DE19605318A1 - Image synthesis for production of optimum image of region to be imaged especially for MR imaging - Google Patents

Abstract

The image synthesis method, using sensors of varying sensitivity varying over the region to be imaged, takes complex output images, these are combined with each other. For the combination, firstly of the images taken by the sensors. Secondly the smoothed variants produced by the additional filtering of their output images by a low pass filter, and thirdly the variants resulting from additional filtering are used. For the additional filtering of the output images, their variants produced by low pass filters are further smoothed by a further low pass filtering or other means. For the additional filtering, the output images are corresponding are more strongly filtered.

Description

The invention relates to an image synthesis method for generating a regarding its signal-to-noise ratio and object-true brightness and contrast Optimal image of an area to be mapped in the complex Output images made with sensors of different types above the one to be imaged Range of varying sensitivity were combined will.

A typical application is e.g. B. in MR methods for imaging Nuclear magnetization distribution in an examination area of the human Body when measuring instead of using a receiving antenna constant Sensitivity across the imaging area with several distributed around the body Surface coils are carried out, the data of which are initially processed separately and in associated images (more complex here in the form of matrices Numbers) can be converted. This practice is increasing applied since it was recognized that each of these attached itself to the object Antennas for a portion of the image near the antennas a better signal Noise ratio (SNR) than when using a conventional, receiving antenna optimized with regard to spatial constancy of sensitivity, which naturally must have a greater distance from the object and therefore next to the signals actually to be mapped also noise from a larger one Takes up space. The sensitivity of these surface coils takes away everything However, the distance increases significantly with increasing distance. To over the whole To achieve an improvement in the SNR, there must be several such antennas are arranged so that their respective sensitive zones additionally cover the whole area.  

From the coils forming with the individual sensors or antennas Use of MR acquired images must be done by post-processing Image synthesis, an optimal image can be generated in each pixel best SNR and the object-true contrast or one Has brightness distribution that is not due to the spatially varying Sensor sensitivity is falsified. So far, the following are for this image synthesis Process used:

Calculate a pixel of the overall picture

• 1. sum of the amounts of the corresponding pixels of the individual images;
• 2. Root of the sum of the squares of the amounts of the corresponding pixels of the individual images;
• - in this, s ^{t is} the transposed vector, formed from the pixels of the same position of the individual images, and S _{L * is} the conjugate complex vector of corresponding pixels from low-pass filtered versions of the images [Liu 1994];
• 4. Weighted sums of the amounts of the pixels were also proposed same position of the individual pictures, whereby the weight factors by Filter operations can be derived from the original images [Reykowski & Wright 1991, 1990].

A special case of this is the method of Okamoto et al. 1989, as weights take the amounts of the pixels themselves, which however corresponds to method 2, without taking the root.  

These methods are all more or less imperfect in terms of achieved SNR improvement measured against the theoretical ideal. None of the methods eliminates the influence of sensor sensitivity on the brightness curve of the Overall picture. Local filtering results in part from applied filter operations Contrast distortions in the object image.

Method 2 shows less noise than method 1, but leaves the contrast-altering sensitivity variation of the sensors and possibly Interference signals that appear during the measurement are more pronounced.

Method 3 suppresses noise better than Method 2, but is still suboptimal. The weighting of the original pixels with the low-pass filtered pixels without correcting the superimposed sensor sensitivities Signal intensity edges for a distorting contrast reduction.

The theoretical ideal with regard to the combination of individual source images too an image with an optimal SNR is known from Roemer et al, Magn Reson Med, 16, 192-225, 1990. The image point of the image is then to be calculated as

s ^t R ^-1 b * (1)

Here b is a vector in which the respective sensitivities of the individual sensors at the object volume element shown in the pixel under consideration are summarized. R is the noise correlation matrix defined by Roemer et al in the respective initial images or in the underlying images Original data, the information about the correlation of the noise in the Contains source images. With MR examinations one can Measure the noise correlation matrix by taking those in the examination area resulting (noise) signals are measured without the nuclear magnetization in the To stimulate the examination area and without magnetic gradient fields activate, and reconstructed (noise) images from it. From the degree of correlation of the  Noise can be heard in the same pixel from two images Derive coefficients of the noise correlation matrix.

The influence of the sensor sensitivities varying over the area to be imaged on the brightness curve of the image is eliminated by dividing by b ^t R ^-1 b * [Roemer 1990]:

The application of this calculation rule encounters two problems in practice:

• 1. b is usually not known or can only be done with considerable effort Measurement technology and computing power can be determined.
• 2. in image areas where | b | is small, that is to say all sensors supply little useful signal, the noise contained in s would be disruptively increased by the division with b ^t R ^-1 b * which effects the sensitivity compensation.

The object of the present invention is therefore an image synthesis method state, according to which the ideal synthesis formula (2) is manageable Effort in measuring technology and computing power as well as by suppressing the disturbing noise can be technically realized as well as possible.

