Patent Publication Number: US-2022230395-A1

Title: Entropy-dependent adaptive image filtering

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 63/199,662, filed Jan. 15, 2021, the contents of which are incorporated herein for all purposes. 
    
    
     BACKGROUND 
     According to conventional positron-emission-tomography (PET) imaging, a radiopharmaceutical tracer is initially introduced into a patient body. Radioactive decay of the tracer generates positrons which eventually encounter electrons and are annihilated thereby. The annihilation produces two photons which travel in approximately opposite directions. 
     A ring of detectors surrounding a portion of the body (e.g., the torso) detects photons emitted therefrom. A coincidence is identified when two detectors disposed on opposite sides of the body detect the arrival of two photons within a particular coincidence time window. Because the two “coincident” photons travel in approximately opposite directions, the locations of the two detectors determine a Line-of-Response (LOR) along which an annihilation event may have occurred. The LORs of the identified coincidences may be used to reconstruct a PET image of the portion of the body. 
     Due to the relatively low number of coincidences (e.g., in comparison to a number of attenuated x-rays received during computed tomography (CT) imaging), PET images often exhibit low signal-to-noise ratios. These low ratios inhibit clinical interpretations based on the delineation of internal structures. Conventional systems therefore apply processing to reconstructed PET images in an attempt to reduce the noise therein. 
     Traditionally, a Gaussian filter may be applied to a PET image to reduce its noise. Such a filter smooths edges and regions of interest within the image, thereby decreasing the visual delineation of structures such as small lesions. Moreover, the actual raw voxel values of the original PET image (i.e., the PET quantitation), which have biochemical significance used in diagnosis, prognosis, and subsequent treatment, are not preserved. Non-local means filtering is an alternative to Gaussian filtering, and has been used to reduce noise while preserving the quantitation of an original PET image. However, such filtering also reduces the contrast of edges, which reduces the level of detail surrounding regions of interest, such as organs and lesions. 
     Modifications to non-local means filtering include filters in which the target voxel of a kernel acquires a weight within an associated filtering sum only if its surrounding region is identical to that of any reference voxel within the kernel. While this modification may address some of the shortcomings of traditional non-local means filtering, the prerequisite condition is unlikely to occur in PET images, limiting its effectiveness in the case of PET images. 
     According to another filtering method, anatomical information of an associated CT image is used to locate region boundaries within the PET image. A traditional non-local means filter is then applied, but the strength of the filter is suppressed within identified regions of interest. This method requires the acquisition of a CT image either immediately before or immediately after the PET acquisition, very accurate registration between the CT and PET images, and manual or automatic segmentation of the CT image to determine the region boundaries. Each of these requirements increases complexity, cost and susceptibility to error. 
     Improved systems for filtering a reconstructed PET image are desired. Such systems may be applicable to any other image data acquired using any other imaging modality. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an architecture to filter an image according to some embodiments. 
         FIG. 2  is a block diagram of an architecture to filter an image according to some embodiments. 
         FIG. 3  comprises a flow diagram of a process to filter a PET image according to some embodiments. 
         FIG. 4  is a block diagram of a PET/CT imaging system according to some embodiments. 
