© 2014 Nature America, Inc. All rights reserved.
nature methods | ADVANCE ONLINE PUBLICATION | ?
RL deconvolution algorithm and subsequently extended it to
multiple-view geometry, yielding
d ( )
( ) (
1( )( ) ( )
where ψ r(ξ) denotes the deconvolved image at iteration r and
φv(xv) denotes the input views, both as functions of their respec-
tive pixel locations ξ and xv, whereas P(xv|ξ) denotes the indi-
vidual PSFs (Supplementary Note 1). Equation (1) denotes a
classical RL update step for one view; equation (2) illustrates
the combination of all views into one update of the deconvolved
image (Supplementary Video 1). In contrast to the maximum-
likelihood (ML) EM5,13 that combines RL updates by addition,
equation (2) suggests a multiplicative combination. We proved
that equation (2), just as the ML-EM5,13 algorithm, converges
to the ML solution (Supplementary Note 2). The ML solution
is not necessarily the correct solution if disturbances such as
noise or misalignments are present in the input images (Fig. 2).
Importantly, previous extensions to multiple views5–10 assume
individual views to be independent observations (Supplementary
Fig. 2). Assuming independence between two views implies
that by observing one view, nothing can be learned about the
other view. We showed that this independence assumption is not
required to derive equation (2) (Supplementary Note 3). Our
solution represents, to our knowledge, the first complete
derivation of RL multiview deconvolution based on probability
theory and Bayes’ theorem.
As we do not need to consider views to be independent, we
next asked whether the conditional probabilities describing the
relationship between two views can be modeled and used to
improve convergence behavior (Supplementary Figs. 1 and 3 and
Supplementary Notes 3 and 4). If we assume that a single pho-
ton is observed in the first view, the PSF of this view and Bayes’
theorem can be used to assign a probability to every location
in the deconvolved image having emitted this photon (Fig. 1b).
On the basis of this probability distribution, the PSF of the second
view directly yields the probability distribution describing where
to expect a corresponding observation for the same fluorophore
in the second view (Fig. 1b). Thus, we argue that it is possible
to compute an approximate image (‘virtual’ view) of one view
from another view provided that the PSFs of both views are
known (Fig. 1c).
We used these virtual views to perform intermediate
update steps at no additional computational cost, decreasing
Stephan Preibisch1–4, Fernando Amat2,
Evangelia Stamataki1, Mihail Sarov1, Robert H Singer2–4,
Eugene Myers1,2 & Pavel Tomancak1
Light-sheet fluorescence microscopy is able to image large
specimens with high resolution by capturing the samples from
multiple angles. multiview deconvolution can substantially
improve the resolution and contrast of the images, but its
application has been limited owing to the large size of the data
sets. here we present a bayesian-based derivation of multiview
deconvolution that drastically improves the convergence time,
and we provide a fast implementation using graphics hardware.
Modern light-sheet microscopes1–3 acquire images of large,
developing specimens with high temporal and spatial reso-
lution typically by imaging them from multiple directions
(Fig. 1a). Deconvolution uses knowledge about the optical system
to increase spatial resolution and contrast after acquisition.
An advantage unique to light-sheet microscopy, particularly
the selective-plane illumination microscopy (SPIM) variant, is
the ability to observe the same location in the specimen from
multiple angles, which renders the ill-posed problem of decon-
volution more tractable4–10.
Richardson-Lucy (RL) deconvolution11,12 (Supplementary
Note 1) is a Bayesian-based derivation resulting in an iterative
expectation-maximization (EM) algorithm5,13 that is often cho-
sen for its simplicity and performance. Multiview deconvolution
has previously been derived using the EM framework5,9,10; how-
ever, the convergence time of the algorithm remains orders of
magnitude longer than the time required to record the data. We
addressed this problem by deriving an optimized formulation of
Bayesian-based deconvolution for multiple-view geometry that
explicitly incorporates conditional probabilities between the
views (Fig. 1b,c and Supplementary Fig. 1) and combining it
with ordered subsets EM (OSEM)6 (Fig. 1d and Supplementary
Fig. 2), achieving substantially faster convergence (Fig. 1d–f).
