WO1993006560A1

WO1993006560A1 - Restoration of computer-tomographic images with neural networks

Info

Publication number: WO1993006560A1
Application number: PCT/NL1992/000154
Authority: WO
Inventors: Frederik Johannes Beekman
Original assignee: Frederik Johannes Beekman
Priority date: 1991-09-13
Filing date: 1992-09-08
Publication date: 1993-04-01
Also published as: AU2645992A; NL9200796A

Abstract

Method and device for making a two-dimensional image of a determined activity distribution in a three-dimensional body along a determined section through that body by restoring a two-dimensional image that has been reconstructed from projections of this activity distribution obtained using an activity detector, using an artificial neural network, wherein in a first step the neural network is trained by supplying to the output thereof at least one set of data corresponding with one determined simulated activity distribution and by supplying to the input thereof a set of data which data corresponds with a two-dimensional image that has been reconstructed from simulated projections of this simulated activity distribution, and in a second step data is supplied to the input of the thus trained network which corresponds with the two-dimensional images reconstructed from the obtained projections.

Description

RESTORATION OF COMPUTER-TOMOGRAFHIC IMAGES WITH NEURAL NETWORKS

The invention relates to a method for making a two-dimensional image of a determined activity distribution in a three-dimensional body, for instance a collection of photon-emitting small volume elements in such a body, along a determined section through that body by restoring a two-dimensional image that has been reconstructed from projections of this activity distribution obtained using an activity detector, for example a photon detector, using an artificial neural network. A neural network is a per se known system for informatio processing consisting of mutually connected units sometimes figuratively referred to as "neurons". A connection between neurons in a neural network has a determined strength or weighting. An important property of a neural network is the autodidactic action, that is, it is possible to change the individual weightings of the connections in a network by supplying to the network both data for transforming and the transformed data desired therefrom. By repeating the supply of such data pairs the connections in the network adjust themselve such that the network is made capable of independently performing the desired transformation after the learning phase.

According to the prior art, two-dimensional images of a determined activity distribution are made into a three-dimensional body by reconstructing images (projections) obtained using a detector, for instance a camera. In nuclear medicine two-dimensional images of the human body for instance are reconstructed in known manner from projections of photons, in particular gamma particles, which are emitted by that body and recorded by a gamma camera. Making two-dimensional images i this manner using single photons is known as SPECT (single photon emission computed tomography) . In the reconstructing of two-dimensional images from the projections obtained with a detector correction must be made for image degradation that has occurred. Causes of image degradation in the making of SPECT images are for example static noise, scattering of gamma radiation on for instance electrons in the body and lack of focus of the projection, for instance as a result of limited collimation. According to the prior art, two-dimensional images from the projections obtained with a detector are obtained by reconstructing these images from these projections by back projecting the latter and correcting (filtering) the back projected images or by filtering the projections prior to back projection thereof. The latter method for reconstructing is known as filtered back projection (FBP) .

Associated with restoration of FBP images or projections for back projecting using the known methods is the drawback tha the corrections applied herein only partially compensate for image errors resulting for example from scattering and absorption.

Known from a publication by C.E. Floyd jr. in IEEE Transactions on Medical Imaging, Vol. 10, No.3, p.485 is a method for reconstructing SPECT images using an artificial neural network. Described herein is how a neural network is developed for tomographic image reconstruction of SPECT projections. Also described is how the network is trained by supplying data thereto which corresponds with an ideal projection image pair. The thus trained network was used as filter in an image reconstruction method according to filtered back projection.

