WO2003090113A1 - Methods and arrangements for biological imaging - Google Patents

Methods and arrangements for biological imaging Download PDF

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Publication number
WO2003090113A1
WO2003090113A1 PCT/SE2003/000643 SE0300643W WO03090113A1 WO 2003090113 A1 WO2003090113 A1 WO 2003090113A1 SE 0300643 W SE0300643 W SE 0300643W WO 03090113 A1 WO03090113 A1 WO 03090113A1
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image
psf
extracting
steps
reconstructing
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PCT/SE2003/000643
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French (fr)
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Jacques Boutet De Monvel
Mats Ulfendahl
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Karolinska Innovations Ab
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Publication of WO2003090113A1 publication Critical patent/WO2003090113A1/en

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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00Image enhancement or restoration
    • G06T5/70Denoising; Smoothing
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00Image enhancement or restoration
    • G06T5/10Image enhancement or restoration using non-spatial domain filtering
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00Image enhancement or restoration
    • G06T5/73Deblurring; Sharpening
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2200/00Indexing scheme for image data processing or generation, in general
    • G06T2200/04Indexing scheme for image data processing or generation, in general involving 3D image data
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/10Image acquisition modality
    • G06T2207/10064Fluorescence image
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/20Special algorithmic details
    • G06T2207/20048Transform domain processing
    • G06T2207/20064Wavelet transform [DWT]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/30Subject of image; Context of image processing
    • G06T2207/30004Biomedical image processing

Definitions

  • the present invention relates generally to the field of image enhancement through signal processing and particularly to determining a point spread function used for deconvolution in 3-dimensional biological imaging.
  • PSF Point Spread Function
  • IRF Impulse Response Functions
  • An active area of imaging for medical and biological purposes is three dimensional (3D) fluorescence microscopy, often utilizing laser scanning confocal microscopes.
  • This kind of microscopy allows one to perform optical sectioning of a specimen without physically cutting it into sections, making it possible to image living cells in three dimensions and with high resolution.
  • the principles of confocal microscopy are described in, "Handbook of Biological Confocal Microscopy", J. Pawley, Plenum Press, New York, 1995. These principles can be briefly described as follows. As in a conventional fluorescence microscope, a laser light beam of a suitable wavelength is focused, by means of an objective lens, into a specimen stained with a fluorescent marker.
  • the emitted light passes through the objective lens a second time, and focus again at some -geometrically conjugate, or confocal - point inside the optical system.
  • This light is then collected by a photomultiplier placed behind a small aperture centred at the point of focus.
  • the purpose of the aperture is to prevent out-of- focus light to reach the photomultiplier. In this way optical sectioning is achieved, i.e. only light originating from a small fluorescence spot surrounding the point of focus inside the specimen is detected.
  • One known limitation of this technique is that, as most of the light reaching the detector is blocked by the aperture, the image receives a small number of photons per pixel and the signal-to-noise ratio is low.
  • two-photon microscopy is based on exciting the fluorescent marker with a two-photon (rather than a one- photon) process ' .
  • a two-photon process As the probability - or cross section - of fluorescent emission by two-photon excitation decreases very rapidly away from the point of focus, this provides a natural optical sectioning without the need for a confocal aperture.
  • This method allows one to perform imaging of living cells deeper into biological tissues, but again the total cross-section of a two-photon process is very small and the signal-to-noise ratio of the resulting images is usually limited.
  • Noise problems can be reduced by processing the images with efficient adaptive denoising algorithms, such as wavelet denoising.
  • This technique requires no specific knowledge of the system's optical characterictics, and it has proven very effective in application to three-dimensional confocal images. The technique is further described in for example, Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl.
  • Deblurring the images preferably by deconvolution typically requires the knowledge of the PSF or IRF of the system.
  • a number of methods of determining the PSF are known in the art.
  • the outcome of deconvolution is very sensitive to mismatches in the gross characteristics of the PSF, such as its size (which corresponds to the system's resolution), and orientation with respect to the optical axis. It is much less sensitive to inaccuracies in finer details, due for example to a smoothing of the images prior to the PSF extraction.
  • test material i.e. beads of well known size and fluorescence
  • the beads are typically of subresolution size and deposited on a slide or immersed inside a gel.
  • Subresolution size is preferred in order to have a point-like source for extracting the PSF.
  • a method of fast image generation is described.
  • This kind of measurement for determining the PSF is time consuming and has an important drawback if applied to images taken inside a thick biological specimen, as it does not allow one to reproduce the typical imaging conditions of the experiments. Indeed, due to the complexity and variability of the samples, even for constant acquisition settings and at low levels of noise, the PSF will vary significantly from one sample to another. By measuring the system's PSF under optimized design conditions, as above described, precise determination may be obtained, but this precision will not be useful if the PSF is overall ill-matched to the conditions of the real imaging experiment.
  • US 5,561,611 teaches a method of image enhancement in confocal microscopy without prior knowledge of the PSF.
  • a Dirac delta function is used as an original estimate of the PSF and through a "blind” iterative deconvolution process in the frequency domain the blur of the image is improved.
  • US 6,229,928 teaches a system and a method of image enhancement in for example confocal microscopy.
  • a "theoretical value" for the PSF is estimated from the wavelength, aperture etc.
  • a spatial filter and a "no-neighbour" algorithm are used for the image deconvolution. The methods are attractive in that they do not require prior knowledge of the PSF, and of use in biological microscopy.