Bayesian-based deconvolution models images and point spread
functions (PSFs) as probability distributions. The goal is to estimate
the most probable underlying distribution (deconvolved image)
that best explains all observed distributions (views) given their
conditional probabilities (PSFs). We first rederived the original
1Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany. 2Janelia Farm Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia,
USA. 3Department of Anatomy and Structural Biology, Albert Einstein College of Medicine, Bronx, New York, USA. 4Gruss Lipper Biophotonics Center, Albert Einstein
College of Medicine, Bronx, New York, USA. Correspondence should be addressed to S.P. (email@example.com) or P.T. (firstname.lastname@example.org).
Received 8 July 2013; accepted 6 MaRch 2014; published online 20 apRil 2014; doi:10.1038/nMeth.2929
© 2014 Nature America, Inc. All rights reserved.
? | ADVANCE ONLINE PUBLICATION | nature methods
the computational effort approximately twofold (Fig. 1d and
Supplementary Note 4). The multiplicative combination (equa-
tion (2)) directly suggests a sequential approach, wherein each RL
update (equation (1)) is directly applied to ψ r(ξ) (Supplementary
Fig. 2 and Supplementary Note 5). This sequential scheme is
equivalent to the OSEM6 algorithm and results in a 13-fold
decrease in convergence time. This gain increases linearly with the
number of views6 (Fig. 1d and Supplementary Fig. 4). To further
reduce convergence time, we introduced ad hoc simplifications
(optimizations I and II) for the estimation of conditional probabil-
ities that achieve up to 40-fold improvement compared to decon-
volution methods that assume view independence (Fig. 1d–f,
Supplementary Figs. 4 and 5 and Supplementary Notes 6 and 7).
The new algorithm also performs well in the presence of noise
and imperfect PSFs (Supplementary Figs. 6–8). If the input views
show a very low signal-to-noise ratio (SNR), atypical for SPIM,
the speedup is preserved, but the quality of the deconvolved image
is reduced. Our Bayesian-based derivation does not assume a
specific noise model, but it is in practice robust with respect to
Poisson noise, which is the dominating source of noise in
light-sheet microscopy acquisitions.
We compared the performance of our method with that of
previously published multiview deconvolution algorithms5–10 in
terms of convergence behavior and run time on the central process-
ing unit (CPU) (Figs. 1e,f and 2d and Supplementary Figs. 4b
and 9a,b). For typical SPIM multiview scenarios consisting of
around seven views with a high SNR, our method requires seven-
fold fewer iterations and is at least threefold faster than OSEM6,
scaled gradient projection (SGP)8 and maximum a posteriori
with Gaussian noise (MAPG)7. At the same time our optimiza-
tion is able to improve the image quality of real and simulated
data sets compared to MAPG7 (Fig. 2e,f and Supplementary
Fig. 9c–h). A further speedup of threefold and reduced mem-
ory consumption is achieved by using our CUDA (Compute
Unified Device Architecture) implementation (Supplementary
Fig. 10g). Moreover, our approach is capable of dealing with
partially overlapping acquisitions typical in multiview imaging
(Supplementary Fig. 10 and Online Methods).
In order to evaluate our algorithm on realistic three-dimensional
(3D) multiview image data, we simulated a ground-truth data set
resembling a biological specimen (Fig. 2a). We next simulated
image acquisition in a SPIM microscope from multiple angles by
applying signal attenuation across the field of view, convolving
the data with the PSF of the microscope, simulating the
multiview optical sectioning and using a Poisson process to generate
the final pixel intensities (Fig. 2b and Online Methods). We
deconvolved the generated multiview data (Fig. 2c) using our
algorithm with and without regularization (regularization adds
smoothness constraints to the deconvolution process to achieve a
more plausible solution for this ill-posed problem) and compared
the results to the content-based fusion14 and the MAPG7 decon-
volution (Fig. 2d–f). Our algorithm reached optimal reconstruc-
tion quality faster (Fig. 2d) and introduced fewer artifacts than
MAPG7 (Fig. 2e,f and Supplementary Videos 2 and 3). Tikhonov
regularization15 was required to converge to a reasonable result
under realistic imaging conditions (Fig. 2d–f).
We applied our deconvolution approach to multiview SPIM
acquisitions of Drosophila melanogaster and Caenorhabditis
Efficient Bayesian based
Efficient Bayesian based (OSEM)
Optimization I (OSEM)
Optimization II (OSEM)
Number of views
Computation time of
Java implementations (s)
2468 10 12
Number of views
Computation time (s)
Bayesian based (OSEM, Java)
Eff. Bayesian based (OSEM, Java)
Optimization I (OSEM, Java)
Optimization II (OSEM, Java)
Number of views
Number of iterations
Observed view 1
Observed view 2
‘Virtual’ view 2
(in 1% agarose,
movement in x,y,z
rotation around y)
to each pixel
(e.g., pixel location = 4)
figure ? | Principles and performance. (a) Basic layout of a light-sheet microscope capable of multiview acquisitions. (b) Illustration of ‘virtual’ views.
