Patent Publication Number: US-11645792-B2

Title: Edge phase effects removal using wavelet correction and particle classification using combined absorption and phase contrast

Description:
RELATED APPLICATIONS 
     This application is a § 371 National Phase Application of International Application No. PCT/US2020/066148, filed on Dec. 18, 2020, now International Publication No. WO 2021/127522 A1, published on Jun. 24, 2021, which International Application claims the benefit under 35 USC 119(e) of U.S. Provisional Application No. 62/951,857, filed on Dec. 20, 2019, both of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Multiphase materials often comprise particles with two or more material phases where the different material phases have different chemistries with possibly insignificant density differences and/or different structures, e.g., amorphous or crystalline states or different crystalline structures. Process control and quality inspection of these materials requires investigation of large volumes of these particles with the requirement of identification of the different material phases, specifically identifying relative volume fractions of different material phases, among other characterization metrics. 
     One example of such a multiphase material are inhalers for drug delivery. Powder formulations for use in dry powder inhalers are commonly composed of a blend of coarse carrier particles, e.g., lactose, and active pharmaceutical ingredient(s), with fine lactose particles sometimes added to improve performance. See Multiscale Tomography: Probing The Nano-, Micro-, And Meso-Scale Resolution Of Inhalation Powder Structure, by Gajjar, et al., RDD Europe 2019 (Vol. 1, pp. 155-168). 
     The distribution of the different particles, particle size and distribution of the different material phases, and particle shape are important metrics for assessing how the drug will be absorbed by the patient and thus critical for quality control. Microstructure equivalency (Q3) concerns characterizing and assessing differences between the same components (Q1) in the same concentration (Q2) under a non-equilibrium state. Its related to the arrangement of matter and/or its state of aggregation. This is important for establishing that the sample will function or perform as expected for its intended use. This often arises in the context of pharmaceutical manufacturing in the context of assessing bioequivalence (BE). This is defined as the absence of a significant difference in the rate and extent to which the active ingredient or active moiety in a pharmaceutical equivalent becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriately designed study. BE must be established in order to infer therapeutic equivalence (TE) between the manufactured pharmaceutical and the corresponding reference pharmaceutical. Important dimensions for inhalers for assessing equivalency include polymorphism, crystal habit, and drug particle size distribution of the drug and the carrier, and particle surface area. 
     Traditionally control and inspection were performed using two dimensional (2D) surface imaging techniques using scanning electron or light microscopy. These approaches have imaging speed limitations for processing a batch of samples. Moreover, the surface scanning approach does not give a good size estimate of the 3D particles, which are usually irregularly shaped. In addition, these analysis modalities can be incompatible with aerosol backed pharmaceuticals possibly under vacuum environments. Moreover, the sample preparation is generally extensive for electron microscopy. For crystallographic/facet information, grain orientation through Electron Backscatter Diffraction (EBSD) can only be done on a single particle or compacted bulk where sample preparation is extensive. 
     SUMMARY OF THE INVENTION 
     The present approach employs X-ray analysis and possibly computed tomography. 3D X-ray tomography can provide very fast volumetric classification of particles by scanning large volumes of a given sample in a single scan. However, the minimal density differences between the material phases pose immense challenges in discerning different material phases since the x-ray absorption contrast between the two material phases is extremely low. When even low density particles are imaged in X-ray tomography at sufficiently high resolution, even on scanners using laboratory-based polychromatic x-ray tubes, the reconstructed image slices demonstrate distinct phase signals or fringes around the edges of the particles that obscure whatever minimal absorption contrast differences exist in the resultant tomography slices. 
     The present approach relies on x-ray microscopy but obtains a classification of different material phases through a combination of image processing involving morphological edge enhancement and possibly resolved absorption contrast differences between the material phases. 
     In examples, it uses a correlative multimodal workflow where the modalities could be phase signals and/or diffraction and/or X-ray fluorescence contrast, and obtains labels for classification of similar looking particles in three dimensions. 
