Ultramicroscopy 160 (2016) 230–238

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Compressed sensing electron tomography of needle-shaped biologicalspecimens – Potential for improved reconstruction fidelity withreduced dose

Zineb Saghi a,n, Giorgio Divitini a, Benjamin Winter b, Rowan Leary a, Erdmann Spiecker b,Caterina Ducati a, Paul A. Midgley a,n

a Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UKb Center for Nanoanalysis and Electron Microscopy (CENEM), Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 6, 91058 Erlangen, Germany

a r t i c l e i n f o

Article history:Received 4 August 2015Received in revised form19 October 2015Accepted 21 October 2015Available online 30 October 2015

Keywords:Electron tomographyIsotropic resolutionCompressed sensingLife science

x.doi.org/10.1016/j.ultramic.2015.10.02191/& 2015 The Authors. Published by Elsevier

esponding authors.ail addresses: saghizineb@gmail.com (Z. Saghicam.ac.uk (P.A. Midgley).

a b s t r a c t

Electron tomography is an invaluable method for 3D cellular imaging. The technique is, however, limitedby the specimen geometry, with a loss of resolution due to a restricted tilt range, an increase in specimenthickness with tilt, and a resultant need for subjective and time-consuming manual segmentation. Herewe show that 3D reconstructions of needle-shaped biological samples exhibit isotropic resolution, fa-cilitating improved automated segmentation and feature detection. By using scanning transmissionelectron tomography, with small probe convergence angles, high spatial resolution is maintained overlarge depths of field and across the tilt range. Moreover, the application of compressed sensing methodsto the needle data demonstrates how high fidelity reconstructions may be achieved with far fewerimages (and thus greatly reduced dose) than needed by conventional methods. These findings open thedoor to high fidelity electron tomography over critically relevant length-scales, filling an important gapbetween existing 3D cellular imaging techniques.& 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

A key challenge in life science microscopy is to image largecellular volumes while maintaining sufficient resolution to iden-tify small features in their original cellular context [1,2]. Withinthe range of techniques employed for this purpose, electron to-mography (ET) offers the highest 3D spatial resolution. Typically,samples are prepared as thin sections, and a series of bright field(BF) transmission electron microscope (TEM) images (projections)are acquired at successive tilt angles. The tilt series of images isthen used as input for 3D reconstruction, often using a weightedbackprojection (WBP) algorithm [3]. Whilst ET has enabled manynew insights into the cellular world, two fundamental limitationsstill hamper attainment of highly accurate and reproducible resultsin an automated fashion.

The first limitation is related to the increase in effective samplethickness during tilt series acquisition: as the sample is tilted byangle θ, the projected thickness of a slab-like section increases bya factor of 1/cos θ. This ultimately leads to a reduction in image

B.V. This is an open access article u

),

contrast in BF-TEM due to an increase in multiple scattering andinelastic scattering, the latter resulting in image blurring due tothe chromatic aberration of the objective lens. Further, the limiteddepth of field (DOF) of the objective lens may lead to regions of thespecimen being out of focus [4]. Reducing the angular incrementbetween projections at high tilt angles, as in the Saxton scheme[5], or adjusting the exposure time so that all projections havesimilar SNR [6], are two acquisition strategies that may help im-prove the overall reconstruction quality, but the usable sectionthickness is still limited. Ellisman and co-workers explored the useof energy-filtered TEM to reduce chromatic blurring, imagingsamples up to 3 mm thick and using an automated most-probableloss technique to choose the position of the energy selecting slit[4]. Alternatively, scanning TEM (STEM) offers advantages such asnear-linearity of contrast and high signal-to-noise ratio (SNR), andthe potential to reduce beam damage, as reported in Refs. [7–9].Leapman and co-workers used BF-STEM to image 1 μm thicksections, achieving a resolution similar to that obtained by con-ventional BF-TEM for sections 300 nm thick [10,11]. Althoughchromatic aberration effects are negligible, STEM images are af-fected by beam divergence through the sample [10] and thus de-creasing the incident convergence angle can lead to an increasedDOF and improved 3D resolution. However, at high tilt angles, thethickness of the section may be larger than the DOF and ultimately

nder the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238 231

beam broadening becomes the key factor limiting resolution.Secondly, the geometry of conventional sample holders and the

limited space within the pole piece gap of the TEM objective lenscan restrict the tilt range to ca. 770° or less. This leads to a‘missing wedge’ of information in Fourier space, and correspond-ing artefacts in the reconstructions [12]. Segmentation of the re-construction often needs to be performed in a manual fashion inorder to extract features that may appear falsely elongated or faint.This can be laborious and more importantly subjective, leading topossible bias and non-repeatability.