A photon detected at a certain location in a view was emitted by a fluorophore in the sample; the PSF assigns a probability to every location in the
underlying image having emitted that photon. Consecutively, the PSF of any other view assigns to each of its own locations the probability to detect a
photon corresponding to the same fluorophore. (c) Example of an entire virtual view computed from observed view 1 and the knowledge of PSF 1 and PSF 2.
(d) Convergence time of the different Bayesian-based methods. We used a known ground-truth image (supplementary fig. 5) and let all variations converge
until they reached precisely the same quality. The increase in computation time for an increasing number of views of the combined methods (black) is due to the
fact that with an increasing number of views, more computational effort is required to perform one update of the deconvolved image (supplementary fig. 4)
(e) Convergence times for the same ground-truth image of our Bayesian-based methods compared to those of other optimized multiview deconvolution
algorithms5–8. The difference in computation time between Java implementations and IDL implementations, OSEM6 and SGP8, results in part from
nonoptimized IDL code. (f) Corresponding number of iterations for our algorithm and other optimized multiview deconvolution algorithms.
© 2014 Nature America, Inc. All rights reserved.
nature methods | ADVANCE ONLINE PUBLICATION | ?
elegans embryos (Fig. 3a–e). We achieved a substantial increase
in contrast as well as resolution with respect to the content-based
fusion14 (Fig. 3b and Supplementary Fig. 11); only a few iterations
were required and computation times were typically in the range of
a few minutes per multiview acquisition (Supplementary Table 1).
We applied the deconvolution to a four-view acquisition of a fixed
C. elegans in larval stage 1 (L1) expressing GFP-tagged lamin
(LMN-1–GFP) labeling the nuclear lamina and stained for
DNA with Hoechst (Fig. 3f,g). Multiview deconvolution
improved contrast and resolution compared to the input data
and enabled unambiguous segmentation of nuclei in problem-
atic areas of the nervous system16 (Supplementary Videos 4–7).
The algorithm dramatically improved multiview data acquired
with OpenSPIM17 (Supplementary Fig. 12), and its effi-
ciency makes it applicable to spatially large multiview data sets
(Supplementary Fig. 13) and to processing of long-term time
lapses from the Zeiss Lightsheet Z.1 (Supplementary Videos 8–11
and Supplementary Table 1).
Multiview deconvolution increases contrast in SPIM data after
acquisition, complementary to hardware-based contrast enhance-
ment achieved by digital scanned laser light-sheet microscopy
(DSLM-SI)18 (Supplementary Fig. 14). Moreover, multiview
deconvolution produced superior results when comparing an
acquisition of the same sample with SPIM and a two-photon
microscope (Supplementary Fig. 15). Finally, the benefits
of the multiview deconvolution approach are not limited to
SPIM, as illustrated by the deconvolved multiview spinning disc
confocal microscope acquisition of a C. elegans in L1 stage14
(Supplementary Fig. 16).
A major obstacle for widespread application of deconvolution
approaches to multiview light-sheet microscopy data is the lack of
usable and scalable multiview deconvolution software. Therefore,
we implemented our fast converging algorithm as a Fiji19 plug-in
taking advantage of ImgLib2 (ref. 20) and GPU processing (http://
fiji.sc/Multi-View_Deconvolution). The only free parameter of
the method that must be chosen by the user is the number of
iterations for the deconvolution process. We facilitate this choice
by providing a debug mode allowing the user to inspect all inter-
mediate iterations and identify optimal trade-off between qual-
ity and computation time. Our Fiji19 implementation synergizes
with other related plug-ins and provides an integrated solution
for the processing of multiview light-sheet microscopy data of
Methods and any associated references are available in the online
version of the paper.
Note: Any Supplementary Information and Source Data files are available in the
online version of the paper.
