Report

Image restoration by deconvolution Volker Bäcker Montpellier Rio Imaging http://www.mri.cnrs.fr/ Pierre Travo IFR3 Giacomo Cavalli Frederic Bantignies Patrice Mollard Nicole Lautrédou-Audouy Jean-Michel Poulin [email protected] Overview ➲ ➲ Part 1 ● introduction ● what is deconvolution ? ● how does it work ? ● when should it be used ? Part 2 ● what are the parameters to know and care about for image restoration by deconvolution? fluorescence microscopy specimen has to be in focal distance ● ● to image 3d specimen move focal plane through specimen ● creating stack of slides ● ● fluorescence microscopy specimen marked with dye that emists light of one wavelength while being stimulated by light of another wavelength ● Microscope types ●widefield ●confocal ●two photon ● whole specimen bathed in light image is constructed point by point to keep out out-of-focus light two photons needed to stimulate emission, similar effect as confocal Example: 2d widefield Image from microscope After deconvolution (same levels) Immunostaining on whole mount drosophila Embryo Using an antibody against a nuclear protein Example 3d confocal Image from microscope After deconvolution Example: time series 2 photon Image from microscope After deconvolution The aquired image is not the „real“ image ➲ Images are degraded due to the limited aperture of the objective ➲ Deconvolution can be used to get an image nearer to the real object ● ➲ by using knowledge of the imaging process and the properties of the microscope Deconvolution can be used for all kinds of fluorescence microscope images: ● 2D, 3D, time series, widefield, confocal, 2 photon Sources of image degradation ➲ Noise ➲ Blur ● ➲ Scatter ● ➲ Can be handled by image restoration random distribution of light due to heterogenous refrection index within specimen Glare ● random distribution of light that occurs within the optical train of the microscope Causes of image degradation Noise ➲ Geben Sie eine Zusammenfassung der momentanen Situation Causes of image degradation Noise ➲ Where does the noise come from ? random fluctuations in the signal intensity ● ● ● variation of the incident photon flux interfering signals from electronic system of the captor device Causes of image degradation Blur Before restoration After restoration Causes of image degradation Blur ➲ Where does the blur come from ? ● contributions of out-of-focus light to the imaging plane ● diffraction ● a result of the interaction of light with matter ● diffraction is the bending of light as it passes the edge of an object How does deconvolution work ➲ Image restoration Get rid of noise ● ● assume random noise with Poisson distribution ● remove it Get rid of blur ● ● Compute real image from sample ● by applying a model of how the microscope degraded the image deconvolution Point Spread Function ➲ Point spread function (psf) ● Model of how one point is imaged by microscope ● Experimental ● aquired by taking an image of „point like objects“ - beads ● Alternatevely, point like object present in the acquired image itself can be usedf. Theoretical ● ● computed from the microscope and captor parameters Convolution (Faltung) ➲ aquired image = real image convolved with psf ➲ Convolution is an integral that expresses ● amount of overlap of functions as g is shifted over f. i x f x' g x x ' dx' i(x) : aquired image f(x) : object function g(x) : point spread function ● N pixel => O(N*N) operations to compute it Fourier Transform (FT) F f x e i2 x dx Signal can be represented as sum of sinoids ● FT transforms from spacial to frequency domain ● Convolution theorem i x f x' g x x ' dx' <=> i(x) : aquired image f(x) : object function g(x) : point spread function I F G I fourier transform of i F fourier transform of f G fourier transform of g * Object function Fourier transform (FT) FT can be computed in O(n * log n) psf inverse FT Object function convolved with psf FT Deconvolution i x f x' g x x ' dx' <=> I F G ➲ Deconvolution: find object function f for given image i and psf g ➲ Unfortunatly it is not practicable to compute I G G has zeros outside certain regions ● ● Setting F zero for these would create artefacts In practice there is noise ● ● ➲ F N/G would amplify noise I F G N It's not possible to reconstruct the real object function Deconvolution algorithms ➲ Solution Find an algorithm that computes a function f' so that ● ● f' estimates f as good as possible ● works in the presence of noise ➲ Different deconvolution algorithms exist ➲ In general best for fluorescent microscopy: ● (Classical) Maximum Liklihood Estimation - MLE Maximum Likelihood Estimation ➲ Tries to optimise f' iteratively ➲ The basic principal is (but there's more to it) ➲ g(i|j) : psf - the fraction of light from true location j that is observed in pixel i Fraction of light from pixel j that hit other pixels f new , j f old , j g i j g j k f old , k ii i k Richardson and Lucy R-L Iteration Fraction of light from other pixels that hit pixel j 0,3 0,2 1 A B C D 0,2 0,1 6 psf 5 1 Numerator 2 1 C3 + 0.1 C4 + 0.2 B3 3 Denominator: realign my light to me get rid of foreign light that hit me 3 4 4 3 1 C3 + 0.3 C4 + 0.2 B3 4 image 5 * [5*1 / (5*1 + 0.3*4 + 0.2*6) + 0,1*4 /(5*1 + 0.3*4 + 0.2*6) + 0,2*6/(5*1 + 0.3*4 + 0.2*6)] 5 * [5 / 7.4 + 0.4/7.4 + 1.2/7.4] 5 * [(5 + 0.4 + 1.2)/7.4] 5 * [6.6 /7.4] 5 * 0.891891 4.459459 fraction of light lost f new , j f old , j g i j g j k f old , k ii i k New estimate last estimate aquired image last estimate fraction of light from others Summary and conclusions 1 ✔ image from microscope is degraded ✔ it contains noise and blur ✔ blur can be described as a convolution of object function and psf ✔ ✔ ➔ ➔ image nearer to the object function can be obtained by image restoration yielding higher resolution and better contrast MLE is a deconvolution algorithm approriate for fluorescent microscope images imaging process is not finished finished without deconvolution do it whenever high quality images are needed Image restoration in practice Many deconvolution software packages are commercially available They use various types of deconvolution algorithms In addition to these algorithms, they might incorporate other imaging tools, such as filters of different kinds. Moreover, different types of algorithms may introduce or not some « assumptions » concerning the image sent to restoration. In general, it is important to test the software. One basic « rule of thumb » is also that the restoration should respect the acquired image in terms of objects visible and of their relative intensity. Objects « appearing », « disappearing » or changing relative intensity with respect to neighboring structures are diagnostic of problems. These problems might be due to the setting of relevant parameters or, in the worst case, of poor quality of the software Image restoration using the huygens2 software from SVI ➲ ➲ http://www.svi.nl/ - website of Scientific Volume Imaging (SVI) It is the software used at the Institute of Human Genetics Relevant parameters in deconvolution Setting Microscope parameters ➲ microscope type ● widefield and multipoint confocal ● work with ccd camera ● single point confocal and two photon ● work with photomultiplier ● ➲ different point spread functions if you don't know ● Ask your imaging facility and look at the specifications of your microscope Microscope parameters ➲ Numerical aperture ● measure of ability to gather light and resolve fine specimen detail at a fixed object distance ● higher magnification doesn't yield higher resolution, higher NA does ➲ Maximal value written on objective ➲ Can't be larger than the the refractive index n of the medium NA n sin Sampling theorem ● Imaging converts an anlog signal into a digital signal When converting an analog signal into a digital signal the sampling theorem applies ● Nyquist-Shannon sampling theorem “the sampling interval must not be greater than one-half the size of the smallest resolvable feature of the optical image” ● sampling at nyquist rate means using exactly this interval ● sampling interval is the pixel size in our image x 4 NA Undersampling and oversampling under sampling loss of information ●aliasing artefacts ● over sampling higher computation times and storage requirements ●longer acquisition times, photobleaching. ● under sampling example. An object of a given shape (dashed line) can be interpreted as a different shape (thick line) if too few points are acquired along any of the x,y,z axes Changing the Numerical Aperture (NA) for widefield / two photon ➲ huygens2 allows under/oversampling within a range ➲ at the borders of this range deconvolution can be done but results are not good ➲ In this case better results when “lying” about NA i i x 0.5 i x x 1.2 x nyquist sample size ➲ if sampling size not in range change NA x 4 NA Microscope parameters ➲ Excitation and emission wavelength ➲ fluorescent dye absorbs light of one wavelength and emits light of another wavelength ➲ filter cubes are used to ensure that only light of a wanted wavelength passes. exitation and emission wavelengths depend on the cube used ● ● GFP 473, 525 Microscope parameters ➲ The objective magnification used ● determines the pixel size in the image ● ccd camera ● Pixel size = ccd element size / magnification (eventually modified by other parameters) photomultiplier ● ● pixel size depends on resolution and magnification Microscope parameters ➲ ➲ Refractive index n of the objective medium ● oil 1,51500 ● water 1,33810 ● air 1,00000 Should match the refractive index of the sample medium Otherwise ● ● Magnification error in axial direction ● Spherical aberration (psf deteriorates with increasing depth) Microscope parameters ➲ Cmount factor ● adaptor that attaches the camera to the microscope ● might contain additional optic that ● ● changes the overall magnification ● and therefore the pixel size value is 1 if no additional optic present ps ccd obm cmf Microscope parameters ➲ Tube factor ● the tube might contain additional optics to change the tube length ● this changes the overall magnification ● and therefore the pixel size ps ccd obm cmf tf Microscope parameters ➲ sample medium ➲ refractive index n ➲ ● default (all media for example water) 1,33810 ● liquid Vectashield (not polymerized) 1,49000 ● 90-10 (v:v) glycerol - PBS ph 7.4 1,49000 ● prolong antifade limits the NA and therefore