This object is achieved in that 1. the sensors recorded output images, 2. from the output images through low-pass filters generated smoothed variants and 3. further created by additional filtering Variants of the original images can be combined.  

With this combination, an image synthesis is achieved which is in terms of SNR and Object-true image contrast is much closer to the theoretical ideal than the previously used methods (1) to (4).

According to a preferred embodiment of the invention, additional Filtering the output images of their variants generated by low-pass filters a further low-pass filtering or further smoothed by averaging. This can the noise is strongly suppressed. This effect is also achieved by that the output images are filtered more strongly for additional filtering will.

According to a further preferred embodiment of the invention, the combination of the output images with the variants is based on their pixels assigned to the area and the combination of the corresponding pixels, which are combined in a pixel vector s, is carried out with a weighting corresponding to the product of an inverse noise correlation matrix R. ^{-1 of} a noise measurable at the sensors and a corresponding conjugate complex pixel vector s _{L *} from pixels of the low-pass filtered variants according to the combination expression s ^t R ^-1 s _{L *} , where s ^{t is} a transposed vector. The pixel vector s and the vectors derived from it (s _{L *} , s ^t etc.) each contain as many components as the output images are to be combined or - in the case of MR - how (surface) coils are present. The components of the pixel vector s each correspond to the same pixel or pixel (more precisely: the - possibly low-pass filtered - value that is assigned to this pixel or pixel) in the different output images.

This combination of the output images with their variants and the weighting described can largely suppress the noise. In particular, the influence of the sensitivity of sensors can be taken into account by the expression s _LL ^t R ^-1 s _{L *} , where s _LL ^{t is} a pixel vector corresponding to the stronger or double filtering.

This makes the image synthesis method according to the invention, which is relative low expenditure on measurement technology and computing power can be carried out, indicated by the following expression, which results from the fact that in the expression (2) b is replaced by two different low-pass filtered versions of s:

In this expression:

s _L : low pass filtered version of s;
s _LL : more low-pass filtered version, preferably with a non-linear portion that contains contrast edges.

This approach is based on the model concept that the pixel data compose from the actual measured variable m (in the pixel at MR the local one Magnetization), multiplied by the respective sensor sensitivities b plus an additional noise term n. where sensitivity b is different from m typical spatially only "slowly" varies:

s = m b + n (4)

Note that the meter portion of the counter in the synthesis expression (2) which contains quadratic sensor sensitivities, firstly by (4) and secondly through the weighting carried out with b *.  

The first low-pass filter for generating s _L is selected so that on the one hand the noise component n and the "fast" local contrast variation of the object information m are well suppressed, but on the other hand the best possible estimate of b is obtained. The second low-pass filter for the generation of s _LL consists preferably of a combination of linear and non-linear filtering, the second part being designed in such a way that image zones of high signal intensity are expanded at intensity edges in areas of low intensity. In this way, it is avoided that after the sensitivity correction, intensity edges in s are displayed by division with an intensity curve smoothed by conventional linear filtering with unnaturally increased contrast.

According to a further preferred embodiment of the invention, the sensitivity of sensors is eliminated by dividing the combination expression s ^t R ^-1 s _{L *} by a sum expression | s _LL ^t R ^-1 s _{L *} | + δ taking into account the influence of the sensitivity of sensors , where δ is a parameter taking into account the background noise. In this way it is avoided that the division with b + ^t R ^-1 b * which effects the sensitivity compensation, according to the invention estimated by | s _LL ^t R ^-1 s _{L *} | the noise contained in s increases strongly. Rather, the undesirable noise increase in image areas of small b's in (2) or in the practical approximation (3) with small s _L or s _LL is avoided by adding the suitably chosen constant 5 in the denominator of the expression (3):

In this way, the sensitivity of sensors is advantageously eliminated in that the combination expression s ^t R ^-1 s _{L *} by the sum expression | s _LL ^t RR ^-1 s _L | taking into account the influence of the sensitivity of sensors + δ is divided.

The increase in noise can be countered even better by adding the quotient δ5 / | s _LL ^t R ^-1 s _{L *} in the denominator so that the expression is as follows:

The addition of δ in the denominator (version 5) limits the noise increase that is unavoidable in sensitivity compensation to a maximum value. If instead of δ the expression δ / | S _LL ^t R ^-1 s _{L *} | added together in the denominator (version 6), the noise level advantageously also drops again as the first term drops further.