We thank T. Pietzsch (Max Planck Institute of Molecular Cell Biology and Genetics
(MPI-CBG)) for helpful discussions, proofreading and access to his unpublished
software; N. Clack, F. Carrillo Oesterreich and H. Bowne-Anderson for discussions;
N. Maghelli for two-photon imaging; P. Verveer (MPI Dortmund) for source
View 1 View 1 SNR = 25
Input for deconvolution (7 views)
View 1View 3
Common for all views
Simulated ground truth
Lateral (view 1)
MAPGOpt. II (–reg)Opt. II (+reg)
Lateral (view 1)e
Cross-correlation with ground truth
Opt. II (OSEM)
Opt. II (OSEM), � = 0.004
Opt. II (–reg)
Opt. II (+reg)
figure ? | Deconvolution of simulated 3D multiview data. (a) Left, 3D rendering of a computer-generated volume resembling a biological specimen.
The red outlines mark the wedge removed from the volume to show the content inside. Right, sections through the generated volume in the lateral
direction (as seen by the SPIM camera, top) and along the rotation axis (bottom). (b) Same slices as in a with illumination attenuation applied (left),
convolved with a PSF of a SPIM microscope (center) and simulated using a Poisson process (right). The bottom right panel shows the unscaled simulated
light-sheet sectioning data along the rotation axis. (c) Slices from views 1 and 3 of the seven views generated from a by applying processes pictured
in b and rescaling to isotropic resolution. These seven volumes are the input to the fusion and deconvolution algorithms quantified in d and visualized
in e. (d) Cross-correlation of deconvolved and ground-truth data as a function of the number of iterations for MAPG7 and our algorithm with and without
regularization (reg). The inset compares the computation (comp.) time. (Both algorithms were implemented in Java to support partially overlapping
data sets; supplementary fig. ?0). (e) Slices equivalent to c after content-based fusion14 (first column), MAPG7 deconvolution (second column), our
approach without regularization (third column) and with regularization15 (fourth column; Tikhonov15 regularization parameter l = 0.004). (f) Areas
marked by boxes in a,c,e at higher magnification. Note the increased artificial ring patterns in MAPG7.
© 2014 Nature America, Inc. All rights reserved.
4 | ADVANCE ONLINE PUBLICATION | nature methods
code and helpful discussions; M. Weber for imaging the Drosophila time series;
S. Jaensch for preparing the C. elegans embryo; J.K. Liu (Cornell University)
for the LW698 strain; S. Saalfeld for help with 3D rendering; P.J. Keller for
supporting F.A. and for the DSLM-SI data set; A. Cardona for access to his
computer; and Carl Zeiss Microimaging for providing us with the SPIM prototype.
S.P. was supported by MPI-CBG in P.T.’s lab, Howard Hughes Medical Institute
(HHMI) in E.M.’s lab and the Human Frontier Science Program (HFSP) Postdoctoral
Fellowship LT000783/2012 in R.H.S.’s lab, with additional support from US
National Institutes of Health (NIH) GM57071. F.A. was supported by HHMI in
P.J. Keller’s lab. E.S. and M.S. were supported by MPI-CBG. R.H.S. was supported
by NIH grants GM057071, EB013571 and NS083085. E.M. was supported by
HHMI and MPI-CBG. P.T. was supported by The European Research Council
Community’s Seventh Framework Program (FP7/2007-2013) grant agreement
260746 and the HFSP Young Investigator grant RGY0093/2012. M.S., E.M. and
P.T. were additionally supported by the Bundesministerium für Bildung und
Forschung grant 031A099.
S.P. and F.A. derived the equations for multiview deconvolution.
S.P. implemented the software and performed all analysis, and F.A. implemented
the GPU code. E.S. generated and imaged the H2Av-mRFPruby fly line.
M.S. prepared, and M.S. and S.P. imaged, the C. elegans L1 sample. S.P. and P.T.
conceived the idea and wrote the manuscript. R.H.S. provided support
and encouragement, E.M. and P.T. supervised the project.
comPeting financiaL interests
The authors declare no competing financial interests.
reprints and permissions information is available online at http://www.nature.
1. Huisken, J., Swoger, J., Del Bene, F., Wittbrodt, J. & Stelzer, E.H.K.
Science ?05, 1007–1009 (2004).
2. Keller, P.J., Schmidt, A.D., Wittbrodt, J. & Stelzer, E.H.K. Science ???,
3. Truong, T.V., Supatto, W., Koos, D.S., Choi, J.M. & Fraser, S.E.
Nat. Methods 8, 757–760 (2011).