Associated with the known method for making a two-dimensional image using a neural network are the same drawbacks inherent to the use of filtered back projection. It can moreover be demonstrated in fundamental manner that the known application of a neural network does not result in a much better method for making images than the other known techniques because a sufficiently unambiguous transformation does not exist between the data pairs supplied to the network during the training phase. The object of the invention is to provide a method as stated in the preamble not having the above described drawbacks. This object is realized according to the invention with a method according to which in a first step the neural network is trained by supplying to the output thereof at least one set of data corresponding with a determined simulated activity distribution and by supplying to the input thereof a set of data which corresponds with a two-dimensional image that has been reconstructed from simulated projections of this simulated activity distribution, and in a second step data is supplied to the input of the thus trained network which corresponds with the two-dimensional images reconstructed from the obtained projections. Understood in each case by data corresponding with a determined activity distribution or a determined image is data which is associated in accordance with a unique operation with that activity distribution, respectively that image.

Making a two-dimensional image according to the invention offers in contrast to known reconstruction techniques the advantage that neural networks can perform the non-linear image and body shape dependent transformations required for the image restoration and they do this furthermore in a very short time. The training in a first step of the neural network using simulated data is more advantageous than training with for instance data obtained on the basis of phantom measurements, because a number of sets of data are preferably supplied to the network. Operation with a plurality of phantoms has drawbacks, for instance because in practice a sufficiently large number of freely selectable body shapes having freely selectable activity distributions therein cannot be made available. In an embodiment of a method according to the invention projections of the simulated activity in each volume element of the body are simulated in the first step.

According to this embodiment a body of which an image must be made is simulated by a collection of data comprising th spatial coordinates of each volume element and a value for the activity attributed to that element. The projections of each of these simulated activities are subsequently simulated on a particular plane. In practical situations in which a determined activity i projected in a three-dimensional image (for example in imaging by means of a gamma camera of an organ injected with a radio isotope) the activity of each volume element of the body is projected with a determined spread. The spreading is dependent on the position of the relevant volume element relative to the projection plane. The method according to the invention advantageously has the feature that in the first step the simulated projections of the simulated activity in each volume element are generated according to a spreading function defined by the spatial coordinates of that volume element.

The simulated projections are for instance corrected by spreading out the intensity of the projected activity for each volume element in the body on the projection plane in accordanc with a spreading function defined by the spatial coordinates of the relevant volume element. In the simulated projections the effect of noise occurring in actual situations can then be simulated with for instance a noise generation algorithm.

The quality of an image to be made according to the invention is further improved when in the first step the simulated projections of the simulated activity distribution ar generated in accordance with a function, in particular a spreading function, defined by the contours of the three-dimensional body.

By generating the simulated projections of the simulated activity distribution in accordance with a spreading function defined by the contours of the three-dimensional body during th training of the neural network, a network is obtained capable o correcting the data supplied to the input in the second step, i the situation that this data corresponds with projections obtained in practice and which are thus not simulated, for errors caused by attenuation and scattering processes within th boundary surface (the contours) of the three-dimensional body.

The method is still further improved when in the first step the neural network is trained by further supplying to the ■ input thereof data which corresponds with the contours of a simulated body comprising the simulated activity, and in the second step data is further supplied to the input of the thus trained network which corresponds with the contours of the three-dimensional body.

A further improvement of the quality of a two-dimensiona image made according to the invention is obtained when in the first step the neural network is trained by further supplying t the input thereof, for each piece of data corresponding with an image element of the two-dimensional image reconstructed from the simulated projections, data corresponding with a determined number of image elements surrounding that image element, and in the second step by further supplying to the input of the thus trained network, for each piece of data corresponding with an image element of the two-dimensional image reconstructe from the obtained projections, data corresponding with a determined number of image elements surrounding that image element. Understood by surrounding image elements are not only the image elements in the relevant two-dimensional image but also image elements from two-dimensional images of planes above and below the imaged plane. According to this latter method the neural network is trained also to process the information relating to surrounding image elements in the restoration of a particular image element

In preference this latter method is performed such that in the first step the neural network is trained by further supplying to the input thereof data corresponding with the simulated relative position of the detector in relation to the determined activity distribution, and in the second step by further supplying to the input of the thus trained network data corresponding with the relative position of the detector in relation to the determined activity distribution.