         FIG. 5  comprises a flow diagram of a process to filter a PET image based on a user-selected filtering strength according to some embodiments. 
         FIG. 6  illustrates an inverse normalized entropy map according to some embodiments. 
         FIG. 7  illustrates a non-local means filtering algorithm according to some embodiments. 
         FIG. 8 a    is a two-dimensional unfiltered PET image. 
         FIG. 8 b    is a two-dimensional filtered PET image based on the  FIG. 8 a    image according to some embodiments. 
         FIG. 9  includes two-dimensional PET images for illustrating filtering using different filtering strengths according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is provided to enable any person in the art to make and use the described embodiments. Various modifications will remain apparent to those in the art. 
     Generally, some embodiments suppress filtering strength based on voxel entropy. Since image regions which exhibit enhanced detail, such as boundaries, organs, and lesions, are typically associated with increased entropy, the strength of the filter applied to voxels in those regions is lower than the strength of the filter applied to voxels in other regions. 
     In some examples, the entropy of every voxel in an image is calculated. The entropy of each voxel is then used to determine a filtering associated with the voxel. For example, and as will be described in detail below, the value of a non-local means filtering strength h for each voxel may be determined as the product of a maximum filtering strength value h max  and an inverse of the entropy of the voxel, wherein the entropies of all voxels are normalized to pre-specified bounding values. The filtering determined for each voxel is applied to each voxel to generate a replacement value for each voxel. A filtered PET image is then generated based on the replacement values of the voxels. Embodiments may efficiently remove noise from an image while substantially preserving details and PET quantitation of important regions. 
     Embodiments also advantageously do not require multi-modal registration or segmentation. Also, since the calculation of entropy is computationally vectorizable, the calculation can be performed quickly via a sequence of vector and matrix operations using modern computing methods. Moreover, because entropy is a general concept and may be calculated for voxels of any image, embodiments are not limited to PET images and are suitable for any image modality. 
       FIG. 1  is a block diagram of architecture  100  to filter an image according to some embodiments. The illustrated elements of architecture  100  may be implemented using any suitable combination of computing hardware and/or software that is or becomes known. In some embodiments, two or more elements are implemented by a single computing device. One or more elements may be implemented as a cloud service (e.g., Software-as-a-Service, Platform-as-a-Service). 
     Three-dimensional image  110  may comprise a set of voxels having a known physical relationship to each other (e.g., via coordinates of a common three-dimensional space), and one or more values associated with each voxel. The values may comprise any type of numerical value of any unit. The voxel values of image  110  may be in units of light intensity, color space parameters, etc. and may represent any physical quantity. In the case of a PET image, each voxel is associated with a value in units of Becquerel(Bq)/ml and represents a concentration of radioactivity over time. Image  110  may be acquired, or reconstructed from data acquired, via any imaging modality. 
     Entropy determination component  120  determines an entropy associated with each voxel of image  110  based on one or more voxel values of image  110 . Entropy determination component  120  may determine the entropy associated with each voxel using any technique that is or becomes known. In some embodiments, the entropy of a voxel is a measure of the possible variations in intensity within a kernel centered on the voxel. According to some embodiments, entropy Z 1  of the ith voxel is calculated as: 
     