4. Swoger, J., Verveer, P., Greger, K., Huisken, J. & Stelzer, E.H.K.
Opt. Express ?5, 8029–8042 (2007).
5. Shepp, L.A. & Vardi, Y. IEEE Trans. Med. Imaging ?, 113–122 (1982).
6. Hudson, H.M. & Larkin, R.S. IEEE Trans. Med. Imaging ??, 601–609
7. Verveer, P.J. et al. Nat. Methods 4, 311–313 (2007).
8. Bonettini, S., Zanella, R. & Zanni, L. Inverse Probl. ?5, 015002 (2009).
9. Krzic, U. Multiple-View Microscopy with Light-Sheet Based Fluorescent
Microscope. PhD thesis, Univ. Heidelberg (2009).
10. Temerinac-Ott, M. et al. IEEE Trans. Image Process. ??, 1863–1873 (2012).
11. Richardson, W.H. J. Opt. Soc. Am. 6?, 55–59 (1972).
12. Lucy, L.B. Astron. J. 79, 745–754 (1974).
13. Dempster, A.P., Laird, N.M. & Rubin, D.B. J. R. Stat. Soc. Series B Stat.
Methodol. ?9, 1–38 (1977).
14. Preibisch, S., Saalfeld, S., Schindelin, J. & Tomancak, P. Nat. Methods 7,
15. Tikhonov, A.N. & Arsenin, V.Y. Solutions of Ill-Posed Problems (Winston, 1977).
16. Long, F., Peng, H., Liu, X., Kim, S. & Myers, E. Nat. Methods 6, 667–672
17. Pitrone, P.G. et al. Nat. Methods ?0, 598–599 (2013).
18. Keller, P.J. et al. Nat. Methods 7, 637–642 (2010).
19. Schindelin, J. et al. Nat. Methods 9, 676–682 (2012).
20. Pietzsch, T., Preibisch, S., Tomancak, P. & Saalfeld, S. Bioinformatics ?8,
Position on line (µm)
Intensity normalized over line
20 µm 100 µm
10 µm20 µm 100 µm
figure ? | Application to biological data. (a) Comparison of reconstruction results using content-based fusion14 (top row) and multiview deconvolution
(bottom row) on a four-cell–stage C. elegans embryo expressing a PH domain–GFP fusion marking the membranes. Dotted lines mark plots shown
in b; white arrowheads mark PSFs of a fluorescent bead before and after deconvolution. (b) Line plot through the volume along the rotation axis
(yz, contrast locally normalized). This orientation typically shows the lowest resolution of a fused data set in light-sheet acquisitions, as all input views
are oriented axially (supplementary fig. ??). SNR is substantially enhanced; arrowheads mark points illustrating increased resolution. (c,d) Cut planes
through a blastoderm-stage Drosophila embryo expressing His-YFP in all cells. (e) Magnified view on parts of the Drosophila embryo. The left panel is a
view in lateral orientation of one of the input views; the right panel shows a view along the rotation axis characterized by the lowest resolution. (f,g)
Comparison of deconvolution and input data of a fixed L1 C. elegans larva expressing LMN-1–GFP (green) and stained with Hoechst (magenta). (f) Single
slice through the deconvolved data set; arrowheads mark four locations of transversal cuts shown below. The cuts compare two orthogonal input views
(0°, 90°) with the deconvolved data. No input view offers high resolution in this orientation approximately along the rotation axis. (g) The left box in
the first row shows a random slice of a view in axial orientation (worst resolution). The second row shows a view in lateral orientation (best resolution).
The third row shows the corresponding deconvolved image. The right boxes each show a slice through the nervous system. The alignment of the C.
elegans L1 data set was refined using nuclear positions (Online Methods). The C. elegans embryo (a,b) and the Drosophila embryo (d,e) are each one time
point of a time series (none of the other time points is used in this paper). The C. elegans L1 larva (f,g) is an individual acquisition of one fixed sample.
© 2014 Nature America, Inc. All rights reserved.
Derivations and proof. The efficient Bayesian-based multi-
view deconvolution is an extension of the classical Richardson-
Lucy11,12 deconvolution, which is based on probability theory and
Bayes’ theorem. We rederive the single-view Bayesian-based
deconvolution and extend it to multiple views (Supplementary
Note 1), and prove the convergence of our new derivation to
the maximum-likelihood solution (Supplementary Note 2).