     In mixed formulations consisting of mixed material phase microscopic particles, the classification of individual material phases and quantification of volume fractions of each material phase within the bulk samples has been challenging. In contrast, the present approach takes advantage of the phase fringe information for improved feature detection and absorption information for resolving material phases. Both these unique information sets can be extracted from a single tomography scan, the latter being extracted through algorithmic post-processing. The two datasets are combined to generate the final contrast enhanced datasets which can be directly used for labeling of particles and quantification of volume fractions of different material phases. 
     Moreover, different samples could be used. They could even be frozen. 
     On a related topic, in the past, phase contrast removal via wavelet deconvolution employed idealized representation of a wavelet the process did not describe its practical determination on real samples under realistic conditions. This is similar to the drawing of a line profile and estimation of appropriate values via that line profile. They do not describe how to exactly determine optimal wavelet parameters, either using automated methods, or visually by the user (as described here). 
     Thus, the invention also concerns the determination of parameters for the removal of phase contrast artifacts via a form of wavelet-style deconvolution. This is used for the material separation correlative multi modal workflow. This process includes initially estimating wavelet width via automated measurement on a line profile. Then a multiple scan series is used, scanning over both wavelet amplitude and width for optimal parameter choice. 
     This approach can be performed on a sub-volume, for computational efficiency. The automated strength selection is performed via signal to noise ratio (SNR) maximization. Image denoising can be applied via non-local means. Moreover, automated parameter selection for non-local means filtering via average noise measurements can be used. 
     In general, empirically, the wavelet width must be determined at +/−0.5 pixel, and the wavelet amplitude must be correct to within a factor of 2, although the impact is not the same for under versus over estimation of amplitude. If wavelet amplitude is under-estimated, phase fringes are not effectively removed. If wavelet amplitude is over-estimated the phase artefacts are removed, but noise is also exacerbated. 
     For example, application for this technology is for inhalers, drug delivery, especially to lungs, by attached cancer drugs. This technology can be used to determine whether the drug will be well distributed across the dose. Other applications include: analysis of other low Z materials, such as carbon materials in Li-ion batteries, graphite, rock samples, petrified bugs in amber, any sample with low intrinsic contrast, and then remove phase fringe artifacts. 
     Moreover, the source spectrum could be shaped to enhance the phase fringes. Sample images with different filters could be used, to build different images under different conditions, especially when the effective wavelength of source is an unknown. 
     In general, according to one aspect, the invention features a method for material analysis, wherein the material comprises particles with two or more phases where the different phases have chemistries with insignificant density differences, and amorphous or crystalline states. The method comprises obtaining a set of x-ray projections containing absorption and phase information for reconstruction of a tomography of a sample, obtaining a reconstructed volume dataset, obtaining morphological edge information from the reconstructed volume dataset, and classifying particles within the sample. 
     In some examples, before classifying the particles, differential absorption contrast enhancement is performed on the set of projections a second reconstructed volume dataset is obtained. The volume datasets are then combined. 
     In some examples, combining the volume datasets comprises performing voxel labeling on one of the volume data sets to create a 3D binary mask that is applied to the other volume dataset. 
     The morphological edge information can be obtained using wavelet based filtering, which is used to remove edge phase effects from the reconstructed volume dataset. 
     In a possible automated process, the wavelet based filtering includes estimating wavelet width via automated measurement on a subvolume. This could be achieved by performing a series of wavelet deconvolutions at a variety of strengths and selecting a strength that maximizes signal to noise ratio. 
     In implementations, a report is generated that provides information including volume fraction estimates of the individual phases, aspect ratios of the particles, and/or the particle size distribution within the sample. 
     In some uses, the sample is a pharmaceutical, such as an inhaler. 
     Also, in addition, x-ray fluorescence can be used to detect different elements to create elemental maps. 
     In general, according to another aspect, the invention features an x-ray microscopy system comprising an x-ray imaging system for obtaining the projections and a computer system for applying the described method. 
     In general, according to another aspect, the invention a method for phase contrast removal. This method comprises obtaining projections of a sample with an x-ray microscopy system having a polychromatic x-ray source and performing a series of wavelet deconvolutions at different strengths, assessing image noise to determine a correction strength value. 