       
         
           
             
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     where P(v j ) is the probability that voxel value v j  is encountered within a kernel of specified size centered on the ith voxel, and the sum is taken over all distinct voxel values v j  within the kernel. 
     Entropy determination component  120  outputs values based on the determined voxel-specific entropies. In some embodiments, component  120  outputs an entropy of each voxel and, in other embodiments, component  120  outputs an inverse entropy (i.e., Z i   −1 ) for each voxel. These output values may be normalized such that they are bound between specified values. For example, entropies determined for all voxels may be normalized to a given range, such that the inverse of the normalized entropies are also bound. Embodiments are not limited to these alternatives. 
     For each voxel, filtering determination component  130  determines a filtering to apply to the voxel based at least on the entropy-based value which was determined for the voxel by entropy determination component  120 . Generally, the filtering applied to a first voxel associated with a first entropy-based value may be different from the filtering applied to a second voxel associated with a second entropy-based value. The difference in filtering between the two voxels is related at least in part to the different entropy-based values associated with each voxel. 
     Filtering may comprise calculating a replacement value for a voxel based on the voxel value and on a filtering equation. In some embodiments, the entropy values are used to determine a value of a parameter used in a filtering equation which is subsequently applied to each voxel value. The entropy values may be used to determine values of two or more parameters of such a filtering equation. In some embodiments, a first filtering equation is used to filter voxels associated with a first range of entropy-based values, and a second filtering equation is used to filter voxels associated with a second range of entropy-based values. Additionally, one or more parameters of the first or second equation may be determined based on the value of a particular voxel to be filtered. 
     The voxel-specific filtering determined by component  130  is passed to filtering component  140 . Filtering component  140  applies the appropriate voxel-specific filtering to each voxel to generate a replacement value for each voxel. Image  150  may then be generated by substituting the original value of each voxel of image  110  with its determined replacement value. 
       FIG. 2  illustrates architecture  200  to filter an image according to some embodiments. Architecture  200  may comprise a specific implementation of architecture  100 , but embodiments are not limited thereto. 
     As described with respect to image  110 , image  210  may comprise any three-dimensional image including voxels and values associated with each voxel. Entropy determination component  220  determines an entropy associated with each voxel of image  210  in any suitable manner, based on one or more voxel values of image  210 . Entropy determination component  220  may also normalize the determined entropies such that the values thereof are bound (e.g., between 1 and 10), and determine an inverse (e.g., Z i   −1 , bound between 0.1 and 1) of each normalized entropy. The inverse normalized entropies associated with the voxels may be referred to as inverse normalized entropy map, and output to filtering component  230 . 
     Filtering component  230  determines a replacement value for each voxel based on the inverse normalized entropy map, and image  240  consists of voxels having the replacement values. In some embodiments, filtering component  230  applies a same filtering equation to each voxel value to determine all replacement values, but, for a given voxel, a value of a parameter of the filtering equation is calculated based on the inverse normalized entropy associated with the voxel. 
     For example, filtering component  230  may apply a non-local means filtering equation to determine a replacement value for each voxel. As will be described in more detail below, the non-local means filtering equation may include a parameter h which is related to a strength of the filtering applied by the non-local means filtering equation. Some embodiments of filtering component  230  may determine h for filtering a given voxel as equal to a product of the inverse normalized entropy associated with the given voxel and a predetermined maximum h max . Accordingly, voxels associated with a low normalized entropy, e.g., 1 (and a high inverse normalized entropy, e.g., 1), are filtered using a larger value of h than voxels associated with a higher entropy, e.g., 10 (and lower inverse normalized entropy, e.g., 0.1). 
       FIG. 3  comprises a flow diagram of process  300  to filter a PET image according to some embodiments. As mentioned above, embodiments are not limited to PET image data. Process  300  and other processes described herein may be executed using any suitable combination of hardware and software. Software program code embodying these processes may be stored by any non-transitory tangible medium, including a fixed disk, a volatile or non-volatile random-access memory, a DVD, a Flash drive, and a magnetic tape, and executed by any suitable processing unit, including but not limited to one or more microprocessors, microcontrollers, processing cores, and processor threads. Embodiments are not limited to the examples described herein. 
     PET data associated with an object is acquired at S 310 . In a typical PET data acquisition, a radionuclide tracer such as fluorodeoxyglucose (FDG) is injected into an object prior to the scan. Detectors surrounding the object detect the arrival of photons resulting from annihilations occurring within the object and coincidences are identified based on the arrivals. PET data is generated which associates each identified coincidence with the two detector crystals which received the photons of the coincidence, the time of the coincidence and, in the case of TOF data, the difference in photon arrival times. The PET data may include additional data associated with each coincidence and with the PET scan in general. 