We show that the Bayesian-based multiview deconvolution
can be derived without assuming independence of the input
views (Supplementary Note 3) and that the conditional prob-
abilities can subsequently be incorporated into the derivation
using ‘virtual’ views (Fig. 1c, Supplementary Figs. 1 and 2 and
Supplementary Note 4). Finally, we discuss further optimizations
(Supplementary Notes 5 and 6) and perform extensive bench-
marks and comparisons (Supplementary Figs. 4–9 and 17 and
Supplementary Note 7).
Multiview registration and PSF estimation. Prerequisite for
multiview deconvolution of light-sheet microscopy data are
precisely aligned multiview data sets and estimates of point spread
functions (PSFs) for all views. We exploit the fact that for the
purposes of registration we include subresolution fluorescent
beads into the rigid agarose medium in which the specimen is
embedded. The beads are initially used for multiview registration
of the SPIM data14 and subsequently to extract the PSF for each
view for the purposes of multiview deconvolution. We average
the intensity of PSFs for each view for all the beads that were
identified as corresponding during registration, yielding a precise
measure of the PSF for each view under the specific experimental
condition. This synergy of registration and deconvolution ensures
realistic representation of PSFs under any imaging condition.
Alternatively, simulated PSFs or PSFs measured by other means
can be provided as inputs to the deconvolution algorithm.
Multiview deconvolution and other optical sectioning micros
copy. In order to better characterize the gain in resolution and
contrast of multiview deconvolution, several experiments and
comparisons were performed. We compared a SPIM multiview
acquisition to a single-view two-photon microscopy acquisition of
the same sample (Supplementary Fig. 15). The fixed Drosophila
embryo stained with Sytox green was embedded in agarose and
first imaged using a 20×/0.5-NA (numerical aperture) water-
dipping objective in the Zeiss SPIM prototype. After acquisition
the agarose was cut, and the same sample was imaged using a
two-photon microscope and a 20×/0.8-NA air objective. The
data sets were aligned using the fluorescent beads visible in both
the SPIM and two-photon acquisitions. The SPIM data set was
reconstructed using content-based fusion14 and multiview decon-
volution and was compared to the two-photon stack as well as
the Richardson-Lucy single-view deconvolution11,12 of the
two-photon acquisition (Supplementary Fig. 15). Although two-
photon microscopy is able to detect more photons in the center
of the embryo, the multiview deconvolution shows substantially
better resolution and coverage of the sample.
Multiview deconvolution can principally be applied to any
optical sectioning microscope that is capable of sample rota-
tion (Supplementary Fig. 16). We acquired a multiview data
set using spinning disc confocal microscopy and a self-built
rotational device14. We compared the quality of one individ-
ual input stack with the multiview deconvolution and the RL
single-view deconvolution11,12 of this stack. Although one view
completely covers the sample, it is obvious that the multiview
deconvolution clearly improves the resolution compared to the
single-view deconvolution (Supplementary Fig. 16d).
Gain in resolution due to multiview deconvolution. To be able
to quantify the gain in resolution, we analyzed images of fluores-
cent beads embedded in agarose (Supplementary Fig. 11). We
extracted all corresponding fluorescent beads from seven input
views, after multiview fusion14 and after multiview deconvolu-
tion. Comparing the input views and the multiview fusion, it
becomes apparent that the multiview fusion14 reduces resolution
in all dimensions except compared to the axial resolution of a
single input view. On the other hand, the multiview deconvolution
increases resolution in all dimensions compared to the multiview
fused data. The multiview deconvolution achieves almost iso-
tropic resolution in all dimensions comparable to the resolution
of each input stack in the lateral direction.
Partially overlapping multiview data sets. In practical multi-
view deconvolution scenarios, where large samples are acquired,
individual views often cover only some parts of the sample
(Fig. 3c–e and Supplementary Figs. 9 and 12–15). The sequential
update strategy (OSEM6) intrinsically supports partially overlap-
ping data sets as it allows updating only parts of the deconvolved
image using subsets of the input data. It is, however, necessary to
achieve a balanced update for all pixels of the deconvolved image
(Supplementary Fig. 10a–f).