     The above and other features of the invention including various novel details of construction and combinations of parts, and other advantages, will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular method and device embodying the invention are shown by way of illustration and not as a limitation of the invention. The principles and features of this invention may be employed in various and numerous embodiments without departing from the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings, reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale; emphasis has instead been placed upon illustrating the principles of the invention. Of the drawings: 
         FIG.  1    is a schematic diagram of an x-ray microscopy system for the volumetric classification of particles in a sample by volume scanning; 
         FIG.  2    is a flow diagram showing a first example of an image processing workflow for 3D reconstruction and processing for multi-phase classification and quantification; 
         FIG.  3    shows another method for 3D reconstruction and processing for multi-phase classification and quantification; 
         FIG.  4    shows another method for 3D reconstruction and processing for multi-phase classification and quantification using diffraction contrast tomography to resolve crystalline material phases; 
         FIG.  5    shows another method for 3D reconstruction and processing for multi-phase classification and quantification using x-ray fluorescence to detect elements and thus elemental maps; 
         FIGS.  6 A and  6 B  are schematic diagrams showing how absorption and phase fringe enhanced images are used to improve particle analysis; 
         FIG.  7 A  is an image and  7 B is a plot of gray value as a function of distance showing the characteristic bright fringe on x-ray microscope image, with distinct bright and dark regions defining phase interfaces across image edges; 
         FIG.  8    is a greyscale histogram of an image exhibiting significant greyscale contrast; 
         FIG.  9    shows a method for determination of the parameters required for phase contrast removal via wavelet deconvolution; 
         FIG.  10 A  is an image and  10 B is a plot of gray value as a function of distance showing the characteristic bright fringe on x-ray microscope image, with distinct bright and dark regions defining material phase interfaces across image edges and fringe width measurement; 
         FIG.  11 A  is an image and  11 B is a plot of gray value as a function of distance showing the accentuated fringes on x-ray microscope image and fringe width measurement; 
         FIG.  12 A  is an image and  12 B is a plot of gray value as a function of distance showing the reduced fringes on x-ray microscope image and fringe width measurement; 
         FIG.  13 A  is an image and  13 B is a plot of gray value as a function of distance showing the blurred edges on x-ray microscope image and fringe width measurement; 
         FIG.  14 A  is an image and  14 B is a plot of gray value as a function of distance showing the incorrect fringe width measurement; 
         FIG.  15 A  is an image and  15 B is a plot of gray value as a function of distance showing the correct fringe width measurement. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The invention now will be described more fully hereinafter with reference to the accompanying drawings, in which illustrative embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. 
     As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Further, the singular forms and the articles “a”, “an” and “the” are intended to include the plural forms as well, unless expressly stated otherwise. It will be further understood that the terms: includes, comprises, including and/or comprising, when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, it will be understood that when an element, including component or subsystem, is referred to and/or shown as being connected or coupled to another element, it can be directly connected or coupled to the other element or intervening elements may be present. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     The present approach generally relates to a correlative, multi-modal imaging technique. It can use diffraction computed tomography for particle and/or material phase separation. It can work even when absolute contrast between particles or material phases is similar. 
       FIG.  1    is a schematic diagram of an x-ray microscopy system  200  for volume scanning a sample  214  to classify including assess and quantify particles in the sample. 
     The microscope  200  generally includes an X-ray imaging system that has an X-ray source system  202  that generates a polychromatic or possibly monochromatic X-ray beam  102  and a stage system  210  with sample holder  212  for holding the sample  214  and positioning it to enable scanning of the sample  214  in the stationary beam  102 . 
     An x-ray detection system  100  detects the beam  102  after it has been modulated by the sample  214 . Currently, the x-ray detection system  100  is as described in U.S. Pat. No. 7,800,072 or PCT International Appl. No. PCT/US2019/059916. 
     This system  200  often includes an x-ray detection system  100  as described in U.S. Pat. No. 7,800,072 or PCT International Appl. No. PCT/US2019/059916, International Publ. No. WO 2020/097111. 
     A base such as a platform or optics table  207  provides a stable foundation for the microscope  200 . The stage system  210  has the ability to position and rotate the sample  214  in the beam  102 . Thus, the stage system  210  will typically include a precision 3-axis stage  250  that translates and positions the sample along the x, y, and z axes, very precisely but over relatively small ranges of travel. This allows a region of interest of the sample  214  to be located within the beam  102 . The 3-stage stage  250  is mounted on a theta stage  252  that rotates the sample  214  in the beam around the y-axis to enable scanning of the sample. The theta stage  252  is in turn mounted on the base  107 . 