Great effort has been expended in the biological and materialsscience communities to develop reconstruction methods that ad-dress the limited-angle tomography problem. Traditionally, usingslab-like specimen geometries, the maximum required and max-imum feasible number of projections is recorded following the so-called Crowther criterion for reconstruction resolution and thedose fractionation approach [3]. WBP reconstructions from data-sets with a typical tilt range of ca. 770° and an increment of 1°–2°shows good delineation of edges, but features with Fourier com-ponents in the missing wedge are highly corrupted and makeautomated segmentation difficult. Iterative reconstruction techni-ques such as simultaneous iterative reconstruction technique(SIRT) [13] or algebraic reconstruction technique (ART) [14] canimprove the reconstruction quality, but missing wedge artefactsare often still evident. Methods have been developed to addressthese limitations, including reconstruction algorithms such asdiscrete ART (DART) [15], regularization using total variation (TV)[16] and second partial derivatives [17], constrained maximumentropy [18] and equally-sloped tomography [19]; and post-pro-cessing routines ranging from anisotropic nonlinear diffusion [20]and bilateral denoising [21] to template matching tools [22]. Pro-mising results have also been reported with more specific priorknowledge incorporated in such methods, as demonstrated in [23]with a shape-based reconstruction technique, and in [24] with adeformable template included in the template matching routine.However, a statistical evaluation performed in [24] showed thatthe amount of information extracted from the tomogram was stillincomplete due to the missing wedge.

Another approach to the problem is to explore alternative ac-quisition strategies and specimen geometries. Dual-axis ET [25],wherein a second, mutually perpendicular tilt series is acquired,helps to minimize reconstruction artefacts by reducing the missingwedge to a ‘missing pyramid’. However, it also implies additionalelectron dose (or, for a fixed total dose, lower dose per image), aswell as challenges in aligning and merging the two tilt series toyield an optimum reconstruction [26]. The ‘missing wedge’ can beeliminated completely if the sample and holder are the correctgeometry to enable a complete 180° rotation. Barnard et al. [27]fabricated a fully rotatable stage in which a glass micropipette, ca.2 mm in diameter, was used as a sample support. However, thetotal sample thickness including the glass was sufficiently largethat a 1 MeV microscope was needed to obtain suitable images. Ina similar vein, Palmer et al. [28] used carbon nanopipettes (ca.400 nm in diameter) attached to standard slot grids for cryo-ET at300 kV. Although this approach overcomes the increase of thick-ness at high tilt angles, as the pipettes were attached to a standardgrid, the tilt range was limited to 145̊. Focused ion beam (FIB)(coupled with scanning electron microscopy, SEM) is used routi-nely in materials science for preparing needle-shaped specimensto enable so-called ‘on-axis’ ET using dedicated tomographyholders (e.g. [29,30]). In the biological context, FIB has been em-ployed mainly for 3D STEM viewing in the FIB-SEM (e.g. [31]) andfor preparation of TEM lamellae [32] as an alternative to ultra-microtomy, avoiding artefacts such as diamond knife compressionand non-flatness of the samples, especially under cryogenic con-ditions [33].

Here, we use the needle geometry for on-axis ET of a resin-embedded biological sample. We demonstrate that the methodyields reconstructions with isotropic resolution and has the po-tential to bridge an important gap between ET of thin sections ca.100 nm thick on the one hand, and FIB-SEM tomography [34] orserial sectioning of samples many microns in thickness [35] on theother. Moreover, the full tilt range dataset is used to show that,with compressed sensing (CS) reconstruction approaches, highfidelity reconstructions can be achieved with undersampled da-tasets, suggesting the possibility to reduce radiation dose.