  • the objective problem is to provide a way of performing a deconvolution of a recorded image giving an image of high quality, the method should be experimentally feasible and fast.
  • the method of reconstructing an image comprising the steps of: converting an optical image to electronic signals, extracting a Point Spread Function (PSF) from a naturally occurring object within the received image, and reconstructing the image by deconvolution using the extracted PSF, providing fast reconstruction of the image without the use of external reference objects.
  • PSF Point Spread Function
  • One advantage afforded by the method of invention is that an image can be reconstructed to a high resolution in a comparable fast and convenient way.
  • Another advantage afforded by the invention is that the difficult and sometimes impossible process of introducing external references objects into the specimen can be avoided.
  • Fig. 1 is a schematic drawing of an image processing system used to implement the methods according to the invention
  • Fig. 2 is a flowchart outlining the method according to the invention.
  • Fig. 3 shows a confocal image of the Reissner's membrane lying above the auditory sensory hair cells of the hearing organ, in which A) is the raw image, B is the denoised image, C is the deconvolved with the design PSF, and D is deconvolved with the extracted PSF. 3E shows normalized intensity profiles.
  • Fig. 4 shows a two-channel confocal image showing nerve fibers crossing the tunnel of Corti inside the inner ear, in which.
  • A) is the raw image
  • B) is the denoised image
  • C) is deconvolved with the design PSF
  • D) is deconvolved with the extracted PSF
  • E) and F are detailed views of A), B), C) and D) respectively.
  • Fig. 5 illustrates PSFs, A) extracted PSFs according to the invention and B) design PSFs.
  • FIG. 6 illustrates the use of a PSF obtained by interpolation from a number of sections through a non-point-like structure.
  • FIG 6A shows three-dimensional sections through a confocal image of nerve fibers inside the hearing organ, B) shows the deconvolution with the extracted PSF, C) shows the perpendicular sections and D) the extracted PSF.
  • an imaging system 100 comprising an image device 110, a signal processing unit 120 and a monitoring device 130 allows generation of digital high resolution images of a sample 140.
  • the image device 110 comprises of an optical imaging system with a lens 150, having a focal length /, as a first functional part.
  • the lens 150 collects an optical image of the sample and a detector 160, being a second functional part, converts the optical image to into electronic signals.
  • the electronic signal are received and processed by the processing unit 120.
  • the image device 110 may be of various types and for various imaging purposes, for example a microscope, confocal microscope or camera.
  • Laser scanning microscopes are commercially available, for example the Bio-Rad MRC1024.
  • a suitable lens system is for example Zeiss Achro-plan 40X/0.75.
  • the detector is typically a high resolution CCD or similar devices capable of transforming an optical image to electronic signals with high resolution.
  • the processing unit 120 typically comprises a memory unit 165 for storing image data prior and during the process and a data processor 170 for performing the image processing steps, further described below and means for storing image data on an exchangeable medium for example a CD.
  • the processing unit is connected to the monitoring device 130 for viewing the produced images and may further be connected to devices for printing the image onto a viewable medium.
  • the processing unit may for example be a PC, a workstation or a special purpose computer.
  • the sample 140 does not need to be a detached isolated specimen. Indeed, in real imaging conditions such as 3D deep biological imaging, the object to be imaged is often well inside a thick biological specimen. Hence, the optical signal is strongly affected by the material surrounding the image object. In addition the optical signal is affected by the optical image system itself, in particular the optical characteristics of the lens. In many experimental occasions the digital image must be thoroughly processed, i.e. reconstructed, in order to reveal any useful information. Most reconstruction principles relies on a prior knowledge, or an estimate, of how the optical signal is effected from the sample to the detector, described as a function, e.g. the PSF. Commonly used methods of reconstruction involves deconvolution using the PSF.
  • the extraction of a relevant PSF is not trivial in biological imaging.
  • the inventors of the present invention have, which should be considered as part of the invention, realized that the PSF may by extracted from the image itself. Not, as in the cited prior art by complex processing of the complete image, but rather by using objects naturally appearing in the image as reference objects for extracting the PSF. These natural reference objects will serve the same purpose as the beads in the currently mostly used method of extracting the PSF.
  • the applicability of the method is further demonstrated by the fact that the inventors have realized, and shown, that the structure does not necessarily have to be absolutely point-like to serve as a reference object for the PSF extraction. In fact, structures significantly larger than the resolution can be utilised. This is an observation that significantly simplifies the process of finding a suitable PSF. If prior knowledge of the chosen reference object is available, for example its shape and size this can be utilised to further facilitate the extraction of a suitable PSF.
  • a determination of the PSF obtained by cropping directly from raw images would have a poor signal-to-noise ratio and would lead to an unstable deconvolution. Averaging is not practical here, as it is unlikely to find suitable isolated structures in more than two or three locations within the same image. Instead, a wavelet denoising technique is first applied to the images as described in Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl, and later the PSF extractions and deconvolutions are performed on the denoised images. Small and isolated enough structures are found by inspection, and a simple box cropping was applied to extract the PSF.
  • the cropping procedure consist of selecting, within the denoised image, a suitable box that contains the structure chosen as the reference object for extracting the PSF.
  • the selected box is then cropped out of the denoised image by conventional methods. Care should be taken to use a box size large enough that the structure would not be truncated in a region in which it produces an intensity above the background level.