With a thus trained network it is possible to reconstruct from the obtained projections images in which correction has been made for the above mentioned possible errors, wherein account is moreover taken of the influence of the relative position of the detector with respect to the body on the qualit of the reconstructed images.

The invention further relates to a device for making a two-dimensional image of a determined activity distribution in three-dimensional body, for instance a collection of photon-emitting small volume elements in such a body, along a determined section through that body, by restoring a two-dimensional image that has been reconstructed from projections of this activity distribution obtained using an activity detector, for example a photon detector, using an autodidactic artificial neural network in accordance with the above described method, comprising an activity detector, for instance a photon detector, and signal processing means, in particular an artificial neural network for reconstructing and restoring a two-dimensional image from projections of the activity distribution obtained using the detector.

According to the invention this device comprises means for training the neural network in the first step by supplying to the output thereof at least one set of data corresponding with one determined simulated activity distribution and by supplying to the input thereof a set of data which data corresponds with a two-dimensional image that has been reconstructed from simulated projections of this simulated activity distribution, and in a second step by supplying to the input of a thus trained network data which corresponds with the two-dimensional images reconstructed from the projections obtained in practice (and thus not simulated) .

An embodiment of such a device is characterized by means for simulating in the first step projections of the simulated activity in each volume element of the body.

A following embodiment is characterized by means for generating in the first step the simulated projections of the simulated activity in each volume element according to a spreading function defined by the spatial coordinates of that volume element.

Yet another embodiment is characterized by means for generating in the first step the simulated projections of the simulated activity distribution in accordance with a function, in particular a spreading function, defined by the contours of the three-dimensional body.

Such a device preferably comprises means for training the neural network in the first step by further supplying to the input thereof data which corresponds with the contours of a simulated body comprising the simulated activity, and in the second step further supplying to the input of the thus trained network data which corresponds with the contours o the three-dimensional body.

Yet a further embodiment is characterized by means for training the neural network in the first step by further supplying to the input thereof, for each piece of data corresponding with an image element of the two-dimensional imag reconstructed from the simulated projections, data correspondin with a determined number of image elements surrounding that image element, and in the second step by further supplying to the input of the thus trained network, for each piece of data corresponding with an image element of the two-dimensional image reconstructe from the obtained projections, data corresponding with a determined number of image elements surrounding that image element. Such a device further comprises for instance means for training the neural network in the first step by further supplying to the input thereof data corresponding with the simulated relative position of the detector in respect of the determined activity distribution, and in the second step by further supplying to the input of the thus trained network data corresponding with the relative position of the detector with respect to a determined activity distribution. A device according to the invention can, depending on the activity detector used in this device, be used for making a two-dimensional image of different types of activity distributions in a three-dimensional body. The device can thus be employed for restoring SPECT images of a body in which a photon-emitting material is included or PET (positron emission tomography) images of a body containing positrons. The photon detector in a SPECT device is for instance a NaJ scintillation camera with which a two-dimensional projection is recorded of photons entering therein. In a PET scanner photons which are created in pairs through annihilation of positrons with electrons in the activity distribution, are imaged for instance on an annular detector.

The invention will now be elucidated in the following with reference to the drawing. In the drawing: figure 1 shows a schematic view of the first step, namely training of a neural network, in a method according to the invention, figure 2 is a simplified block diagram of a device for making a two-dimensional image of a determined activity distribution in a determined body.

