Abstract:
In one aspect, the invention is a method of medical image processing. The method includes receiving data representing a medical image. The method also includes generating the medical image based on a model. The model characterizes the medical image as a composition of at least two components having processing constraints.

Description:
TECHNICAL FIELD 
     This invention relates generally to image processing and more specifically to medical images. 
     BACKGROUND 
     There are a number of systems used for generating medical images. For example, a computed tomography (CT) system generates three-dimensional (3-D) images by generating a series of two-dimensional (2-D) X-ray images about an axis of rotation. In another example, a positron emission tomography (PET) system measures positron emissions from human tissue as a result of absorption of a radioactive molecule injected in to a human body. Other medical imaging systems include a magnetic resonance imaging system (MRI) which generates images by applying magnetic fields and radio frequency (RF) energy to the human body and recording the resultant effects on the nuclei in the human tissue. 
     SUMMARY 
     In one aspect, the invention is a method of medical image processing. The method includes receiving data representing a medical image and generating the medical image based on a model. The model characterizes the medical image as a composition of at least two components having processing constraints. 
     In another aspect, the invention is an apparatus. The apparatus includes a memory that stores executable instructions for medical image processing. The apparatus also includes a processor that executes the instructions to receive data representing a medical image and to generate the medical image based on a model, the model characterizing the medical image as a composition of at least two components having processing constraints. 
     In a further aspect, the invention is an article. The article includes a machine-readable medium that stores executable instructions for medical image processing. The instructions cause a machine to receive data representing a medical image and to generate the medical image based on a model, the model characterizing the medical image as a composition of at least two components having processing constraints. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagrammatic view of a computed tomography (CT) system. 
         FIG. 2A  is a diagrammatic view of an artery having calcification. 
         FIG. 2B  is a CT image of the artery. 
         FIG. 3  is a flowchart for a process of processing an image. 
         FIG. 4  is a flowchart for a process of minimizing total energy functional across all image components. 
         FIG. 5  is a diagrammatic view of a computer system on which the processes of  FIG. 3  and  FIG. 4  may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     A key problem in medical imaging is the removal of artifacts which degrade the quality of the image for diagnostic purposes. To address this problem, described herein is a model-based approach to image processing wherein the structures or areas of interest in the image are explicitly partitioned according to their behavior and different constraints are imposed separately on each structure or area. This approach can be employed as either a post-processing (restoration) method or as an image formation (reconstruction) method. This approach differs considerably from conventional deblurring and filtered back projection reconstruction techniques. To partition the image structures significant features of the different structures are used. These are flexible, but could include characteristics such as smoothness, concentration of energy or brightness, intensity, etc. A single functional or energy is then defined which combines all these model elements. The minimum of this combined energy is then sought. 
     While the system and techniques described herein uses an embodiment that includes computed tomography (CT), the system and techniques are not limited to CT. For example the system and techniques may be used in any image processing or acquisition system such as a magnetic resonance imaging (MRI) system, a positron emission tomography (PET) system, ultrasound and so forth. While the system and techniques described herein are used for image processing to detect calcium in an artery, the system may be used in any image processing system such as to minimize blurring or blooming effects between any different materials. The method described herein uses two components to distinguish between materials, but the method may be used with any number of components. 
     Referring to  FIG. 1 , a computed tomography system  10  includes an x-ray source  12 , a patient  14 , a detector  16 , a computer  18  and a display  20 . The X-ray source  12  emits an x-ray beam  13  which impinges upon or illuminates a portion (sometimes referred to as a slice) of patient  14 . Portions of the x-ray beam are absorbed by structures within the patient (both physiological and non-physiological structures) and a portion of the beam  15  reached a detector  16 . Detector  16  measures the absorption along numerous paths with both radial and tangential components. The computer  18  uses the measured absorption information collected by the detector  16  to form a cross-sectional image, which may be viewed on display  20 . 
     Referring to  FIGS. 2A and 2B , an artery  22  includes a wall  24  having an inner wall portion  24   a  and an outer wall portion  24   b . Inner wall portion  24   a  defines, a lumen  26 . A portion of wall  24  may include a calcified region  28 . Referring briefly to  FIG. 2B , a CT image  30  of an artery similar to artery  22  ( FIG. 2A ) is shown. CT image  30  is provided using known image processing techniques. Despite the well-localized nature of the calcium region  28 , the resulting image  30  shows nearly total obscuration of the luminal region  26 , rendering the image  30  non-evaluable. A calcium artifact in coronary CT arises when the intensity of small dense calcium regions in the vessel wall spills into adjacent pixels due to the blurring induced by the resolution-limited image formation process. The CT system  10  together with the reconstruction process spreads the intensity of such calcified regions over the image, resulting in an over-representation of the size of the calcification (“calcium blooming”) and often an under-representation of the size of the lumen  26 . In this sense, the “blooming” effect is intrinsic to any imaging modality in which the point-spread function is of a scale comparable to the size of the objects that are of interest, and the field of view may contain bright objects which, due to the point-spread function, obscures nearby lower-intensity objects of interest. 
     Turning now, to  FIG. 3 , an image processing technique (e.g., a process  50 ) which may be performed, for example, by computer  18 . The image processing described in  FIG. 3  may be performed at post-processing, for example, after filtered back projection processing or with no image pre-processing. 
     Process  50  assumes an underlying desired ideal image f exists and that f is composed of multiple components as determined by the user or operator. Process  50  determines the number of components (52). The number of such components depends on factors including the complexity of the anatomy or object to be imaged, the degree to which a priori models exist for each component, and the resulting computational complexity. In the case of imaging an artery having a calcified portion, for example, one simple scenario is to model the ideal image f as the sum of two components: a calcium components f c , and a non-calcified structured components f s , so that
 