     The source system  102  will typically be either a synchrotron x-ray radiation source or alternatively a “laboratory x-ray source” in some embodiments. As used herein, a “laboratory x-ray source” is any suitable source of x-rays that is not a synchrotron x-ray radiation source. Laboratory x-ray source  202  can be an X-ray tube, in which electrons are accelerated in a vacuum by an electric field and shot into a target piece of metal, with x-rays being emitted as the electrons decelerate in the metal. Typically, such sources produce a continuous spectrum of background x-rays combined with sharp peaks in intensity at certain energies that derive from the characteristic lines of the selected target, depending on the type of metal target used. Furthermore, the x-ray beams are divergent and lack spatial and temporal coherence. 
     In one example, source  202  is a rotating anode type or microfocused source, with a Tungsten target. Targets that include Molybdenum, Gold, Platinum, Silver or Copper also can be employed. Preferably a transmission configuration is used in which the electron beam strikes the thin target from its backside. The x-rays emitted from the other side of the target are used as the beam  102 . 
     The x-ray beam generated by source  202  is preferably conditioned to suppress unwanted energies or wavelengths of radiation. For example, undesired wavelengths present in the beam are eliminated or attenuated, using, for instance, energy filters (designed to select a desired x-ray wavelength range (bandwidth)) held in a filter wheel  260 . Conditioning is also often provided by collimators or condensers and/or an x-ray lens such as a zone plate lens. 
     When the sample  214  is exposed to the X-ray beam  102 , the X-ray photons transmitted through the sample form a modulated x-ray beam that is received by the detection system  204 . In some other examples, a zone plate objective x-ray lens is used to form an image onto x-ray detection system  204 . 
     Typically, a magnified projection image of the sample  214  is formed on the detection system  204 . The magnification is equal to the inverse ratio of the source-to-object distance  302  and the source-to-detector distance  304 . 
     Typically, the x-ray source system  202  and the detection system  204  are mounted on respective z-axis stages. For example, in the illustrated example, the x-ray source system  202  is mounted to the base  207  via a source stage  254 , and the detection system  204  is mounted to the base  207  via a detector stage  256 . 
     The operation of the system  200  and the scanning of the sample  214  is controlled by a computer system  224  that often includes an image processor subsystem and a controller subsystem. The computer system is used to readout the optical image detected by the camera  110  of the detection system  204 . The computer system  224 , with the possible assistance of its image processor, accepts the set of images from the detection system  204  associated with each rotation angle of the sample  214  to build up the scan. The image processor combines the projection images using a CT reconstruction algorithm to create 3D tomographic volume information for the sample as described hereinabove. The reconstruction algorithm may be analytical, where convolution or frequency domain filtering of the projection data is combined with back projection onto a reconstruction grid. Alternatively, it may be iterative, where techniques from numerical linear algebra or optimization theory are used to solve a discretized version of the projection process, which may include modeling of the physical properties of the imaging system. 
     From the projection images and/or the 3D tomographic volume information, the computer system  224  analyzes the sample. Phase fringe contrast effects, however, are a major issue in x-ray imaging, especially at high resolutions. They develop due to wave-front interactions caused by differing wave-speeds in differing constituent materials and material phases. These lead to characteristic bright fringes that impede further quantitative image segmentation and analysis and thus classification of particles within the sample. They also impede image denoising algorithms which are designed to work most effectively when applied to images exhibiting clear and distinguishable greyscale contrast. 
     The size of these fringes (measured at the detector) is usually extremely small ion the order of microns), so they typically do not play a significant role when imaging at low resolution, or when using large pixel size detectors (such as flat panel detectors). That said, the imaging architecture used by ZEISS X-ray microscopy and disclosed in U.S. Pat. No. 7,800,072 or PCT International Appl. No. PCT/US2019/059916, published as WO 2020/097111, is particularly susceptible to these artefacts, due to the extremely small pixel size at the scintillator, especially at higher (20×/40×) magnifications. 