the possible resolution 1,4 NA nsin Captor parameters ➲ size of the unitary ccd captor ➲ image sensor of the camera ➲ ● ccd – charge coupled device ● diodes that convert light into electrical charge property of the camera ● Coolsnap 6450 nm ● Micromax 6700 nm For photomultiplier ● the pixel size is asked ● see table in help pages Captor parameters ➲ Binning ➲ take nxn elements as one ➲ more light per pixel ➲ reduces noise ➲ higher signal to noise ratio ➲ lower resolution ps ccd bin obm cmf tf Captor parameters ➲ in case of XZY ● ➲ z step size in case of time series ● time interval Captor parameters ➲ in case of confocal ● pinhole radius ● pinhole ● keep out out of focus light ● pinhole either fixed or adjustable ● Backprojected radius in nm ● ● Size of pinhole as it appears in the specimen plane rb size should match airy disk (2d psf) size 6.66 for LSM510 r phys m system mobj task parameter ➲ Style of processing step ● process image slide by slide ● ● converts stack into time series for processing ● converts result back into stack volume ● ● use 3d information step combined ● ● do step processing ● followed by volume processing with fixed parameters Full restoration parameters ➲ signal/noise ratio ● the ratio of signal intensity to noise intensity ● high noise case can be measured in the image ● Single photon hit intensity ● ● find low intensity voxels from one photon hit – add values – subtract background Max voxel value ● ● value of brightest voxel low noise case ● S N ● single photon hits can´t be seen ● rough guess is sufficient maxVoxelValue singlePhotonHitIntensity Full restoration parameters ➲ background offset ● empty regions should be black ● but contain some light in reality ● subtract mean background to see object clearly Full restoration parameters ➲ number of iterations too low ● f new , j f old , j g i j g j k f old , k ii i k ● too high ● ● optimal restoration not yet achieved ● takes longer to compute ● some signal may be removed Usually between 30-70 Summary and conclusions 2 ➲ deconvolution should be used to obtain high quality images for all kind of fluorescent microscope images ➲ parameters of the imaging system have to be entered to create a model of the image degradation End of presentation [email protected] [email protected] Links participants ➲ Montpellier RIO Imaging http://www.mri.cnrs.fr/ ➲ IFR3 / CCIPE http://www.montp.inserm.fr/ifr3.htm ➲ ➲ IGH http://www.igh.cnrs.fr/ CRIC http://www.iurc.montp.inserm.fr/cric/index.htm literature ● ● Introduction to Fluorescence Microscopy http://www.microscopyu.com/articles/fluorescence/fluorescenceintro.html How does a confocal microscope work? http://www.physics.emory.edu/~weeks/confocal/ ● Two-Photon Fluorescence Microscopy http://www.fz-juelich.de/ibi/ibi-1/Two-Photon_Microscopy/ ● Deconvolution in Optical Microscopy http://micro.magnet.fsu.edu/primer/digitalimaging/deconvolution/deconintro.html Links literature ● Diffraction of Light http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/ ● Image restoration: getting it right http://www.svi.nl/support/talks/GettingItRight.pdf ● Image Restoration in Fluorescence Microscopy http://www.ph.tn.tudelft.nl/Publications/PHDTheses/GMPvanKempen/thesis_kempen.ht ml ● Image restoration in one- and two-photon microscopy http://www.svi.nl/support/talks/Vancouver97.pdf ● Introduction to Convolution http://cnx.rice.edu/content/m11542/latest/ ● An Introduction to Fourier Theory http://aurora.phys.utk.edu/~forrest/papers/fourier/ ● ● A Self Contained Introduction to Fourier Transforms http://www.doc.eng.cmu.ac.th/course/cpe496/notes/fourier.pdf Convolution theorem http://www.fact-index.com/c/co/convolution_theorem.html Links literature ● Three-Dimensional Imaging by Deconvolution Microscopy Article ID meth.1999.0873, available online at http://www.idealibrary.com on IDEAL ● Deconvolution of confocal images of dihydropyridine and ryanodine receptors in developing cardiomyocytes http://www.sfu.ca/~tibbits/research/JAP04.pdf ● Maximum likelihood estimation via the ECM algorithm: A general framework http://www.jbs.agrsci.dk/~lfo/talks/ECM_talk.pdf ● The influence of the background estimation on the superresolution properties of non-linear image restoration algorithms http://www.ph.tn.tudelft.nl/People/lucas/publications/1999/SPIE99GKLV/SPIE99GKLV.pdf ● Numerical Aperture and Resolution http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html ● User guide for Huygens Professional and Deconvolution Recipes ● http://www.svi.nl/download/ Digital Image Sampling Frequency http://www.olympusmicro.com/primer/java/digitalimaging/processing/samplefrequency/index.html ● ● Filter Cubes http://www.olympusmicro.com/primer/techniques/fluorescence/filters.html Filters for fluorescence microscopy http://www.nikon-instruments.jp/eng/products/option/index1.aspx Links literature ● Immersion Media http://www.olympusmicro.com/primer/anatomy/immersion.html ● How Digital Cameras Work http://electronics.howstuffworks.com/digital-camera2.htm ● Pixel Binning ● http://micro.magnet.fsu.edu/primer/digitalimaging/concepts/binning.html CCD Signal-To-Noise Ratio http://www.microscopyu.com/tutorials/java/digitalimaging/signaltonoise/