Fourier spectrum method to remove grid line artifacts without changing the diagnostic quality in X-ray images

A method for removing "grid line artifacts" from x-ray images without changing the diagnostic quality of the x-ray image is presented. The method utilizes the Fourier spectrum of the image to detect the grid line frequencies and employs spectral domain filtering to remove the grid line spectral components. The diagnostic information is preserved by modifying the grid line spectral components to be indistinguishable from local variations in image intensity values, and edge density of the x-ray image.

BACKGROUND OF THE INVENTION
 This invention relates to a Fourier spectrum method for removing "grid line
 artifacts" from x-ray images, and more particularly to a Fourier spectrum
 method for removing "grid line artifacts" without changing the diagnostic
 quality in x-ray images.
 In a x-ray radiography imaging system, an x-ray source projects a
 cone-shaped pattern of beams. This cone beam passes through the object
 being imaged, such as a medical patient, and impinge upon a
 two-dimensional array of radiation detectors. The signal generated from
 the measurement of the intensity of the transmitted radiation is dependent
 upon the attenuation of the x-ray beam by the object. Each detector
 produces a separate electrical signal that is a measurement of incident
 beam attenuation.
 A metallic anti-scatter grid used in the x-ray radiography imaging system
 is typically placed against the detector array to allow the x-rays that
 trend along a substantially perpendicular path to the respective detector
 to strike the respective detector, and x-rays that do not trend along a
 substantially perpendicular path to the detector are blocked by the
 anti-scatter grid, as is illustrated in FIG. 1. As such, the anti-scatter
 grid enhances image diagnostic quality by preventing undesired x-rays from
 striking a detector. A disadvantage of using the anti scatter grid is that
 it may cause "grid line artifacts" to appear in the x-ray image. The grid
 line artifact appears in x-ray images as intensity modulation of the image
 in lines parallel to the anti-scatter grid. The grid line artifact occurs
 when the grid lines run perpendicular to the scan lines on the display
 device. The grid line artifact is very sensitive to display image
 magnification and can be made worse or be made to disappear by changing
 the image magnification. It would be desirable to remove the "grid line
 artifacts" from the x-ray image without changing the diagnostic quality in
 the x-ray image, irrespective of image magnification.
 Another cause of "grid line artifacts" on the x-ray image include errors
 generated by the detector array signal measurement electronic circuits.
 For example, when there is a difference in gain between two respective
 signal measurement circuits, "grid line artifacts" may appear in the x-ray
 image.
 Yet another source of "grid line artifacts" may be caused by the
 repositioning of the anti-scatter grid at non-standard positions during
 successive scans called "over-sampling." Additionally, "grid line
 artifacts" may be caused by variations in the x-ray dose during
 over-sampling. It would be desirable to remove grid lines from the x-ray
 image caused by over-sampling without changing diagnostic quality.
 SUMMARY OF THE INVENTION
 A method for removing "grid line artifacts" from x-ray images in an x-ray
 radiography imaging system is presented. The method utilizes the Fourier
 spectrum of the image to identify grid line frequencies and employs
 spectral domain filtering to remove the grid line spectral components. The
 diagnostic information is preserved by modifying the grid line spectral
 components so as to be indistinguishable from local variations in image
 intensity values, and edge density of the x-ray image. Grid line spectral
 components are removed by the method consisting of the following steps:
 first, replacing the edgy regions with non edgy regions to generate a
 modified x-ray image; next, replacing the high intensity regions with low
 intensity regions within the modified x-ray image; next, converting the
 modified x-ray image to the frequency domain; then, eliminating "grid line
 artifacts" from the modified x-ray image; and finally, converting the
 modified x-ray image to a human readable format.

DETAILED DESCRIPTION OF THE INVENTION
 In a x-ray radiography imaging system, an x-ray source (not illustrated)
 projects a cone-shaped pattern of beams which pass through an object 124
 being imaged and impinge upon an array of radiation detectors 130, as
 illustrated in FIG. 1. Each detector 130 produces a separate electrical
 signal that is a measurement of incident beam attenuation. The attenuation
 measurements from all detectors 130 are acquired separately to produce an
 x-ray image. A metallic anti-scatter grid 114 is typically placed against
 a detector base 112 to channel the x-rays so that only substantially
 perpendicular x-rays (e.g. rays 118 and 122) to a detector strike the
 detector 130 and x-rays that are not substantially perpendicular (e.g.
 x-rays 116 and 120) are blocked by anti-scatter grid 114. Substantially
 perpendicular x-rays are those x-rays that strike detector 130 and do not
 striking anti-scatter grid 114.