     This effect is compounded when imaging at these length scales as it is typical to use small samples and image at low energies (to maximize contrast), and these low energies exhibit a stronger phase fringe contrast effect than the high energies more commonly used when imaging large samples at higher resolution. The magnitude of these effects may be, for low kV or high resolution images, many times the magnitude of any (real) absorption contrast. 
       FIG.  2    shows a first example of a workflow for 3D reconstruction and processing for multi-phase labeling and quantification  100  of the sample  214 , according to the principles of the present invention. It leverages the fringe effects to classify particles by discriminating between particles and their material phases. For example, it could be used to distinguish between lactose particles and active pharmaceutical ingredient particles in a dry powder inhaler. The particles can then be further quantified by other metrics including volume fraction estimates of the individual material phases, aspect ratios of the particles, and the particle size distribution. The workflow is typically performed by the computer system  224  or another computer system based on the projections obtained by x-ray microscopy system  200   
     In more detail, there is an acquisition of a set of projections, which are reconstructed into a high resolution three dimensional (3D) x-ray tomography volume set by the microscopy system  200  in step  110 . Optimally, this set of projections is enhanced by phase fringe contrast. 
     The set of projections are used two ways by the computer system  224 , although it should be noted that both paths are not always needed. 
     First, in step  112 , the morphological edge information is retrieved from the reconstructed volume data. Any phase fringes are preferably reduced along edges. Wavelet based filtering can be used as described below. 
     In parallel, differential absorption contrast enhancement is performed on the set of projections in step  116  by the computer system  224 . Specifically, automated phase retrieval factor estimation is performed on the 2D projection images. The phase is retrieved and enhanced absorption contrast 3D reconstruction is performed on the set of projections. Preferably, the Bronnikov algorithm, Paganin algorithm, modified Bronnikov Algorithm (MBA) or Bronnikov-aided correction (BAC) are used. These methods/algorithms apply corrections to the mixed (absorption and phase fringe contrast) projections to remove the phase fringe signal. These corrected projection images can then be processed many times using a standard filtered backprojection algorithm to obtain reconstructions with lower or no phase fringe artifacts. 
     Volumetric intensity averaging is then performed by the computer system  224  on the absorption contrast 3D reconstruction in step  118 . 
     In parallel, 3D particle separation workflow and 3D watershed segmentation and object splitting are performed in step  120  on the phase corrected volume set  114 . 
     Both the phase-corrected 3D reconstruction  112  and the differential absorption contrast enhanced 3D reconstruction  116  are used in an intensity based object labeling process in step  122  that allows for the classification of the different particles in terms of material phase, i.e., different chemistries and/or different structures, e.g., amorphous or crystalline states or different crystalline structures. From this classification, further statistical measures since as particle size distributions, particle distribution and other metrics can be determined. Then histogram based phase separation is performed in step  124 . 
     Finally, a report is generated in step  126  by the computer system  224  based on the classifications, including providing information such as labeled particles, the volume fraction estimates of the individual material phases, aspect ratios of the particles, and the particle size distribution. 
     It should be noted that when the 2D projection based phase fringe retrieval algorithms  116  are applied alone, there is an undesirable excessive smoothing of features (in Pagannin and Bronnikov case) which leads to blurred edges which can be a considerable drawback when resolving small particles that are close to the resolution limits of the imaging system, or in the accurate particle size estimation. 
       FIG.  3    shows another method for 3D reconstruction and processing for multi-phase labeling and quantification  200  according to the principles of the present invention to classify particles by a computer system. 
     Again, there is an acquisition of a set of projections for use in reconstructing a high resolution three dimensional (3D) x-ray tomography volume set in step  110  by the microscopy system  200 . Optimally, this set of projections is enhanced by phase fringe contrast. 
     The set of projections can be used in two ways by the computer system  224 . 
     Optionally in parallel, a Paganin filter is applied to the set of projections in step  210 . This removes or reduces phase fringes in the projections and/or amplifies the absorption differences in the material phases. 