The diagram of figure 1 shows a method for training an autpdidactic artificial neural network 1, wherein a set of data is supplied to an output 2 of that network 1 which corresponds with a simulated activity distribution 3. An activity distribution is for instance simulated by a collection of volume elements (voxels), wherein a numerical value is attributed to each volume element which simulates the activity. The simulated activity distribution is then a collection of combinations of i each case four numbers, that is, three for the coordinates of a voxel and one for the intensity, which numbers can be stored in the memory of a computer. Using a projection algorithm develope for the purpose a projection 5 of the activity distribution 3 i simulated by a computer. In practical conditions a projection o an activity distribution is for example an image of a gamma camera stored in a computer and can be simulated by a collectio of two-dimensional image elements (pixels) to which is attributed a numerical value corresponding with the intensity. simulated projection then comprises a collection of combination of in each case three numbers wherein two numbers represent the coordinates of a point in a projection plane and the third number represents the intensity of the image in that point. In the projection algorithm 4 the occurrence in practical situations of image errors can be simulated, for instance by imaging the simulated activity in each volume element according to a point spreading function which depends on the position of the volume element relative to the detector, the detector properties and the body geometry. After all activity has been projected noise can be generated in the pixels. The inclusion o such a point spreading function in the projection algorithm 4 i shown by a block 6. From one or more simulated projections 5 a determined image 8 corresponding with a determined section through the activity distribution 3 is reconstructed in per se known manner, for example with an algorithm for filtered back projection 7. Corresponding in turn with the simulated two-dimensional image 8 is a collection of data which for instance again comprises combinations in each case of three numbers, wherein in each case two numbers represent the coordinates of a pixel and a third number represents the value of the image intensity of that pixel. These numbers are supplie to the input 9 of the neural network 1 in which this data is transformed to a restored image 10 which is compared in a comparator 11 in the neural network 1 with the data supplied to the output 2 and corresponding with the original activity distribution 3. Additional data can further be supplied to an input 18 of the neural network, such as for example data corresponding with the contours of a simulated body or data corresponding with the simulated relative position of a detecto in relation to a determined activity distribution. In the supplying of mutually differing data to comparator 11 the weighting of the connections between the neurons in network 11 will be adapted to that difference in accordance with per se known operating principles of a neural network, whereafter a following activity distribution 3 is simulated and the described method repeated. After supplying a sufficient number of simulated activity distributions the neural network is trained in restoring images with image errors and the network can be employed in a practical measuring arrangement as shown in figure 2.

In the disposition according to figure 2, using a trained neural network 1, an image 10 is made of an activity distribution 12, for example the head of a patient to whom a low-radioactive photon-emitting substance has been administered. Using a detector 13, for instance a gamma camera, the activity distribution 12 is imaged on a projection 14, wherefrom an image 16 is reconstructed using a per se known image reconstruction algorithm 15. Due to various causes such as for instance photon noise, scattering and attenuation of gamma radiation and deficiencies of the detector and collimator the reconstructed image 16 is of very poor quality. These error sources are shown in the figure in the form of an information block 17 connected to the detector 13. The information of this reconstructed image 16 is very rapidly transformed in the trained neural network 1 to the restored image 10 which forms a faithful reconstruction of a predetermined section of the activity distribution 12. The quality of the image 10 is further improved by supplying information relating to the body contour of the activity distribution 12 and the geometry of the detector 13 to a second input 18 of the network 1.

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Claims

1. Method for making a two-dimensional image of a determined activity distribution in a three-dimensional body, for instance a collection of photon-emitting small volume elements in such a body, along a determined section through tha body by restoring a two-dimensional image that has been reconstructed from projections of this activity distribution obtained using an activity detector, for example a photon detector, using an artificial neural network, characterized in that in a first step the neural network is trained by supplying to the output thereof at least one set of data corresponding with one determined simulated activity distribution and by supplying to the input thereof a set of data which data corresponds with a two-dimensional image that has been reconstructed from simulated projections of this simulated activity distribution, and in a second step data is supplied to the input of the thus trained network which corresponds with the two-dimensional images reconstructed from the obtained projections.

2. Method as claimed in claim 1, characterized in that in the first step projections of the simulated activity in each volume of the body are simulated.

3. Method as claimed in claim 2, characterized in that in the first step the simulated projections of the simulated activity in each volume element are generated according to a spreading function defined by the spatial coordinates of that volume element.