     A three-dimensional image of the object is then reconstructed based on the PET data as is known in the art. In some embodiments, the reconstruction uses an attenuation map of the object, which may be generated based on anatomical information derived from a prior CT scan of the object. As is known in the art, the PET data may be corrected for randoms and scatter prior to reconstruction. 
     Rather than perform S 310  and S 320  substantially contemporaneously with the remaining steps of process  300 , embodiments may simply receive at S 330  a stored three-dimensional PET image which reconstructed in the past by the same entity performing S 330  to S 360  or by another entity, based on PET data previously acquired by the same or other entity. 
       FIG. 4  illustrates PET system  400  to execute one or more of the processes described herein. Embodiments are not limited to system  400 . 
     System  400  includes gantry  410  defining bore  412 . As is known in the art, gantry  410  houses PET imaging components for acquiring PET image data. The PET imaging components (not shown) may include an arbitrary number of adjacent and coaxial rings of detectors, and with each detector comprising any number of scintillator crystals and electrical transducers. The scintillator crystals of each detector receive 511 keV photons which result from annihilation events and, in response, create photons having energies of a few electron volts. The electrical transducers convert these low-energy photons to electrical signals. According to some embodiments, the electrical transducers may comprise, for example, silicon-based photomultipliers (SiPMs), photomultiplier tubes (PMTs), or semiconductor-based detectors. 
     In some embodiments, scanner  400  is a PET/CT scanner and also includes CT imaging components for acquiring CT image data. The CT imaging components may include one or more x-ray tubes and one or more corresponding x-ray detectors as is known in the art. 
     Bed  415  and base  416  are operable to move a patient lying on bed  415  into and out of bore  412  before, during and after imaging. In some embodiments, bed  415  is configured to translate over base  416  and, in other embodiments, base  416  is movable along with or alternatively from bed  415 . Movement of a patient into and out of bore  412  may allow scanning of the patient the PET imaging elements of gantry  410 . In the case of a PET/CT scanner, a CT scan may be conducted immediately before or after a PET scan while a patient remains in a substantially same position on bed  415 . This approach facilitates registration of the CT data with the PET data. 
     Control system  420  may comprise any general-purpose or dedicated computing system. Accordingly, control system  420  includes one or more processing units  422  configured to execute processor-executable program code to cause system  420  to operate as described herein, and storage device  430  for storing the program code. Storage device  430  may comprise one or more fixed disks, solid-state random-access memory, and/or removable media (e.g., a thumb drive) mounted in a corresponding interface (e.g., a USB port). 
     Storage device  430  stores program code of control program  431 . One or more processing units  422  may execute control program  431  to, in conjunction with PET system interface  423 , bed interface  425 , and monitor interface  427 , control hardware elements to inject a radiopharmaceutical into a patient, move the patient into bore  412  past PET detectors of gantry  410 , and detect coincidences occurring within the patient. The detected coincidences may be stored in memory  430  as PET data  434 . Control program  431  may also be executed to reconstruct PET data  434  into a three-dimensional PET image  435  using any currently- or hereafter-known technique. 
     Entropy determination program  432  may be executed to determine a value based on the entropy of each voxel of a PET image  435  as described herein. Entropy determination program  432  may be executed to determine an entropy value, an inverse entropy value, a normalized entropy value, an inverse normalized entropy value, an entropy-related filtering parameter value, or any other suitable entropy-related value or values for each voxel. 
     Filtering component  433  may be executed to apply filtering to a PET image  435 . Filtering may comprise determination of a replacement value of each voxel of the PET image  435 . As described herein, the particular filtering applied to a given voxel may be dependent upon the entropy associated with the voxel. While entropy determination program  432  and filtering component  433  are illustrated separately in  FIG. 4 , either or both may comprise elements of control program  431  or another program in some embodiments. 
     PET images  435  may be transmitted via terminal interface  426  to terminal  440  for display. Terminal  440  may comprise a display device and an input device coupled to system  420 . Terminal  440  may receive user input for controlling display of the data, operation of system  400 , and/or the processing described herein. In some embodiments, terminal  440  is a separate computing device such as, but not limited to, a desktop computer, a laptop computer, a tablet computer, and a smartphone. 
     Each component of system  400  may include other elements which are necessary for the operation thereof, as well as additional elements for providing functions other than those described herein. Each functional component described herein may be implemented in computer hardware, in program code and/or in one or more computing systems executing such program code as is known in the art. Such a computing system may include one or more processing units which execute processor-executable program code stored in a memory system. 
     Returning to process  300 , an entropy-based value associated with each voxel of the reconstructed three-dimensional image is determined at S 320 . The entropy-based value associated with a voxel is determined based on one or more voxels of the image. According to some embodiments, the entropy Z i  of voxel V i  is calculated at S 330  as the negative of the sum of the product of the probability that a particular value v j  is encountered within a kernel and the logarithm of the probability, or, as noted above: 
     