     The FDK (Feldkamp, Davis and Kress) reconstruction algorithm is preferably used to reconstruct a phase corrected volume data set in step  212 . This is a widely used filtered-backprojection (FBP) algorithm for 3D image reconstruction from circular cone-beam projections such as produced by laboratory x-ray sources. 
     Generally, the resulting phase corrected volume data  114  set will have somewhat fuzzy boundaries but high absorption contrasts for different but similar density particles. 
     First, a FDK reconstruction is also directly performed on the original set of projections in step  214 . A wavelet filter is then applied to the enhanced absorption contrast 3D reconstruction in step  216  to yield an enhanced absorption contrast volume set  217 . This yields a volume set with absorption contrast, no phase fringes, and no fuzzy edges. 3D particle separation is then performed on the enhanced absorption contrast volume set. 
     3D particle separation can then be performed in the enhanced absorption contrast volume set in step  218 . This process is facilitated by reference to the phase corrected volume data set  114  that can be used for voxel labeling. This produces a 3D binary mask  220 . 
     A 3D binary mask  220  is then applied in step  222  on the phase corrected volume data set  114  in a combination operation to improve the images and yield a 3D classified particle volume in step  224 . 
       FIG.  4    shows another method  300  for 3D reconstruction and processing for multi-phase labeling and quantification using diffraction contrast tomography to resolve crystalline between material phases and thus classify different particles to be performed by a computer system. 
     This is similar to the previous example but diffraction contrast tomography is used in step  310  to detect material phases with crystalline structure and the orientation of those structures. 
       FIG.  5    shows still another method for 3D reconstruction and processing for multi-phase labeling and quantification by a computer system. 
     This is similar to the previous examples but x-ray fluorescence  410  is used to detect different elements to create elemental maps. 
       FIGS.  6 A and  6 B  are schematic diagrams showing absorption and phase enhanced images used to improve particle analysis. 
     Wavelet Filtering: 
       FIG.  7 A  is an image and  7 B is a plot of gray value as a function of distance showing the characteristic bright fringe on x-ray microscope image, with distinct bright and dark regions defining material phase interfaces across image edges. 
       FIG.  8    is a greyscale histogram of an image exhibiting significant greyscale contrast. This distribution shows no clear threshold, which would allow for image segmentation and subsequent quantitative analysis between different material phases. 
     It should be noted that these effects in an image are sometimes viewed as desirable, as they allow for easy determination of edge profiles by a manual observer, however they provide extremely challenging images for quantitative segmentation and analysis, and as such are usually viewed as not desirable for these other applications. 
     As these phase fringe contrast effects display theoretically very predictable properties (in the frequency domain) several approaches have been suggested to remove phase fringe effects from images, either in the projection or reconstructed domain (e.g. Paganin phase fringe removal as described in Paganin, et al., “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” published Journal of Microscopy, Vol. 206, Issue 1, pages 33-40 (2002), (https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-2818.2002.01010.x)). Such algorithms are typically developed for the synchrotron community, however, and are either developed for monochromatic x-ray beams, or use a concept of an “effective wavelength” when dealing with polychromatic x-rays. They also require extensive knowledge of the acquisition parameters (particularly sample-detector distance and pixel size) to perform effective phase fringe removal. These parameters are typically extremely challenging to determine for real samples under real conditions. 
     The disclosed workflows allow for the effective determination of these parameters for a lab-based (polychromatic) x-ray source. Specifically the workflow involves the determination of the properties “A” and “W” from the description of phase fringes as edge-convolved wavelets, as Understanding phase contrast artefacts in micro computed absorption tomography described by Wernersson, Erik L G et al, “Understanding Phase Contrast Artefacts in Micro Computed Absorption Tomography.” SSBA Symposium, Proceedings. Swedish Society for Automated Image Analysis (SSBA), 2014 (https://biblio.ugent.be/publication/5721759). 
       FIG.  9    shows a workflow  500  that makes it possible for the computer system to accurately and robustly determine the parameters required for phase contrast removal via wavelet deconvolution. 
     It comprises several steps. 
     First a line profile is drawn across a specific edge in step  510 , and then wavelet width is estimated in step  512  by measuring the distance (along the line profile) between the maximum and minimum portion of the line profile. This is shown in  FIGS.  10 A and  10 B . 