 In this Specification, "grid line artifacts" are defined as extraneous
 visible data in the x-ray image generated in association with the use of
 anti-scatter grid 114, detector 130 electronics, and any other source
 which causes extraneous data to be seen in the x-ray image which result in
 high frequency spectral components having a spectral magnitude
 significantly greater than high frequency object data spectral components.
 Object data spectral components comprise those frequency components that
 result from the x-ray image and not from artifacts.
 The method of removing "grid line artifacts" is illustrated by the method
 flowchart shown in FIG. 2. This method includes: a step 210, subdividing
 the x-ray image into a plurality of windows; a step 212, replacing regions
 with a substantial number of edges within each window with regions with
 less number of edges in the respective window; a step 214, replacing high
 intensity regions within each window with low intensity regions; a step
 216, converting each window into the Fourier domain and removing "grid
 line artifacts"; and a step 218, conducting an inverse-Fourier transform
 on each window so that the modified x-ray image may be presented in a
 human readable format. Regions with a substantial number of edges
 hereinafter will be identified as "edgy regions" in this Specification.
 Edgy regions are further discussed below.
 The x-ray image is divided into windows to facilitate computer based
 evaluation, as identified by the method of step 210 in FIG. 2. The window
 size is selected to be large enough to generate frequency resolution at
 about the expected frequency of the grid line artifact and alternatively,
 small enough to ensure that the grid line artifact has a substantially
 constant spatial grid line frequency. The size of each window selected is
 such that it has substantially constant grid frequency. A grid frequency
 is considered substantially constant if there is at most one local maximum
 frequency component which is three standard deviations larger than the
 average value of the neighboring frequency components. For example, in a
 typical x-ray image having 1024 by 1024 pixels, the image may be divided
 into sixty-four windows. It is also understood that a window may have
 rectangular dimensions rather than square dimensions as illustrated in
 this case.
 The "edgy region" of the x-ray image provides the necessary definition of
 object 124 (FIG. 1) so that the human observer may easily identify
 important features of the x-ray as identified by the method of step 212 in
 FIG. 2. These features aid in diagnosis. For this reason it is important
 to preserve the detail of the "edgy region" of the x-ray image. The method
 employed in this invention preserves the "edgy regions" of the x-ray image
 by removing them before processing the image and replacing them after
 processing the image. "Edgy regions" are defined by the method identified
 below.
 High intensity regions of the x-ray image are also removed before
 processing, as identified by the method of step 214. This is necessary
 first to preserve the high intensity regions produced by the object and
 second, to facilitate removal of "grid line artifacts" in windows with
 high intensity regions.
 Next, "grid line artifacts" are removed from the x-ray image, as identified
 by the method of step 216. This is accomplished by converting the x-ray
 image to the Fourier domain where frequency components representing the
 x-ray image are generated, as illustrated by graph 370 in FIG. 7. In FIGS.
 7 and 8 the vertical axis is defined as the frequency component magnitude,
 expressed in Decibels. The horizontal axis is defined as the frequency
 axis, expressed in Hertz. The frequency component of a grid line artifact
 380 is distinguished from the frequency components of the image (e.g.
 components 372-378, and 382-386) in one respect in that spectral component
 380 is usually the highest spectral component of the high frequency
 components. As such, by eliminating low frequency components, (i.e. those
 components identified by range 371), the grid line artifact is usually the
 highest spectral component remaining, as is further discussed below. Grid
 line spectral component 380 is adjusted so that component 380 is no
 greater in magnitude than the average adjacent magnitude. The adjacent
 magnitude is defined by range 388 as illustrated in FIG. 7.
 The x-ray image is then restored to a human readable format, as identified
 by the method of step 218 of FIG. 2. This is accomplished by conducting an
 inverse Fourier transform on the frequency components. It may also be
 necessary to adjust the mean value of the image, as is discussed below.
 Method 200 for removing "grid line artifacts" as shown in FIG. 2, is
 presented in greater detail in method 250, as illustrated in FIG. 3
 through FIG. 5. The steps identified in FIG. 3 identify the method of
 generating a gradient image of the x-ray image 252 and an intensity
 quantized image from the x-ray image 252. The gradient image is generated
 by first convolving the image 252 with a gradient operator, as identified
 by step 254. For digital images, such as those in this invention, gradient
 operators represent finite difference approximations of either the
 orthogonal gradient or the directional gradient. These masks are defined,
 for example, in the reference entitled, Fundamentals of Digital Image
 Processing, Anil K. Jain, Prentice Hall, 1989, chapter 9, pages 347
 through 350, herein incorporated by reference. Next, a histogram of the
 gradient image is computed, as identified by step 260. From the histogram
 a threshold "T" is chosen such that a range of the pixels with the largest
 gradient are defined as edges, as identified by step 262. For example,
 threshold value "T" may be selected from a range to identify about 10% to
 about 20% of the pixels with the largest gradient. A gradient image is
 therefore generated using the threshold "T" to define edges, as identified
 by step 266.