  • a soft thresholding baseline subtraction
  • This background removal was necessary in order to avoid truncation artifacts when applying deconvolution.
  • the relevant background level was determined by looking at the intensity profile of the PSF along its focal axes, and chosen so that the PSF intensity after thresholding would be zero near the borders of the cropping box.
  • An optical image is received and converted to electronic signals by the detector 160 and the electronic signals are transmitted to and received by the processing unit 120.
  • the image may be denoised, preferably with the wavelet denoising technique.
  • a suitable structure is selected from the image.
  • the PSF is extracted from the selected structure by utilising simple box cropping.
  • the background is removed.
  • the relevant background level is determined from intensity profiles of the PSF along its focal axes.
  • the deconvolution is performed utilising the extracted PSF for reconstruction of the image.
  • the structure selected in step 220 should preferably be as point-like as possible. However, it is in many cases also possible to select and utilize reference objects that for the given resolution have an extension in space and still after the deconvolution step 250 achieve an image of acceptable quality. Examples of objects that could serve as reference objects are nerve fibres and nerve ends commonly found in tissue.
  • prior knowledge of the reference objects could be used for improving the PSF.
  • the prior knowledge of the reference object is in this case used to obtain constraints in size and shape that would be useful to construct a model PSF.
  • the prior knowledge could be an expected size and shape.
  • the prior knowledge is used to model the PSF.
  • a theoretical model describing the PSF in full generality require many parameters and will be difficult to manage, simpler approximate models depending on a few parameters can be designed.
  • a model describing variations in size, and a possible tilt of the PSF with respect to the optical axis of the imaging system can be used.
  • the image of a nerve fibre will typically allow an estimate of the PSF size along one of the axes, and will provide information on the PSF orientation. This information will be used to constrain the parameters of the model.
  • a further embodiment use of the prior knowledge comprises of reconstructing a PSF by performing a constrained interpolation based on one or more sections taken through a selected reference object.
  • the PSF was extracted by interpolation from two perpendicular sections taken through the same structure, here a nerve fiber.
  • the selected structure may differ significantly from a point-like source, each section provides a good approximation to the corresponding section of the true PSF, and therefore the interpolation allows one to obtain a reliable PSF approximation.
  • the searching and selection of a structure, steps 220-225, is preferably performed by manual inspection of the denoised, but otherwise unprocessed image.
  • a user may on the image display on the monitoring device, mark the area in which the selected reference object is found.
  • the process of searching and selecting a suitable reference object may be fully or partly automated. An automation would have to rely on automated image interpretation.
  • the steps in the method according to the invention may be repeated in an iterative process in order to reach an acceptable level of quality of the images:
  • a structure is selected and the extraction of the PSF and the reconstruction of the image are performed.
  • An improvement of the image is achieved, but not to the level expected.
  • the improved image can eventually be used to find and select a reference object that gives a better PSF and hence, after deconvolution using the new PSF, an image of higher quality.
  • the method according to the invention could be advantageously utilized with prior art methods founded on "blind" deconvolution. Such methods typically relie on an initial crude estimate of the PSF, which is refined through iterations. If a PSF extracted with the method according to the invention is used as the initial estimate of the PSF, the process would be considerably more effective and the risk of not finding a solution significantly reduced.
  • the method is preferably implemented by means of a computer program product comprising the software code means for performing the steps of the method.
  • the computer program product is typically executed on the processing unit 120.
  • the computer program is loaded directly or from a computer usable medium, such as a floppy disc, a CD, the Internet etc.
  • a computer usable medium such as a floppy disc, a CD, the Internet etc.
  • extracted PSF PSF extracted according to the invention
  • design PSF PSF extracted with the prior art method utilising beads
  • FIG. 3A shows a confocal image of the Reissner's membrane lying above the auditory sensory hair cells of the hearing organ.
  • FIG. 3B correspond to the denoised image
  • FIG. 3C shows the image deconvolved with the design PSF
  • FIG. 3D show the image deconvolved with the extracted PSF. It should be noted that apart from using different PSFs in the deconvolution, images C and D were processed and displayed in exactly the same way.
  • FIG. 3E the normalized intensity profiles of these four images along the white line shown in FIG. 3A are plotted.
  • the dashed line corresponds to the unprocessed image (3A), the tireted line to the denoised image (3B), the x-marked line to the image deconvolved with the design PSF (3C) and the .-marked solid line corresponds to the image deconvolved with the extract PSF (3D).
  • the increase in effective resolution is visible from image C to image D, and is clearly apparent on the profiles. If assumed that variations caused by artifacts are not significant in C and D, the increase in resolution can be quantified by comparing the frequency bandwidths (FBDW) of the corresponding profiles.
  • FBDW frequency bandwidths
  • FIG. 4 shows a two-channel confocal image showing nerve fibers crossing the tunnel of Corti inside the inner ear.
  • FIG. 4A correspond to the raw image
  • FIG. 4B correspond to the denoised image
  • FIG. 4C shows the image deconvolved with the design PSF
  • FIG. 4B shows the image deconvolved with the design PSF
  • FIGS. 4E,4F,4G and 4H are detail views of 4A,4B,4C and 4D, respectively, in a region of low contrast, showing the process of two branching nerve fibers.
  • FIG 5A shows the PSFs extracted according to the invention from the images of FIG. 3 and 4 (Ei from FIG 3 and E 2r and E 2g from FIG 4).