 f=f   c   +f   s .
 
     Process  50  determines functions for each of the components identified in processing block  56 . For example, f s , is assumed to have a behavior having a lower amplitude and greater spatial extent than f c . 
     Corresponding to the ideal image f is a set of observed data g. The observed data g may be an image formed using standard techniques (e.g., back filter projection), which exhibit calcium blooming or the data could be raw data, which corresponds to a set of tomographic projections obtained prior to image formation. 
     H denotes an image blurring operator that maps the ideal image f to a set of observed data g. Thus, in an example using an image formed using standard techniques, H represents convolutional blurring with the point spread function corresponding to the imaging process. In some embodiments, a filtered back projection generated image may be approximated as being shift invariant and convolutional. In another example, using raw data, H represents the tomographic projection process. The operator H may be linear, though this is not essential. An enhanced estimate of the ideal image by minimization of an energy function may be represented as: 
     
       
         
           
             
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     where E denotes the “component energy”, d denotes the data term, and α s , and α c  are positive weights balancing the contributions of the different terms. The three terms capture the imaging process and the behavior of the underlying image. The term E d (f, g), represents the data generation process H and ensures fidelity to the observations. A common choice in the image processing literature is to set this term to the negative log likelihood of data. If the observations are assumed conditionally Gaussian, then:
 
 E   d ( f,g )=∥ g−Hf∥   2   2  
 
     In other examples, a Poisson observation model may be used. 
     The term E s (f, g ) represents the behavior of the non-calcified tissue image. Since it is assumed that the non-calcium image is somewhat smooth, then
 
 E   s ( f   s )=∥ Df   s ∥ 2   2  
 
where D is a discrete approximation to a derivative operator. Since the non-calcium component is assumed to have a lower amplitude, then f s ≦T s , for a positive threshold T s . In one embodiment, T s  is about 0.05 times the density of water.
 
     Finally, the term E c (f c ) represents the behavior of calcified regions in cardiac CT. With the assumption that calcium should be spatially localized, then the calcium distribution may be represented as:
 
 E   c ( f   c )=∥ Df   c ∥ p   p  
 
where D is a discrete approximation to a derivative operator and 0&lt;p≦2. Penalty, p, has localization and super-resolution ability when p≈1. In addition, under the assumption that the calcium component will generally be denser than non-calcific tissue, then T c ≦f c  for a positive threshold T c . In one embodiment, T c  is about 1.2 times the density of water.
 