 An intensity quantized image is generated by first computing an intensity
 histogram of the image, as identified by step 256 in FIG. 3. From this
 histogram a threshold "I" is chosen so that a fixed percentage of the
 pixels with the largest intensity are defined as high intensity regions,
 as identified by step 258. Using threshold "I", an intensity quantized
 image is generated, as identified by step 264. Regions with a low
 intensity are associated with a zero and regions with a high intensity are
 associated with a one. The ones and zeros are grouped together to define a
 matrix identified as the intensity quantized image 270. Intensity
 threshold "I" may be selected, for example, such that at most about 25% of
 the pixels with the largest intensity are defined as "high intensity
 regions."
 The gradient image 265, intensity quantized image 270 and x-ray image 268
 are all then divided into a plurality of number of respective windows as
 identified by step 210.
 Next, the mean value of each window is computed as identified by step 274,
 in FIG. 4. It is necessary to determine the mean value of the pixels of
 each window because mathematical manipulation as defined in subsequent
 operations within this Specification may change the mean value of the
 image within a respective window, resulting in undesirable artifacts.
 Thus, it may be necessary to adjust the mean value of each respective
 window so that the mean value of the respective window remains unchanged,
 as is discussed below.
 The next step in method 250 is to remove high frequency edges and high
 frequency intensity regions as identified by the method identified in step
 280, in FIG. 4. In order to remove "grid line artifacts" from the x-ray
 image it is first necessary to remove high frequency edges and high
 frequency intensity regions from each window, as discussed above. Block
 280 is further subdivided into several sub-steps, as is identified by the
 method in FIG. 6.
 First, a window comprising a respective intensity window, gradient window,
 and x-ray window is subdivided into a plurality of sub-windows so that
 most sub-windows are substantially non-edgy, as identified by sub-step
 282, in FIG. 6. For example, in an x-ray image having 1024 by 1024 pixels
 wherein sixty-four windows are selected, each window may be divided into
 sixty-four sub-windows.
 Next, edgy sub-windows are replaced with the nearest non-edgy sub-windows
 based on the results from the test illustrated by the method in sub-step
 284. Where twenty or more percent of the gradient pixels of a sub-window
 are larger than threshold "T" the sub-window is replaced by the nearest
 non-edgy sub-window, as identified by sub-step 292. Non-edgy sub-windows
 are defined as those sub-windows wherein less than 20% of the gradient
 pixels are larger than threshold "T". The nearest sub-window is determined
 by comparing the distance between the center pixel of alternative
 sub-windows meeting the named criteria (wheather the sub-window is
 non-edgy) to the center pixel of the sub-window being replaced, then
 selecting the sub-window meeting the named criteria, and being closest in
 distance to the sub-window being replaced.
 Following sub-step 292, high intensity sub-windows are replaced by low
 intensity sub-windows and sub-windows which are non-edgy, as defined by
 sub-step 296. A high intensity sub-window is defined to be one in which
 50% or more of the pixels have an associated intensity quantized number of
 one. When a high intensity sub-window is identified, as illustrated by
 sub-step 294, the high intensity sub-window is replaced by the nearest low
 intensity sub-window, as illustrated by sub-step 296. A low intensity
 sub-window is defined as a sub-window where less than 50% of the pixels in
 the intensity quantized sub-window are associated with a one and
 sub-windows which are non-edgy, as previously defined. This method is
 repeated until all sub-windows have been evaluated for high intensity
 regions and edgy regions, as identified by sub-step 298.
 After edgy regions and high intensity regions have been removed from the
 image, a Fourier transformation is performed on the image window and "grid
 line artifacts" are removed, as identified by steps 300 and 303, in FIG.
 4. Removing "grid line artifacts" is best illustrated by the graphs 370
 and 392 in FIGS. 7 and 8. FIG. 7 illustrates a typical graph 370 of the
 magnitudes of the frequency components of a Fourier transform of a
 respective window of the x-ray image having object data spectral
 components and grid line artifact spectral components. Grid line artifact
 spectral component 380 is distinguished from object data spectral
 components of the x-ray image window because grid line spectral component
 380 is typically the high frequency component with largest magnitude. Grid
 line artifact spectral component 380 is the spectral component having a
 magnitude about three standard deviations greater than the average
 magnitude of the object data spectral components in a range 388. Range 388
 is defined as the range of object data spectral components having
 substantially constant magnitudes.