     A small subvolume (for computational speed) is then extracted from the large image in step  514 . 
     A series of wavelet deconvolutions are then performed on this subvolume at a variety of strengths, ranging from 0 to 50, in step  516 . 
     This sequence can be visualized as a “scan series” through the range of parameters by selecting one where the phase contrast is minimized in step  518 . Several examples of different strengths are shown below in  FIGS.  11 A and  11 B and  12 A and  12 B . 
     A too high value of phase fringe strength, while having the effect of removing the phase artefacts, will tend to increase noise in the image. As such, a method for automated optimum deconvolution strength selection is preferred. 
     In more detail, at each point in this scan series, an automated (universal threshold based) segmentation is performed in step  520 . Any of a number of auto-thresholding techniques can be used. Otsu&#39;s method has been tested. 
     Signal to noise ratio is measured in step  522  using this segmentation at each point in the scan series. This is defined as: 
     
       
         
           
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     Where μ 1  and μ 2  are the average greyscale value, and σ 1  and σ 2  are the standard deviations of greyscale values, for material phases 1 and 2, respectively (as defined in the automated segmentation step). 
     At too-low correction values, the phase fringes add to the standard deviation of each phase, decreasing SNR. At too-high correction values, the random noise content of the image is increased, decreasing SNR. There exists, therefore, a correction strength value which maximizes SNR (as defined above), corresponding to the optimum parameter choice which is determined in step  524 . 
     A fringe width scan is then performed (from fringe widths of 0 to 10 pixels), allowing the user to select the exact width value optimal for the image in step  524 . An example of incorrect and correct parameter choice is shown in  FIGS.  13 A / 13 B where the wavelet width is too small and too much high frequency domain information is removed from the images, which blurs the data. The example of  FIGS.  14 A and  14 B  shows the case where the wavelet width is too large and fringes are missed, with wavelet peaks occurring past the phase contrast peaks. The example of  FIGS.  15 A and  15 B  show a correct wavelet width since the image is not blurred but the phase fringes are removed. 
     The previous step can then be repeated to determine the correct strength parameter choice in step  526 . 
     In any case, once the strength parameter has been chosen, denoising may then be performed on the image in step  528 . This is likely to be more effective than when performed on the original image containing phase artefacts, as edge-preserving noise suppression filters commonly assume the image exhibits significant absorption type contrast. 
     Also presented is an algorithm whereby the noise threshold parameter for the Nonlocal means denoising filter is determined as part of the de noise step  528 . See Buades, et al., Non-Local Means Denoising, Image Processing On Line (IPOL), Sep. 13, 2011, http://www.ipol.im/pub/art/2011/bcm_nlm/article.pdf. 
     a. Perform an automated segmentation on the (phase corrected) image. Any of a number of auto-thresholding techniques can be used. Otsu&#39;s method has been tested. 
     b. Determine the average noise level: 
     
       
         
           
             
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     Where σ av  is the inter-label averaged standard deviation and σ 1  and σ 2  are the standard deviation of the greyscale in each of the label regions defined using the automated segmentation step. 
     c. An appropriate noise threshold for the non-local means an algorithm can be assigned as a simple multiple of that value. A value of 1.2×σ av  was determined as empirically appropriate in most cases. 
     Finally, referring back to  FIG.  9   , a final volumetric deconvolution (and subsequent denoising) is performed using the parameters determined by the scan series in step  530 . 
     Generally, it is important to determine parameters for the removal of phase contrast artefacts via wavelet deconvolution and initially estimate wavelet width via automated measurement on a line profile. It is also important to use multiple scan series, scanning over both wavelet amplitude and width for optimal parameter choice. 
     On the other hand, it is not always critical to employ sub-volumes, for computational efficiency. Further, the automated strength selection via SNR maximization is optional, along with image denoising via non-local means. 
     Empirically, the wavelet width must be determined at +/−0.5 pixels, and the wavelet amplitude must be correct to within a factor of 2, although the impact is not the same for under vs over estimation of amplitude. If wavelet amplitude is under-estimated phase fringes are not effectively removed. If wavelet amplitude is over-estimated the phase artifacts are removed, but noise is also exacerbated. 
     While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.