Therefore, a weight image wv(ξ) is computed for each input
view. It consists of a blending function returning 1 in central parts
of a view; close to the boundaries, weights are decreasing from
1 to 0 following a cosine function and thus avoiding artifacts at
image borders. By default, the sum of all weights for each pixel
over all views is normalized, Σv ∈Vwv(ξ) = 1, providing a balanced
update of all pixels (Supplementary Fig. 10a,b). For each sequen-
tial update v ∈V contributed by one view v, the weight at every
pixel location defines the fraction of the Richardson-Lucy11,12
update that is applied to the deconvolved image
1( ) ( ) ( )
Normalizing the sum of weights to 1 is, however, equivalent
to not using OSEM6 in terms of performance (Supplementary
Fig. 10f). In order to benefit from the OSEM6 speedup, the weights
have to be summed to values greater than 1. At the same time,
individual weights for each view must be smaller or equal to 1
as the Bayesian-based iterative deconvolution becomes unstable
otherwise. The OSEM6 speedup that can be achieved is therefore
dependent on the coverage of the deconvolved image by input
views (Supplementary Fig. 10b–f). Choosing this number too
high will lead to an uneven deconvolution, i.e., some parts of the
sample will be more deconvolved than others (Supplementary
Fig. 10b–d). In most cases the minimal number of overlapping
views (Supplementary Fig. 10c) will provide a reasonable trade-off
between speedup and uniformity. Some areas close to the boundaries
© 2014 Nature America, Inc. All rights reserved.
of the output image might still be less deconvolved in case they
map to areas in the input views that are subject to the cosine
blending function. However, those areas close to the boundaries
in the input views typically contain only background.
In order to facilitate the choice of a reasonable number of
overlapping data sets for a given acquisition, the Fiji19 plug-in
offers the option to output an image containing the number
of contributing views at every pixel in the deconvolved image
(Supplementary Fig. 10e). This also gives hints on how to adjust
the imaging strategy regarding the number of views, size of stacks
and their overlap. Please note that for smaller or more trans-
parent specimens, data sets are usually completely overlapping
(Fig. 3a,b,f,g and Supplementary Fig. 16).
Simulation of SPIM data sets. We simulate a 3D ground-truth
data set that resembles a biological object such as an embryo
or a spheroid (Fig. 2a). The simulated multiview microscope
rotates the sample around the x axis, attenuates the signal, con-
volves the input, samples at lower axial resolution and creates
the final sampled intensities using a Poisson process (Fig. 2b).
Finally, the acquired 3D image is rotated back into the orienta-
tion of the ground-truth image, which corresponds to the task
of multiview registration in real multiview data sets and results
in the final input stacks for the multiview deconvolution
(Fig. 2c). Computation time is measured until the maximal cross-
correlation to the ground truth is achieved. Note that manual
stopping of the deconvolution at earlier stages can reduce noise
in the deconvolved image and optimize computation time.
To simulate the biological object, we use ImgLib2 (ref. 20) to
draw a 3D sphere consisting of many small 3D spheres that have
random locations, size and intensity. We simulate at twice the
resolution of the final ground-truth image and downsample the
result to avoid artificial edges.
An initial rotation around the x axis orients the ground truth-
image so that the virtual microscope can perform an acquisition.
However, every transformation of an image introduces artifacts
owing to interpolation. Although on a real microscope this initial
transformation is performed physically and thus does not intro-
duce imaging artifacts, it is required for the simulation. To avoid
the situation where artifacts are present in only the simulated
views and not the ground-truth image (Fig. 2a), the ground-truth
image is also rotated by 15° around the rotation axis of the simu-
lated multiview microscope, i.e., all simulated input views are
rotated by (n + 15)° around the x axis.
The signal degradation along the light sheet is simulated using
a simple physical model of light attenuation21. With an initial
amount of laser power (or number of photons), the sample will
absorb a certain percentage of photons at each spatial location,
depending on the absorption rate (δ = 0.01) and the probability
density (intensity) of the ground-truth image (Fig. 2b).
To simulate excitation and emission PSFs as well as light-sheet
thickness, we measured effective PSFs from fluorescent beads of a
real multiview data set taken with the Zeiss SPIM prototype and a
40×/0.8-NA water-dipping objective. The attenuated image is sub-
sequently convolved with a different PSF for each view (Fig. 2b).
To simulate the reduced axial resolution, we sampled every third
slice in the axial (z) direction and every pixel in lateral direction (xy).
This corresponds to the anisotropy of a typical multiview acqui-
sition (Supplementary Table 1). The sampling process for each
pixel is an individual Poisson process, with the intensity of the
convolved pixel being its average (Fig. 2b).