       
         
           
             
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     The kernel may be 7×7×7 voxels in size, for example, but embodiments are not limited thereto. 
     Entropy Z 1  in this scenario may be considered a measure of the total number of variations in voxel intensity which exist in the vicinity of voxel V i , i.e., a measure of an amount of detail centered on voxel V i . Since boundaries, organs, and lesions are represented as highly detailed areas within a PET image, the voxels representing these structures tend to be associated with higher entropy values than other voxels. 
     An entropy-based value is determined for each voxel based on the determined voxel-specific entropies. Depending on the implementation of subsequent processing, the entropy-based value may be equal to the entropy of each voxel, inversely related to the entropy of each voxel, normalized, or otherwise determined. 
     At S 340 , a filter is determined for each voxel based at least on the entropy-based value which was determined for the voxel at S 330 . Determination of a filter for a voxel may comprise, for example, substituting the entropy-based value associated with the voxel for a corresponding parameter of a filtering equation, selecting one or more parameter values of a filtering equation based on the entropy-based value, or selecting one of several filtering equations based on the entropy-related value. In some embodiments, the filter determined for a voxel associated with a greater entropy is of lower strength than the filter determined for a voxel associated with a lesser entropy. Suppressing filtering strength in higher-entropy regions (e.g., boundaries, organs, and lesions) results in preservation of detail within these regions as compared to regions of lower-entropy (and lower detail), in which preservation of detail may be less important than in higher-entropy regions. 
     For each voxel, the determined filter is applied to the value of the voxel at S 340  to generate a replacement value for the voxel. A filtered three-dimensional image is then generated at S 360  by substituting the original value of each voxel of the original image with its determined replacement value. 
       FIG. 5  is a flow diagram of process  500  to filter a three-dimensional image according to some embodiments. Process  500  may comprise a specific implementation of process  300 , and may be implemented by an architecture such as architecture  200 , but embodiments are not limited to either scenario. 
     S 510  and S 520  of process  500  may proceed as described above with respect to S 310  and S 320  of process  300 . At S 530 , an entropy Z i  associated with each voxel V i  of the three-dimensional image is determined in any suitable known manner, for example as described above. Next, at S 540 , the entropy value associated with each voxel is normalized such that all values are bound between a lower and upper bound. For example, each Z i  is rescaled to the interval [1, 10]. Each normalized entropy value is then converted at S 550  to an inverse entropy value (e.g., Z i   −1 ). Continuing the example, the Z i   −1  values corresponding to Z i  values which were rescaled to the interval [ 1 ,  10 ] are necessarily bound between 0.1 and 1. Normalizing the entropy values at S 540  ensures that the associated inverse entropy values determined at S 550  will not be indefinite and thereby guarantees that every voxel will be filtered to some extent in the following processing. 
     The inverse normalized entropy values associated with the voxels may comprise a three-dimensional inverse normalized entropy map.  FIG. 6  depicts a two-dimensional projection (i.e., a slice projection) of such a map according to some embodiments. Map  600  depicts higher inverse normalized entropy values with higher-intensity (i.e., lighter) pixels and lower inverse normalized entropy values with lower-intensity (i.e., darker) pixels. As shown, regions having more complex structure are associated with smaller inverse normalized entropy values. 
     A filter is determined for each voxel at S 560  based on the inverse normalized entropy value associated with the voxel and a filtering parameter. For example, the same filtering equation may be determined for each voxel but, for a given voxel, a value of a parameter of the filtering equation is calculated based on the inverse normalized entropy value associated with the voxel. In some embodiments, the filtering equation is a non-local means filtering equation and the parameter is filter strength h: 
     