2. Methods

2.1. Section preparation

The sample analyzed here comprises a stained resin-embeddedportion of the nucleus accumbens shell from a rat brain. A maleSprague-Dawley rat (Harlan Laboratories Srl, S. Pietro al Natisone(UD)) was anesthetized with chloral hydrate (450 mg/kg) in ac-cordance with the European and Italian legislation on the use andcare of laboratory animals (EU Directive 2010/63 of September 22,2010 and Italian D.L. 27.011992, n. 116). Under deep anesthesia, therat was subjected to trans cardiac perfusion with ice-cold PBS(Phosphate Buffered Saline: 137 mM, 2.7 mM KCl, 10 mMNa2HPO4, 2 mM KH2PO4, pH 7.4), 2% paraformaldehyde and 2%glutaraldehyde. After perfusion, the brain was removed and post-fixed overnight in the same fixative used for transcardiac perfu-sion. Coronal brain sections (thickness: 40 μm) of the regions ofinterest, the nucleus accumbens, were cut according to the ratbrain atlas of Paxinos and Watson [36] on ice-cold PBS with a vi-bratome (LeicaVT1000, Leica, Germany), kept in ice-cold PBS. Forelectron microscopy, the brain sections were post-fixed in 1% os-mium tetroxide in distilled water for 2 h, stained overnight at 4 °Cin an aqueous 0.5% uranyl acetate solution, dehydrated in a gradedethanol series, infiltrated with propylene oxide and embedded inSPURR resin.

2.2. FIB-SEM needle-shaped sample preparation

The needle-shaped sample was prepared in a Helios Nanolabdual beam FIB-SEM (FEI company), equipped with a Gaþ ion beamand a field emission gun SEM. The section was placed inside theFIB-SEM and a sequential set of images were analyzed using aslice-and-view approach until a region of interest was found.

A 4 mm thick platinum layer was deposited on the top surface inorder to protect the selected region from implantation of Gaþ ions(Fig. S1(a)). The volume of interest was isolated by FIB milling overan annular area with an external diameter of 8 mm, leaving acentral needle �3 mm wide (Fig. S1(b)). An additional rectangulartrench was milled adjacent to the volume of interest, to allow theion beam to reach the base of the needle and for it to be cut fromthe support. An Omniprobe micro-manipulator was then used toremove the needle, following a lift-out procedure [37], and weld itto a specimen cartridge compatible with the Fischione on-axistomography holder (model 2050). Further annular thinning wascarried out by employing lower currents, down to a value of 20 pAfor a target diameter of ca. 450 nm. Fig. S1(c) shows a low mag-nification view of the needle. Care was taken to ensure that theneedle was parallel to the holder axis. This is crucial for eucentricspecimen rotation, and for automated tracking and focusing. FIB-induced damage to the structural integrity of the sample was notobserved, although a thin layer of Gaþ ions was detected by en-ergy dispersive X-ray spectroscopy, in agreement with [33] (seeFig. S2).

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238232

2.3. Tomography experiment

The boxed region in Fig. S1(c) shows the region of the needlechosen for the ET experiment. An annular dark-field (ADF) STEMtilt series was acquired from �90° to þ90° with 1° increment,using a TITAN³ 80-300 TEM (FEI company) equipped with aSchottky field-emission gun, a post-specimen Cs corrector (CEOS),a Fischione HAADF detector located above the viewing screen anda 2 k�2 k Gatan CCD camera. Imaging conditions were as follows:accelerating voltage¼300 kV, extraction voltage¼4500 V, gunlens¼6, microprobe mode, condenser aperture¼50 mm. A cameralength of 145 mm (corresponding to a detector inner angle of36 mrad) was used, seeking the best trade-off between SNR andmass-thickness contrast. The probe convergence semi-angle was1.5 mrad, corresponding to a diffraction-limited probe size of ca.0.8 nm and a DOF of ca. 650 nm, sufficient to encompass theneedle diameter throughout the full tilt series. The effective spatialresolution in the ADF-STEM images depends on the probe dia-meter at the exit surface of the needle, and is estimated to be 4–5 nm for this experiment, taking into account the beam spreadingfrom multiple elastic scattering [10]. The ADF-STEM tilt series wascollected with Xplore3D software (FEI company), with each imagecomprising 2048�2048 pixels at 16-bit grayscale and with a pixelsize of 0.8 nm. Automated tilting, tracking and focusing wereperformed before each image acquisition. Images were recordedwith a frame time of 10 s, corresponding to a total acquisition timeof 3 h and electron dose of 3.4�106 e�/nm2. The stability of theneedle can be appreciated in the video of the tilt series (movie S5).Following acquisition, the tilt series was re-binned by a factor of2 and aligned by cross-correlation using Inspect3D (FEI company).Weighted backprojection reconstructions were also performedusing Inspect3D.

Supplementary material related to this article can be foundonline at http://dx.doi.org/10.1016/j.ultramic.2015.10.021.

Although a needle provides a more restricted field of view inthe xy plane (perpendicular to the electron beam) compared toconventional single-axis or dual-axis tomography using a slab-likesection, a full tilt range with no missing wedge is accessible andthe near-constant thickness profile of the needle sample enablesacquisition of high quality data across the entire tilt series. There isno loss of resolution at high tilt angles or encroachment of featuresin part of the tilt series leading to truncated projection artefacts(the ‘region-of-interest’ problem) [38].