To align all simulated views, we first scaled them to an isotropic
volume and then rotated them back into the original orientation
of the ground-truth data (Fig. 2c). Linear interpolation was used
for all transformations.
Nucleibased registration of C. elegans. In order to achieve a
good deconvolution result, the individual views must be registered
with very high precision. To achieve that, we match fluorescent
beads that are embedded into the agarose with subpixel accu-
racy14. However, in C. elegans during larval stages, the cuticle itself
acts as a lens, refracting the light sheet, which results in a slight
misalignment of data inside the specimen. We therefore apply a
secondary alignment step, which identifies corresponding nuclei
in between views using redundant geometric local descriptor
matching, and from that estimate an affine transformation model
for each view correcting for the refraction due to the cuticle. The
algorithm works similarly to the bead-based registration14 and is
implemented in Fiji19 as a plug-in called “descriptor-based series
registration” (S.P., unpublished software).
Implementation details. The simulation of multiview data
(Fig. 2) and the 3D rendering (Fig. 2a) are implemented in
ImgLib2 (ref. 20). The source code for the simulation is avail-
able as Supplementary Software 1; links to the current source
code hosted on GitHub are available in the “readme” file and in
Supplementary Note 8.
The multiview deconvolution is implemented in Fiji19 using
ImgLib2 (ref. 20). Performance-critical tasks are the convolutions
with the PSFs or the compound kernels. They are implemented
using Fourier convolutions, and an alternative implementation
of Fourier convolution is provided for the GPU. Note that it is
currently not possible to implement the entire pipeline on the
GPU owing to the limited size of graphics card memory. All
significant parts of the implementation including per-pixel opera-
tions, copy and paste of blocks and the fast Fourier transform
are completely multithreaded to allow maximal execution
performance on the CPU and GPU. The source code is available
as Supplementary Software 2; links to the GitHub repository
containing the current source code versions are listed in the
“readme” file and in Supplementary Note 8. Please note that an
updated version of the multiview deconvolution is already shipped
within Fiji. To simply use the deconvolution, building the source
code is not required; an updated Fiji19 is sufficient.
The GPU implementation based on CUDA alternatively executes
the Fourier convolution on Nvidia hardware. The native code is
called via Java Native Access. The source code and precompiled
libraries for CUDA5.5 for Windows 64 bit and CUDA5.0 for
Linux 64 bit are available as Supplementary Software 3. Note
that for Windows the DLL has to be placed in the Fiji directory;
for Linux, in a subdirectory called lib/linux64; and that the
current version of the Nvidia CUDA driver needs to be installed
on the system.
The native CUDA code is platform dependent. If the provided
precompiled libraries do not work, make sure you have the current
Nvidia CUDA driver (https://developer.nvidia.com/cuda-
downloads) installed and the Nvidia samples are working. If
Fiji19 still does not recognize the Nvidia CUDA capable devices,
© 2014 Nature America, Inc. All rights reserved. Download full-text
compile the CUDA code from source. You can use CMAKE, which
is set up to compile the code platform independently. Alternatively,
it can be compiled using the following command under Linux:
nvcc convolution3Dfft.cu --compiler-options ‘-fPIC’ -shared -
lcudart -lcufft -I/opt/cuda5/include/ -L/opt/cuda5/lib64 -lcuda
-o libConvolution3D fftCUDAlib.so
FIJI plugins. The multiview deconvolution is integrated
into Fiji19 (http://fiji.sc/). Please make sure to update Fiji19 before
running the multiview deconvolution. The typical workflow
consists of three steps.
1. Run the bead-based registration on the data (http://fiji.sc/
2. Perform a simple average multiview fusion in order to define
the correct bounding box on which the deconvolution should be
3. Run the multiview deconvolution using either the GPU
or the CPU implementation (http://fiji.sc/Multi-View_
Detailed instructions for the individual plug-ins can be found
on their respective Fiji wiki pages, summarized on this page
http://fiji.sc/SPIM_Registration. Note that owing to the script-
ing capabilities of Fiji, the workflow can be automated and exe-
cuted on a cluster (http://fiji.sc/SPIM_Registration_on_cluster).
An example data set is available for download: http://fiji.sc/SPIM_
21. Uddin, M.S., Lee, H.K., Preibisch, S. & Tomancak, P. Microsc. Microanal.
?7, 607–613 (2011).