4. Method as claimed in claim 1, characterized in that in the first step the simulated projections of the simulated activity distribution are generated in accordance with a function, in particular a spreading function, defined by the contours of the three-dimensional body.

5. Method as claimed in claim 4, characterized in that in the first step the neural network is trained by further supplying to the input thereof data which corresponds with the contours of a simulated body comprising the simulated activity, and in the second step data is further supplied to the input of the thus trained network which corresponds with the contours of the three-dimensional body.

6. Method as claimed in claim 1, characterized in that i the first step the neural network is trained by further supplying to the input thereof, for each piece of data corresponding with an image element of the two-dimensional imag reconstructed from the simulated projections, data correspondin with a determined number of image elements surrounding that image element, and in the second step by further supplying to the input of the thus trained network, for each piece of data corresponding with an image element of the two-dimensional image reconstructe from the obtained projections, data corresponding with a determined number of image elements surrounding that image element.

7. Method as claimed in claim 6, characterized in that i the first step the neural network is trained by further supplying to the input thereof data corresponding with the simulated relative position of the detector in relation to the determined activity distribution, and in the second step by further supplying to the input of the thus trained network data corresponding with the relative position of the detector in relation to the determined activity distribution.

8. Device for making a two-dimensional image of a determined activity distribution in a three-dimensional body, for instance a collection of photon-emitting small volume elements in such a body, along a determined section through tha body, by restoring a two-dimensional image that has been reconstructed from projections of this activity distribution obtained using an activity detector, for example a photon detector, using a self-teaching artificial neural network in accordance with a method as claimed in claim 1, comprising an activity detector, for instance a photon detector, and signal processing means, in particular an artificial neural network for reconstructing and restoring a two-dimensional image from projections of the activity distribution obtained using the detector, characterized in that this device comprises means for training the neural network in a first step by supplying to the output thereof at least one set of data corresponding with one determined simulated activity distribution and by supplying to the input thereof a set of data which data corresponds with a two-dimensional image that has been reconstructed from simulated projections of this simulated activity distribution, and in a second step by supplying to the input of a thus trained network data which corresponds with the two-dimensional images reconstructed from the projections obtained.

9. Device as claimed in claim 8 for making an image according to a method as claimed in claim 2, characterized by means for simulating projections of the simulated activity in each volume element of the body in the first step.

10. Device as claimed in claim 8 for making an image according to a method as claimed in claim 3, characterized by means for generating in the first step the simulated projections of the simulated activity in each volume element according to a spreading function defined by the spatial coordinates of that volume element.

11. Device as claimed in claim 8 for making an image according to a method as claimed in claim 4, characterized by means for generating in the first step the simulated projections of the simulated activity distribution in accordance with a function, in particular a spreading function, defined by the contours of the three-dimensional body.

12. Device as claimed in claim 11 for making an image according to a method as claimed in claim 5, characterized by means for training the neural network in the first step by further supplying to the input thereof data which corresponds with the contours of a simulated body comprising the simulated activity, and in the second step further supplying to the input of the thus trained network data which corresponds with the contours o the three-dimensional body.

13. Device as claimed in claim 8 for making an image according to a method as claimed in claim 6, characterized by means for training the neural network in the first step by further supplying to the input thereof, for each piece of data corresponding with an image element of the two-dimensional imag reconstructed from the simulated projections, data correspondin with a determined number of image elements surrounding that image element, and in the second step by further supplying to the input of the thus trained network, for each piece of data corresponding with an image element of the two-dimensional image reconstructe from the obtained projections, data corresponding with a . determined number of image elements surrounding that image element.

14. Device as claimed in claim 13 for making an image according to a method as claimed in claim 7, characterized by means for training the neural network in the first step by further supplying to the input thereof data corresponding with the simulated relative position of the detector in respect of the determined activity distribution, and in the second step by further supplying to the input of the thus trained network data corresponding with the relative position of the detector with respect to a determined activity distribution.

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