  • FIG5b shows the corresponding design PSFs (obtained by imaging fluorescent beads in agarose gel). Each PSF is shown in maximum projection along the optical axis (upper square) and along one of the focal axes (lower rectangle image) . Note the significant differences in size and shape between the extracted and the corresponding design PSFs.
  • the ratio between the half-maximum widths (HMW) of the PSFs Ei and Di along the optical axis is 1.6, and about 3 along the focal plane.
  • the HMW ratios between E 2r , E 2g and D r ,D2 g are about 1.2 along the optical axis, and 2 along the focal plane.
  • the extracted PSFs can be considered as smoothed and thresholded approximations of the true in situ PSFs.
  • the structures used for cropping these PSFs (which can be seen in the images at the intersection of the displayed sections) are presumably a bit larger than the system's resolution, as smaller structures emit a signal too low to be really distinguishable from the background.
  • these extracted PSFs are better matched to the images than are the corresponding design PSFs. Indeed, it is evident from FIG. 5 that the extracted PSFs have a significantly larger extenssion in space than the design PSFs.
  • the design PSFs show no appreciable tilt with respect to the optical axis, whereas the extracted PSFs are tilted.
  • FIG. 6 is illustrates the embodiment of the method according to the invention, reconstructing a model of the PSF by a constrained interpolation based on one or more sections taken through a nerve fiber.
  • the image of FIG 6 A shows three- dimensional sections through a confocal image of nerve fibers inside the hearing organ. This is a detail view of a larger image, that has been processed by wavelet denoising (the raw image is not shown).
  • the image of FIG 6B shows the result of a deconvolution with the extracted PSF shown in FIG. 6D. This extracted PSF was obtained by interpolation from two perpandicular sections taken through the nerve fiber seen on the image (the sections are shown in FIG. 6C). Note the clear gain in resolution in the deconvolved image.

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Abstract

The present invention relates to a method and a system of reconstructing an image in 3-dimensional biological imaging. The method of reconstructing an image according to the invention comprises the steps of: converting an optical image to electronic signals, extracting a Point Spread Function (PSF) from a naturally occurring object within the received image, and reconstructing the image by deconvolution using the extracted PSF, providing fast and accurate reconstruction of the image without the use of external reference objects.

Description

Methods and Arrangements for biological imaging
Field of the Invention
The present invention relates generally to the field of image enhancement through signal processing and particularly to determining a point spread function used for deconvolution in 3-dimensional biological imaging.
Background of the invention
In many areas of imaging the use of advanced signal processing is vital for producing images of useful quality. Commonly used techniques for image enhancement comprises use of Point Spread Functions (PSF) or Impulse Response Functions (IRF). These functions are used to describe the blurring due to the optical system's finite resolution, distortions, artifacts, the influence from elements surrounding the object under investigation etc. By determining the PSF (or IRF) and by the use of deconvolution algorithms the image may be reconstructed with a level of quality, regarding for example resolution and sharpness, which constitute a crucial improvement compared with the original non-processed image. However, it is of crucial importance to determine and use a point spread function that correctly describes the optical situation. In practice a determined PSF will always be an approximation to an ideal PSF and to what degree the approximation is acceptable will be dependent on a number of factors, including intended use of the pictures.
An active area of imaging for medical and biological purposes is three dimensional (3D) fluorescence microscopy, often utilizing laser scanning confocal microscopes. This kind of microscopy allows one to perform optical sectioning of a specimen without physically cutting it into sections, making it possible to image living cells in three dimensions and with high resolution. The principles of confocal microscopy are described in, "Handbook of Biological Confocal Microscopy", J. Pawley, Plenum Press, New York, 1995. These principles can be briefly described as follows. As in a conventional fluorescence microscope, a laser light beam of a suitable wavelength is focused, by means of an objective lens, into a specimen stained with a fluorescent marker. The emitted light passes through the objective lens a second time, and focus again at some -geometrically conjugate, or confocal - point inside the optical system. This light is then collected by a photomultiplier placed behind a small aperture centred at the point of focus. The purpose of the aperture is to prevent out-of- focus light to reach the photomultiplier. In this way optical sectioning is achieved, i.e. only light originating from a small fluorescence spot surrounding the point of focus inside the specimen is detected. One known limitation of this technique is that, as most of the light reaching the detector is blocked by the aperture, the image receives a small number of photons per pixel and the signal-to-noise ratio is low. A more recent technique, two-photon microscopy, is based on exciting the fluorescent marker with a two-photon (rather than a one- photon) process'. As the probability - or cross section - of fluorescent emission by two-photon excitation decreases very rapidly away from the point of focus, this provides a natural optical sectioning without the need for a confocal aperture. This method allows one to perform imaging of living cells deeper into biological tissues, but again the total cross-section of a two-photon process is very small and the signal-to-noise ratio of the resulting images is usually limited.
Biological applications of three-dimensional fluorescence microscopy are faced with two main imaging problems: the presence of often important levels of random noise due to a low signal-to-noise ratio, and the blurring due to the optical system's finite resolution. These two problems are all the more acute in applications of confocal and two-photon microscopy, especially when imaging deep inside a thick biological sample. In such cases, the scattering and refraction of light by cells, tissue and other structures surrounding the region of interest in the sample often induce a significant loss in intensity and various distortions in the optical response of the system.
Noise problems can be reduced by processing the images with efficient adaptive denoising algorithms, such as wavelet denoising. This technique requires no specific knowledge of the system's optical characterictics, and it has proven very effective in application to three-dimensional confocal images. The technique is further described in for example, Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl.
