image within the single image sequence, characterized in that the control device ( 52 ) Contains means for selecting the pixels of the same spatial position successive along the temporal coordinate as the value sequence E (n). Combination according to claim 22, characterized in that the control device ( 52 ) Comprises means for sequentially selecting all value sequences each describing successive pixels of equal spatial position along the temporal coordinate, and in that the control device ( 52 ) Medium ( 55 ) to provide an edited version of the image information in which all values of a selected sequence of values are set to the fixed value E _f , respectively, when the evaluation value W determined for the sequence in question delivers the quality judgment "unusable". Combination according to claim 23, characterized by an overlay device ( 46 ) for superimposing the frames of processed image information with frames of second image information describing a structure of the observed space area, the fixed value E _f for the "unusable" value sequences in the processed image information being a value which makes the relevant pixels transparent in the overlay power. Combination according to one of Claims 20 to 24, characterized by connecting means ( 53 ) for receiving the or each value sequence E (n) of the image information to be processed from a source ( 44 ) describing the pixels of image information taken by magnetic resonance imaging. Combination according to claim 24, characterized by connecting means ( 53 ) for receiving the or each value sequence E (n) of the image information to be processed from a source ( 44 ) which describes the pixels of image information taken by magnetic resonance imaging, which is representative of flow processes in the observed space area; Connection means for transmitting the second image information to the superimposition device ( 46 ) from a source ( 45 ), which describes the pixels of image information taken by magnetic resonance imaging, which is representative of the structure of biological tissue in the observed spatial region.