Further preferred embodiments of the invention carry special ones Use cases for the combination of output images. If at the image synthesis, the optimization of the SNR is in the foreground and in favor a simplified calculation for sensitivity compensation then the whole denominator

δ / | s _LL ^t R ^-1 s _{L *} | or | s _LL ^t R ^-1 s _{L *} | + δ / | S _LL ^t R ^-1 s _{L *} |

in synthesis expression (5) or (6) are replaced by one of the following expressions, the to what extent the sensitivity compensation must be selected Compromises can be made:

or | R ^1/2 s _L | (7b)

or | R ^-1 s _L | (7c)

or | s _L | (7d)

By using these simplifications you can already do this without disadvantage the counter optimized SNR the computing effort can be considerably reduced and nevertheless a good compensation of the sensitivity can be brought about.

Beyond that, too

be used in the denominator of the expression (3). However, this should be taken into account that the second low-pass filtering contained in this expression for the Image synthesis achieved in this way is not necessary, so it can be omitted.

The simplified expressions according to the invention for image synthesis with denominators according to (7) produce an image with a virtually noise-independent noise level, but only eliminate the portion of the sensor sensitivity in the numerator added by the weighting with s _L , not the portion inherent in the data s (factor b ). This eliminates the undesirable increase in the noise contained in s in areas of low sensor sensitivities, so that all measures that aim to limit this effect are superfluous. In contrast to expressions (5) and (6), the additional δ term contained in the denominator is superfluous here.

The images produced in a simplified manner according to the invention have a better SNR than that Results of the previously used methods according to expressions (1) to (4), but still contain in a similar way as these terms overlay the Sensitivity curve of the sensors.

Claims (14)

1. Image synthesis method for generating an image of an area to be imaged that is optimal in terms of its signal-to-noise ratio and object-true brightness and contrast curve, in which complex output images are recorded with sensors of differently varying sensitivity over the area to be imaged , can be combined with one another, characterized in that firstly the output images recorded by the sensors, secondly smoothed variants produced by the output images by low-pass filters and thirdly further variants of the output images resulting from additional filtering are used for the combination. 2. Image synthesis method according to claim 1, characterized in that for additional filtering of the output images Variants generated by low-pass filters by further low-pass filtering or can be further smoothed by averaging. 3. Image synthesis method according to claim 1, characterized in that for additional filtering the output images are filtered accordingly more strongly. 4. Image synthesis method according to one of claims 1 to 3, characterized in that the additional filtering is not linear. 5. Image synthesis method according to one of claims 1 to 4, characterized in that the combination of the output images with their variants are based on the pixels assigned to the area to be imaged and the combination of the corresponding pixels, which are combined in a pixel vector s with a weighting corresponding to the product of an inverse noise correlation matrix R ^{-1 of} a noise measurable at the sensors and a corresponding conjugate complex pixel vector s _{L *} , which consists of pixels of the low-pass filtered variants according to the combination expression s ^t R ^-1 s _{L * is} formed, where s ^{t is} the transposed vector s. 6. Image synthesis method according to claim 5, characterized in that in the case of negligible noise correlation, the combination of the pixels is carried out in a simplified manner by s ^t s _{L *} . 7. image synthesis method according to claim 5 or 6, characterized in that in a nonexistent in the area locally detailed phase variation the noise in the background and / or in Ranges of a low signal-to-noise ratio continue to be suppressed will be that only the positive real part of the result of the combination Pixel values is used. 8. Image synthesis method according to one of claims 1 to 7, characterized in that a contained in the combination expression s ^t R ^-1 s _{L *} , over the area to be imaged, sensor sensitivity is eliminated. 9. image synthesis method according to claim 8, characterized in that when used for MR a due to the vari Sensitivity of around the area to be imaged Influence resulting receiving body coils is eliminated. 10. Image synthesis method according to claim 2, 3, 8 or 9, characterized in that the influence of the sensitivity of sensors is taken into account by the expression s _LL ^t R ^-1 s _{L *} , with one of the s _LL ^t stronger or double filtering corresponding pixel vector is designated. 11. Image synthesis method according to claim 10, characterized in that the sensitivity of sensors is eliminated in that the combination expression s ^t R ^-1 s _{L *} by a sum expression taking into account the influence of the sensitivity of sensors | s _LL ^t tR ^{- 1} s _{L *} + δ is divided, where δ is a parameter taking into account the background noise. 12. Image synthesis method according to claim 11, characterized in that the sensitivity of sensors is eliminated in that the combination expression s ^t R ^-1 s _{L *} by | s _LL ^t R ^-1 s _{L *} | + δ / | s _LL ^t R ^-1 s _{L * is} divided. 13. Image synthesis method according to claim 11 or 12, characterized in that with negligible noise correlation, the noise correlation matrix R ^{-1 is} eliminated. 14. Image synthesis method according to one of claims 5 to 13, characterized in that the sensitivity of the sensors which varies over the image area for generating an almost constant noise level over the area to be imaged is only partially eliminated, in that the combination expression s ^t R ^{- 1} s _{L * is} divided by or or | R ^1/2 s _L | or | R ^-1 s _L | or | s _L |.