Deblurring the images preferably by deconvolution typically requires the knowledge of the PSF or IRF of the system. A number of methods of determining the PSF are known in the art. The outcome of deconvolution is very sensitive to mismatches in the gross characteristics of the PSF, such as its size (which corresponds to the system's resolution), and orientation with respect to the optical axis. It is much less sensitive to inaccuracies in finer details, due for example to a smoothing of the images prior to the PSF extraction.
In US 5,737,456 a method is described using test material, i.e. beads of well known size and fluorescence, for obtaining the PSF. The beads are typically of subresolution size and deposited on a slide or immersed inside a gel. Subresolution size is preferred in order to have a point-like source for extracting the PSF. After the PSF is obtained a method of fast image generation is described. This kind of measurement for determining the PSF is time consuming and has an important drawback if applied to images taken inside a thick biological specimen, as it does not allow one to reproduce the typical imaging conditions of the experiments. Indeed, due to the complexity and variability of the samples, even for constant acquisition settings and at low levels of noise, the PSF will vary significantly from one sample to another. By measuring the system's PSF under optimized design conditions, as above described, precise determination may be obtained, but this precision will not be useful if the PSF is overall ill-matched to the conditions of the real imaging experiment.
US 5,561,611 teaches a method of image enhancement in confocal microscopy without prior knowledge of the PSF. A Dirac delta function is used as an original estimate of the PSF and through a "blind" iterative deconvolution process in the frequency domain the blur of the image is improved. US 6,229,928 teaches a system and a method of image enhancement in for example confocal microscopy. A "theoretical value" for the PSF is estimated from the wavelength, aperture etc. A spatial filter and a "no-neighbour" algorithm are used for the image deconvolution. The methods are attractive in that they do not require prior knowledge of the PSF, and of use in biological microscopy. However, in the area of deep imaging the methods are of limited value since it is at present unknown how to set constrains to the reconstructed PSF in order to make the iterative deconvolution process to converge, at least not in an acceptable number of iterations. Similarly, it is at present not possible to theoretically model the imaging situation in deep imaging, to a degree useful for effective deconvolution.
Summary of the invention
The objective problem is to provide a way of performing a deconvolution of a recorded image giving an image of high quality, the method should be experimentally feasible and fast. In particular, to meet the demand of experimentally feasibility, it is an object of the present invention to avoid using external reference objects, for example fluorescent latex micro-beads, which must be introduced inside the specimen in order to reproduce the conditions of the experiments.
The problem is solved by the method as defined in claim 1 and the computer program product as defined in claims 11 and 12.
The method of reconstructing an image according to the invention, comprising the steps of: converting an optical image to electronic signals, extracting a Point Spread Function (PSF) from a naturally occurring object within the received image, and reconstructing the image by deconvolution using the extracted PSF, providing fast reconstruction of the image without the use of external reference objects.
One advantage afforded by the method of invention is that an image can be reconstructed to a high resolution in a comparable fast and convenient way.
Another advantage afforded by the invention is that the difficult and sometimes impossible process of introducing external references objects into the specimen can be avoided. Brief description of the figures
The features and advantages of the present invention outlined above are described more fully below in the detailed description in conjunction with the drawings where like reference numerals refer to like elements throughout.
Fig. 1 is a schematic drawing of an image processing system used to implement the methods according to the invention;
Fig. 2 is a flowchart outlining the method according to the invention;
Fig. 3 shows a confocal image of the Reissner's membrane lying above the auditory sensory hair cells of the hearing organ, in which A) is the raw image, B is the denoised image, C is the deconvolved with the design PSF, and D is deconvolved with the extracted PSF. 3E shows normalized intensity profiles.
Fig. 4 shows a two-channel confocal image showing nerve fibers crossing the tunnel of Corti inside the inner ear, in which. A) is the raw image, B) is the denoised image, C) is deconvolved with the design PSF, and D) is deconvolved with the extracted PSF, E), F), G) and H) are detailed views of A), B), C) and D) respectively.
Fig. 5 illustrates PSFs, A) extracted PSFs according to the invention and B) design PSFs.
Fig. 6 illustrates the use of a PSF obtained by interpolation from a number of sections through a non-point-like structure. FIG 6A shows three-dimensional sections through a confocal image of nerve fibers inside the hearing organ, B) shows the deconvolution with the extracted PSF, C) shows the perpendicular sections and D) the extracted PSF.
Detailed description of the invention
Embodiments of the invention will now be described with reference to the figures. Referring first to FIG 1 an imaging system 100 comprising an image device 110, a signal processing unit 120 and a monitoring device 130 allows generation of digital high resolution images of a sample 140. The image device 110 comprises of an optical imaging system with a lens 150, having a focal length /, as a first functional part. The lens 150 collects an optical image of the sample and a detector 160, being a second functional part, converts the optical image to into electronic signals. The electronic signal are received and processed by the processing unit 120. The image device 110 may be of various types and for various imaging purposes, for example a microscope, confocal microscope or camera. In the following the method according to the invention will be exemplified in the area of laser scanning confocal microscopy. Laser scanning microscopes are commercially available, for example the Bio-Rad MRC1024. A suitable lens system is for example Zeiss Achro-plan 40X/0.75. The detector is typically a high resolution CCD or similar devices capable of transforming an optical image to electronic signals with high resolution.