     In summary, a formulation for enhanced cardiac CT imaging is: 
     
       
         
           
             
               
                 
                   
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     The formulation explicitly represents a single unified approach to calcium deblurring. The formulation may be readily extended to capture other effects, including Poisson observation models, additional field constraints, components for additional biological structures, etc. 
     Referring to  FIGS. 3 and 4 , process  50  minimizes the functions for the components using, for example, a process  60 . In particular, the energy function are minimized with respect to the values of the components f s  and f c  across an image to obtain a reconstructed image with enhanced behavior (i.e., better image) than a standard filtered back projection image. Minimization for the optimal enhanced image may be conducted through a series of iterative steps, for example, using a block coordinate descent approach and defining an outer iteration, which alternatively minimizes with respect to the tissue components f s  and f c  while the other component is held fixed. 
     Referring now to  FIG. 4 , process  60  begins with an initialization as shown in processing block  64 . For example, initializing f s   (k)  where k=0. Process  60  minimizes the first component ( 68 ). For example, minimizing the calcium component: 
     
       
         
           
             
               
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     Process  60  minimizes the second component ( 72 ). For example, minimizing the non-calcified component: 
                 f   ^     s     (     k   +   1     )       =       arg   ⁢           ⁢       min       f   s     ≤     T   s         ⁢            g   -     H   ⁡     (       f   c     (     k   +   1     )       +     f   s       )              2   2         +       α   s     ⁢            Df   s          2   2               
Each subminimization is solved using an algebraic reconstruction technique (ART)-like iteration. Such ART-like techniques are well-known to persons of ordinary skill in the art. Process  60  determines if there are additional components ( 78 ). If so, process  60  minimized the additional components ( 82 ). Process  60  determines if there is convergence ( 86 ).
 
     In some embodiments, process  60  may be initialized with, for example, a filtered back projection based reconstruction to provide an initial estimate of {circumflex over (f)} s   (0) . 
       FIG. 5  shows a computer  18  using process  50  including process  60 . Computer  100  includes an image processor  102 , a volatile memory  104 , and a non-volatile memory  106  (e.g., hard disk). Non-volatile memory  106  stores operating system  110 ; image data  112 ; and computer instructions  114 , which are executed by the image processor  102  out of volatile memory  104  to perform all or part of process  50  and process  60 . 
     Processes  50  and  60  are not limited to use with the hardware and software of  FIG. 5 ; it may find applicability in any computing or processing environment and with any type of machine that is capable of running a computer program. Processes  50  and  60  may be implemented in hardware, software, or a combination of the two. Processes  50  and  60  may be implemented in computer programs executed on programmable computers/machines that each includes a processor, a storage medium or other article of manufacture that is readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and one or more output devices. Program code may be applied to data entered using an input device to perform processes  50  and  60  and to generate output information. 
     The system can be implemented, at least in part, via a computer program product (i.e., a computer program tangibly embodied in an information carrier (e.g., in a machine-readable storage device or in a propagated signal) for execution by, or to control the operation of, data processing apparatus (e.g., a programmable processor, a computer, or multiple computers)). Each such program may be implemented in a high level procedural or object-oriented programming language to communicate with a computer system. However, the programs can be implemented in assembly or machine language. The language may be a compiled or an interpreted language and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network. A computer program may be stored on a storage medium or device (e.g., CD-ROM, hard disk, or magnetic diskette) that is readable by a general or special purpose programmable computer for configuring and operating the computer when the storage medium or device is read by the computer to perform process  80 . Process  80  may also be implemented as a machine-readable storage medium, configured with a computer program, where upon execution, instructions in the computer program cause the computer to operate in accordance with process  50 . 
     The processes described herein are not limited to the specific embodiments described herein. For example, the processes are not limited to the specific processing order of  FIGS. 3 and 4 . Rather, any of the blocks of  FIGS. 3 and 4  may be re-ordered, combined, repeated or removed, as necessary, to achieve the results set forth above. 
     The system described herein is not limited to use with the hardware and software described above. The system can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. 
     Method steps associated with implementing the system can be performed by one or more programmable processors executing one or more computer programs to perform the functions of the system. All or part of the system can be implemented as, special purpose logic circuitry (e.g., an FPGA (field programmable gate array) and/or an ASIC (application-specific integrated circuit)). 
     Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. Elements of a computer include a processor for executing instructions and one or more memory devices for storing instructions and data. 
     Elements of different embodiments described herein may be combined to form other embodiments not specifically set forth above. Other embodiments not specifically described herein are also within the scope of the following claims.