       
         
           
             
               
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     where V iR  is the replacement value of the ith voxel, M i  and M j  are distributions of specified size centered on the ith and jth voxel, respectively, h i  is the filtering strength for the ith voxel, and N i  normalizes the sum of the exponential weights to 1. V j  is the value of the jth voxel within the kernel of specified size centered on the ith voxel, and the sum is taken over all of the voxels within the kernel. According to some embodiments, the normalization factor N i  is defined as follows: 
     
       
         
           
             
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       FIG. 7  illustrates application of a non-local means filtering equation within an example 7×7×7 image kernel  700 . The filtering equation determines replacement value V iR  of voxel V i  at the center of kernel  700 , denoted as a weighted sum over each other voxel V j  within kernel  700 . By virtue of the inverse exponential function in the equation above, the weight attributed to a particular voxel V j  in the summation is high if the cubic region M j  surrounding V j  is similar to the cubic region M i  surrounding V i . Otherwise, the weight attributed to V j  is lower. Accordingly, the resulting summation removes contributions from spurious noise maxima and minima within kernel  700 . The degree to which the weights impact result can be enhanced or reduced by increasing or reducing parameter h, which appears in the denominator of the power of the exponential function. h may therefore be referred to as the filter strength. 
     In some embodiments, h is determined at S 560  for each voxel as equal to a product of a predetermined maximum h max  (e.g., 0.0075) and the inverse normalized entropy value associated with the voxel. Voxels associated with a low entropy value (and high inverse normalized entropy value, e.g., 1) are thereby filtered using a larger value of h than voxels associated with a higher entropy value (and lower inverse normalized entropy value). In other words, the degree to which a voxel will be filtered is directly related to its degree of homogeneity. 
     Next, at S 570 , the filter determined for each voxel is applied to the value of each voxel to generate a replacement value for each voxel. A filtered three-dimensional image is then generated at S 580  based on the generated replacement values. The filtered three-dimensional image may be displayed to a clinician in any known format for presenting a three-dimensional image (e.g., slices, fly-through, exploded), and used for subsequent diagnosis, prognosis or treatment planning, for example. 
       FIG. 8 a    depicts two-dimensional PET slice image  800  prior to filtering according to some embodiments. As shown, many areas of image  800  depict noise. In comparison,  FIG. 8 b    shows two-dimensional PET slice image  850  which consists of replacement values generated based on the voxel values of image  800  as described herein. The low-entropy areas of image  800  have been filtered to remove noise, while the delineation of structures in the higher-entropy areas remains satisfactory due to suppression of the filtering strength in those areas. 
     In some embodiments of process  500 , h max  may be selected by an operator in order to a desired maximum possible filtering strength. According to one non-exhaustive example, a “low” setting corresponds to h max =0.005, a “medium” setting corresponds to h max =0.0075, and a “high” setting corresponds to h max =0.01. 
       FIG. 9  depicts two-dimensional PET slice image  900  prior to filtering according to some embodiments. Two-dimensional PET slice image  910  consists of replacement values generated based on the voxel values of image  900  and a low h max  setting, two-dimensional PET slice image  920  consists of replacement values generated based on the voxel values of image  900  and a medium h max  setting, and two-dimensional PET slice image  930  consists of replacement values generated based on the voxel values of image  900  and a high h max  setting. As the value of h max  increases, the noise within the low-entropy and high-entropy regions decreases. However, the noise within the high-entropy regions decreases to a lesser degree than in the low-entropy regions, thereby better preserving detail within regions of interest as compared to prior filtering systems. 
     Those in the art will appreciate that various adaptations and modifications of the above-described embodiments can be configured without departing from the claims. Therefore, it is to be understood that the claims may be practiced other than as specifically described herein.