Once transformed into digital form, the data corresponding to the image of the sample is processed in the processing unit 120. The processing unit typically comprises a memory unit 165 for storing image data prior and during the process and a data processor 170 for performing the image processing steps, further described below and means for storing image data on an exchangeable medium for example a CD. The processing unit is connected to the monitoring device 130 for viewing the produced images and may further be connected to devices for printing the image onto a viewable medium. The processing unit may for example be a PC, a workstation or a special purpose computer.
It should be understood that the sample 140 does not need to be a detached isolated specimen. Indeed, in real imaging conditions such as 3D deep biological imaging, the object to be imaged is often well inside a thick biological specimen. Hence, the optical signal is strongly affected by the material surrounding the image object. In addition the optical signal is affected by the optical image system itself, in particular the optical characteristics of the lens. In many experimental occasions the digital image must be thoroughly processed, i.e. reconstructed, in order to reveal any useful information. Most reconstruction principles relies on a prior knowledge, or an estimate, of how the optical signal is effected from the sample to the detector, described as a function, e.g. the PSF. Commonly used methods of reconstruction involves deconvolution using the PSF.
As described above the extraction of a relevant PSF is not trivial in biological imaging. The inventors of the present invention have, which should be considered as part of the invention, realized that the PSF may by extracted from the image itself. Not, as in the cited prior art by complex processing of the complete image, but rather by using objects naturally appearing in the image as reference objects for extracting the PSF. These natural reference objects will serve the same purpose as the beads in the currently mostly used method of extracting the PSF.
The principle of using in the image natural occurring objects to extract a PSF is known in the area of astronomy, which is recognized by the inventors. In astronomical imaging point-like sources are often readily available in the form of distant stars, being almost ideal candidates for the extraction of a PSF. The PSF are then typically used for compensating the degradation caused by the turbulent air flow in the earth's atmosphere. The main difference in applying the same principle into the area of microscopic biological imaging is, apart from the area of technology being widely separated, the lack of naturally occurring pointlike sources in a biological specimen. By nature, a biological specimen is more homogenous, and finding well defined isolated point-like structures is not obvious. A method of finding structures suitable for extracting a PSF in a biological specimen will be described below. The applicability of the method is further demonstrated by the fact that the inventors have realized, and shown, that the structure does not necessarily have to be absolutely point-like to serve as a reference object for the PSF extraction. In fact, structures significantly larger than the resolution can be utilised. This is an observation that significantly simplifies the process of finding a suitable PSF. If prior knowledge of the chosen reference object is available, for example its shape and size this can be utilised to further facilitate the extraction of a suitable PSF.
A determination of the PSF obtained by cropping directly from raw images (i.e. the digital but not processed images) would have a poor signal-to-noise ratio and would lead to an unstable deconvolution. Averaging is not practical here, as it is unlikely to find suitable isolated structures in more than two or three locations within the same image. Instead, a wavelet denoising technique is first applied to the images as described in Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl, and later the PSF extractions and deconvolutions are performed on the denoised images. Small and isolated enough structures are found by inspection, and a simple box cropping was applied to extract the PSF. The cropping procedure consist of selecting, within the denoised image, a suitable box that contains the structure chosen as the reference object for extracting the PSF. The selected box is then cropped out of the denoised image by conventional methods. Care should be taken to use a box size large enough that the structure would not be truncated in a region in which it produces an intensity above the background level. A soft thresholding (baseline subtraction) is applied to the cropped image in order to remove the background. This background removal was necessary in order to avoid truncation artifacts when applying deconvolution. The relevant background level was determined by looking at the intensity profile of the PSF along its focal axes, and chosen so that the PSF intensity after thresholding would be zero near the borders of the cropping box.
Once a suitable determination of the PSF is obtained the method of Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl is utilized, i.e. a standard deconvolution algorithm is applied to the wavelet denoised image. The deconvolution algorithm used is the Richardson-Lucy (RL) algorithm, supplemented with a maximum-entropy regularization constraint. Details on this algorithm are expanded in Biophys. J. 80, 2455 (2001) by J. Boutet de monvel, S. Le Calvez and M. Ulfendahl. A padding is applied to the images prior to the deconvolution in order to minimize boundary artifacts. This consisted of adding a number of layers to the six faces of the original 3D-stack, using symmetry with respect to the original boundary layers in order to set the values of the added layers. The number of layers added on each face is determined in such a way that a PSF centered somewhere on the original boundary layers would not appear truncated in the padded image. The codes used for the processing (wavelet denoising and deconvolution) are implemented with the Matlab language (The Mathworks, Inc.) and can be executed on any workstation supporting this language and with enough memory to allow processing of images of the preferred size. As appreciated by the skilled in the art various computer languages as well as different hardware can be utilized. The exact implementation will of course vary on the chosen language, hardware and experimental conditions.
The steps of the method of extracting the PSF from a digital image according to the invention will now be described with reference to the flowchart of FIG 2.
200: An optical image is received and converted to electronic signals by the detector 160 and the electronic signals are transmitted to and received by the processing unit 120.
210: The image may be denoised, preferably with the wavelet denoising technique.
220: The image is searched for small and isolated structures.
225: A suitable structure is selected from the image.
230: The PSF is extracted from the selected structure by utilising simple box cropping.
240: The background is removed. The relevant background level is determined from intensity profiles of the PSF along its focal axes.