 Grid line spectral component 380 is removed by first removing the low
 frequency spectral components in a range 371 of graph 370. Range 371 is
 defined as object data spectral component range having object data
 spectral component frequencies in the bottom ten percent of the spectral
 component frequency range. Component 380 is then removed as replaced by a
 new spectral component 381 that has a magnitude substantially equally to
 the average of adjacent spectral components identified in range 388. This
 spectral component modification is illustrated by graph 392 in FIG. 8.
 Although FIGS. 7 and 8 illustrate the grid line artifact spectral component
 removal method for a one-dimensional Fourier transform, a two-dimensional
 Fourier transform may be utilized to remove grid line artifact spectral
 components having "x" and "y" Cartesian coordinates. Steps in the
 two-dimensional method are substantially the same as those defined above
 in the one-dimensional method, with the primary difference being that
 spectral components have an "x" and a "y" coordinate defining each
 component's location, whereas in the one-dimensional Fourier transform
 magnitudes of the spectral component will only have one coordinate
 defining each component's location. The two-dimensional Fourier transform
 approach may be preferred over the one-dimensional Fourier transform
 approach if the grid-line artifacts are not perpendicular to the "x" and
 "y" co-ordinates of the image.
 The step of dividing the x-ray image into windows and variations in the
 mean value of the image within a window may cause noticeable artifacts
 known as a "ringing artifacts" along the periphery of a number of windows.
 "Ringing artifacts" occur because image data utilized in the Fourier
 transform is not infinite. Theoretically, a Fourier transform is a method
 of transforming data from the spatial domain to the frequency domain
 utilizing an infinite series, however, the x-ray images utilized in this
 invention have a finite number of windows and as such do not closely
 approximate an infinite series.
 Variations in the mean value of the pixels within each window may be
 removed by subtracting the error signal generated by calculating the mean
 value of the pixels within the initial window identified in step 210, of
 FIG. 2, and the mean value of the pixels of the modified window identified
 in step 218, of FIG. 2, and then adjusting each modified window by
 subtracting the pixel mean value of the initial window from the pixel mean
 value of the modified window, as identified by step 274, in FIG. 4. The
 modified window is defined as the window in which "edgy regions," "high
 intensity regions" and "grid line artifacts" have been removed by the
 above-described method.
 Next, "ringing artifacts" caused in part by dividing the x-ray image into
 widows may be eliminated by a method called "window substitution." In this
 method each respective window along the perimeter of a respective modified
 window are replaced by a equivalent respective modified window to generate
 a super-window. An equivalent respective modified window is defined as a
 copy of the respective modified window. The resulting super-window has
 nine identical modified windows. Method 250 is then continued beginning at
 step 302, in FIG. 4, where the super-window is substituted for the
 modified window. Mathematical operations performed on the superwindow
 causes ringing effects that normally would have appeared in the periphery
 of the modified window to appear in the outer periphery of the equivalent
 respective modified windows. Each respective equivalent modified window is
 discarded leaving only the modified window having no "ringing artifacts."
 The x-ray image is restored next to a human readable format by performing
 an inverse Fourier transform converting the image from the frequency
 domain back into the original spatial domain image, as identified by the
 method of step 218. Next, all edgy regions and high intensity regions that
 were replaced, as identified by steps 212 and 214 of FIG. 2, are added
 back to the modified image as identified by step 306, of FIG. 5.
 The windows are then equalized by subtracting the pixel mean value of the
 modified window from the pixel mean value of the initial window to
 generate a difference value, and multiplying the resulting difference
 value by each pixel in the modified image to obtain an adjusted modified
 image, as identified by step 308, in FIG. 5.
 Finally, the steps of method 250 described above are repeated for each
 window until all windows have been evaluated and processed according to
 the method described above as identified by steps 310 and 312, in FIG. 5.
 At the conclusion of this method "grid line artifacts" have been removed
 from the x-ray image, "ringing artifacts" caused by this method have been
 eliminated, and the x-ray image has been converted to a human readable
 format for diagnosis and review, as illustrated by step 314, in FIG. 5.
 The present invention provides a method for removing "grid line artifacts"
 from an x-ray image. This method utilizes the Fourier spectrum of the
 image to detect grid line frequencies and employs a spectral domain
 filtering method to remove grid line spectral components. The diagnostic
 information is preserved by modifying the grid line spectral components so
 as to be indistinguishable from local variations and image intensity
 values and edge density of the x-ray image.
 It will apparent to those skilled in the art that while the invention has
 been illustrated and described herein in accordance with the patent
 statutes, modifications and changes may be made in the disclosed
 embodiments without departing from the true spirit and scope of the
 invention. It is, therefore, to be understood that the appended claims are
 intended to cover all such modifications and changes as fall within the
 true spirit of the invention.