250: The deconvolution is performed utilising the extracted PSF for reconstruction of the image.
The structure selected in step 220 should preferably be as point-like as possible. However, it is in many cases also possible to select and utilize reference objects that for the given resolution have an extension in space and still after the deconvolution step 250 achieve an image of acceptable quality. Examples of objects that could serve as reference objects are nerve fibres and nerve ends commonly found in tissue.
If prior knowledge of the reference objects is available it could be used for improving the PSF. The prior knowledge of the reference object is in this case used to obtain constraints in size and shape that would be useful to construct a model PSF. In the examples of the nerve ends the prior knowledge could be an expected size and shape. In one embodiment of the invention the prior knowledge is used to model the PSF. Although a theoretical model describing the PSF in full generality require many parameters and will be difficult to manage, simpler approximate models depending on a few parameters can be designed. As an example a model describing variations in size, and a possible tilt of the PSF with respect to the optical axis of the imaging system, can be used. The image of a nerve fibre will typically allow an estimate of the PSF size along one of the axes, and will provide information on the PSF orientation. This information will be used to constrain the parameters of the model.
A further embodiment use of the prior knowledge comprises of reconstructing a PSF by performing a constrained interpolation based on one or more sections taken through a selected reference object. In the example shown, the PSF was extracted by interpolation from two perpendicular sections taken through the same structure, here a nerve fiber. Although the selected structure may differ significantly from a point-like source, each section provides a good approximation to the corresponding section of the true PSF, and therefore the interpolation allows one to obtain a reliable PSF approximation.
From numerical experiments it can be shown that a significant deconvolution is achieved with the image of a rectangular object of pixel size 5x5x3, when the pixel size of the PSF (as measured from its half-maximum -widths), was about 3.8x3x3.3. Hence the reference object was about 1.3x1.7x0.9 times the resolution in size. When translated into microns for typical confocal imaging conditions, this amounts to using a reference object of size 0.75μmx0.75μmx3.6μm for a resolution of 0.56μmx0.45μmx4.0μm. In practice reference objects up to a size of approximately 1.5 times the resolution can be used for extracting a PSF. This size corresponds to about 5 times the typical diameter (about 100-200 nm) of the beads used in prior art PSF measurements. This shows that there is in fact considerable flexibility in the choice of a "pointlike" reference object.
The searching and selection of a structure, steps 220-225, is preferably performed by manual inspection of the denoised, but otherwise unprocessed image. A user may on the image display on the monitoring device, mark the area in which the selected reference object is found. Alternatively, the process of searching and selecting a suitable reference object may be fully or partly automated. An automation would have to rely on automated image interpretation.
The steps in the method according to the invention may be repeated in an iterative process in order to reach an acceptable level of quality of the images: In a first attempt a structure is selected and the extraction of the PSF and the reconstruction of the image are performed. An improvement of the image is achieved, but not to the level expected. However, the improved image can eventually be used to find and select a reference object that gives a better PSF and hence, after deconvolution using the new PSF, an image of higher quality. The method according to the invention could be advantageously utilized with prior art methods founded on "blind" deconvolution. Such methods typically relie on an initial crude estimate of the PSF, which is refined through iterations. If a PSF extracted with the method according to the invention is used as the initial estimate of the PSF, the process would be considerably more effective and the risk of not finding a solution significantly reduced.
The method is preferably implemented by means of a computer program product comprising the software code means for performing the steps of the method. The computer program product is typically executed on the processing unit 120. The computer program is loaded directly or from a computer usable medium, such as a floppy disc, a CD, the Internet etc. Example of an application the invention
To demonstrate the applicability of the method according to the invention an example of an imaging procedure is given. The images are confocal images of a hearing organ. This realization of the method according to the invention should only be regarded as exemplary and not limiting the scope of the invention.
To verify the method and device according to the invention a series of deconvolutions will be performed on the confocal images using the PSF extracted according to the invention (referred to as extracted PSF) and as a reference PSFs extracted with the prior art method utilising beads (referred to as design PSF ).
FIG. 3A shows a confocal image of the Reissner's membrane lying above the auditory sensory hair cells of the hearing organ. FIG. 3B correspond to the denoised image, FIG. 3C shows the image deconvolved with the design PSF, and FIG. 3D show the image deconvolved with the extracted PSF. It should be noted that apart from using different PSFs in the deconvolution, images C and D were processed and displayed in exactly the same way. In FIG. 3E, the normalized intensity profiles of these four images along the white line shown in FIG. 3A are plotted. The dashed line corresponds to the unprocessed image (3A), the tireted line to the denoised image (3B), the x-marked line to the image deconvolved with the design PSF (3C) and the .-marked solid line corresponds to the image deconvolved with the extract PSF (3D). The increase in effective resolution is visible from image C to image D, and is clearly apparent on the profiles. If assumed that variations caused by artifacts are not significant in C and D, the increase in resolution can be quantified by comparing the frequency bandwidths (FBDW) of the corresponding profiles. Using a common mean-square measure σ (defined empirically for a given profile f(x) by the formula σ =\ k? I F[k) 12d/c / J | F{k) 12dk, where F{k) denotes the Fourier transform of f[x)), it is seen that the FBDW of image 3D (extracted PSF) (along the given line) is about 1.4 times that of image 3C (design PSF), and 2.1 times that of image 3B (only denoised) . FIG. 4 shows a two-channel confocal image showing nerve fibers crossing the tunnel of Corti inside the inner ear. FIG. 4A correspond to the raw image, FIG. 4B correspond to the denoised image, FIG. 4C shows the image deconvolved with the design PSF, and FIG. 4D show the image deconvolved with the extracted PSF according to the present invention. The FBDW of image 4D, computed through the displayed XY projection, appeared only slightly higher than that of image 4C, by less than 1%, i.e. the effective resolutions of the two deconvolved images are not significantly different. However the contrast of image 4C is lowered by artifacts that appear suppressed in the image deconvolved with the method according to the invention, 4D. This is especially noticeable in Figs. 4E,4F,4G and 4H, which are detail views of 4A,4B,4C and 4D, respectively, in a region of low contrast, showing the process of two branching nerve fibers.
FIG 5A shows the PSFs extracted according to the invention from the images of FIG. 3 and 4 (Ei from FIG 3 and E2r and E2g from FIG 4). FIG5b shows the corresponding design PSFs (obtained by imaging fluorescent beads in agarose gel). Each PSF is shown in maximum projection along the optical axis (upper square) and along one of the focal axes (lower rectangle image) . Note the significant differences in size and shape between the extracted and the corresponding design PSFs. The ratio between the half-maximum widths (HMW) of the PSFs Ei and Di along the optical axis is 1.6, and about 3 along the focal plane. The HMW ratios between E2r, E2g and D r,D2g are about 1.2 along the optical axis, and 2 along the focal plane.
The extracted PSFs can be considered as smoothed and thresholded approximations of the true in situ PSFs. The structures used for cropping these PSFs (which can be seen in the images at the intersection of the displayed sections) are presumably a bit larger than the system's resolution, as smaller structures emit a signal too low to be really distinguishable from the background. However these extracted PSFs are better matched to the images than are the corresponding design PSFs. Indeed, it is evident from FIG. 5 that the extracted PSFs have a significantly larger extenssion in space than the design PSFs. In addition, the design PSFs show no appreciable tilt with respect to the optical axis, whereas the extracted PSFs are tilted. Such size and orientation mismatches are very difficult to predict, and they induce much worse effects on the deconvolution than a smoothing and/ or thresholding of the PSF. For both images it is found that the deconvolution using the extracted PSF according to the invention yields images which are better resolved and/ or contains fewer artifacts than the image deconvolved with the design PSF.
FIG. 6 is illustrates the embodiment of the method according to the invention, reconstructing a model of the PSF by a constrained interpolation based on one or more sections taken through a nerve fiber. The image of FIG 6 A shows three- dimensional sections through a confocal image of nerve fibers inside the hearing organ. This is a detail view of a larger image, that has been processed by wavelet denoising (the raw image is not shown). The image of FIG 6B shows the result of a deconvolution with the extracted PSF shown in FIG. 6D. This extracted PSF was obtained by interpolation from two perpandicular sections taken through the nerve fiber seen on the image (the sections are shown in FIG. 6C). Note the clear gain in resolution in the deconvolved image.
Whether structures useful as reference objects are easily found or not, will of course depend upon the sample under study. In the above example, confocal images of the intact inner ear labelled with fluorescence markers, such structures are readily available. Also in many other samples of biological tissue suitable structures can be found. The method according to the invention does, which should be clearly demonstrated in the above example, provide the possibility to also use structures that are not point-like, in order to extract a PSF allowing significant restoration of the image quality.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

Claims
1. Method for biological imaging of reconstructing an image using an imaging system, the method comprising the steps of:
-converting (200) an optical image to electronic signals,
-extracting (230) a Point Spread Function (PSF) describing the optical path of the image,
-reconstructing (250) the image by deconvolution using said PSF, characterized in that the PSF is extracted from a naturally occurring object within the received image.
2. Method according to claim 1, wherein the method comprises the further step, to be taken prior to the step of extracting the PSF, of denoising (210) the image.
3. Method according to claim 2, wherein the denoising of the image is performed with a wavelet denoising technique.
4. Method according to any of claims 1-3, wherein the step of extracting the PSF is proceeded by a step comprising background removal by determining a suitable background level from intensity profiles of the Point Spread Function along its focal axes.
5. Method according to claim 1, wherein the step of extracting the PSF comprises the further steps of:
-searching (220) the received image for naturally occurring isolated structures;
-selecting (225) one or more structures to be used as a reference object for extracting the PSF;
-extracting (230) the PSF by box cropping.
6. Method according to claim 5, wherein the steps of searching and selecting are performed by manual inspection of the image.
7. Method according to claim 5, wherein the steps of searching and selecting are performed by the use of automated image interpretation.
8. Method according to any of claims 5-7, wherein the references object has a size in the order of up to two times the resolution of the imaging system.
9. Method according to any of claims 5-8, wherein the references object is a part of a nerve fibre.
10. Method according to any of claims 5-8, wherein the steps of searching, selecting, extracting and reconstructing are repeated one or more times for further improving the quality of the reconstructed image.
11.A computer program product directly loadable into the internal memory of a processing means within a processing unit for image processing, comprising the software code means adapted for controlling the steps of any of the claims 1-10.
12. A computer program product stored on a computer usable medium, comprising readable program adapted for causing a processing means in a processing unit for image processing, to control an execution of the steps of any of the claims 1-10.
13.A system comprising an image device (110), a signal processing unit (120) and a computer program product according to any of claims 11-12 adapted for performing the steps of the method according to any of claims 1-10.
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