2.4. Compressed sensing electron tomography (CS-ET) reconstruction

To improve the reliability of the reconstructions from a limitednumber of projections, CS methods [39,40] are explored andcompared to WBP. CS-ET has recently been applied successfully toinorganic materials [41–45], and was shown to be capable ofgenerating high quality tomograms from a limited number ofprojections.

We give here only a brief description of the CS-ET algorithm.The foundation of CS theory and its application to ET can be foundin [42] and references therein.

2.4.1. Principles of CS-ETCS relies on two key principles: (1) sparsity (or compressibility)

of the signal via an appropriate sparsifying transform, wherein thesignal can be well-approximated in a more compact form (i.e. fewcoefficients with nonzero values); and (2) incoherence betweenthe sampling and the sparsifying systems. In the context of CS-ET,acquiring projections around a tilt axis is, according to the Fourierslice theorem, equivalent to radial sampling in the Fourier domain.This form of sampling of Fourier space has been shown to besufficiently incoherent to allow the application of CS to ET [39].

Appropriate choice of the sparsifying transform is signal/object-dependent, with the aim to capture the salient information con-tent of the particular signal using a small number of coefficients.Common transforms are spatial finite-differences (leading to eva-luation of the so-called ‘total variation’ (TV)) and wavelets, andsimply the identity transform if the signal is intrinsically sparse inits native domain. TV-minimization is often suitable for objectsconsisting of homogeneous regions with sharp edges, while pie-cewise smooth signals can be represented sparsely in a waveletdomain.

2.4.2. CS-ET applied to the needle-shaped sampleThe CS-ET implementation used here was performed in MA-

TLAB (MathWorks, Natick, MA) and is described in [42]. Re-construction of the 3D tomogram was performed sequentially onindependent 2D slices along the tilt axis. The images were firstFourier transformed to obtain radial samples of the object in theFourier domain. An initial reconstruction was then obtained fromthe radial Fourier data using the non-uniform fast Fourier trans-form (NUFFT) developed by Fessler and Sutton [46]. In conjunctionwith the NUFFT, the conjugate gradient descent algorithm of Lustiget al. [39] was then used to solve the optimization problem de-fined by:

⎧⎨⎩⎫⎬⎭x x b xarg min

1x

2

2 1λ^ = Φ^ − + Ψ^

( )λ ^ ℓ ℓ

where x̂ is the reconstruction of the true signal x, Φ is the un-dersampled Fourier transform operator, b is the Fourier transformof the acquired tilt series, and Ψ is the chosen sparsifying trans-form. The 1ℓ -norm term in (Eq. (1)) promotes sparsity in thechosen transform domain, and is defined as the sum of the abso-lute values. λ is a Lagrange multiplier that determines the relativeimportance of sparsity in the reconstruction. In essence, the al-gorithm promotes sparsity in the Ψ basis, subject to consistencywith the measured data, which CS theory asserts is a powerfulapproach for recovering the signal.

For the needle-shaped specimen, sparsity was promoted in theimage domain to retrieve the thin curve-like structures, and in thegradient domain for denoising purposes. In this case, (Eq. (1)) canbe written as:

⎧⎨⎩⎫⎬⎭TVx x b x xarg min

2I I TVx

,2

I TV2 1

( )λ λ^ = Φ^ − + Ψ ^ + ^( )λ λ ^ ℓ ℓ

where IΨ is the identity transform, and Iλ and TVλ are weightingparameters that reflect the degree of sparsity imposed in the im-age and gradient domains, respectively. These Iλ and TVλ valueswere chosen by visual assessment of reconstruction quality onselected slices, aiming for the optimal trade-off between mini-mization of reconstruction artefacts and loss of genuine signal. Inparticular, TVλ was carefully chosen: setting TVλ too high wouldreduce the noise and streaking artefacts, but also lead to erroneousflattening of the edges (i.e. loss of high frequency details) andmerging of closely spaced features.

2.5. Visualization and post-processing

Voxel projection views were generated in Avizo Fire (Visuali-zation Sciences Group), while orthoslices through the tomographicreconstruction were produced in ImageJ [47].

Resolution estimation was performed by calculating a FourierShell Correlation (FSC) curve in Bsoft [48]. Tomograms were cal-culated from even and odd members of the �90°:1°:þ90° tiltseries. A mask was then applied to the tomograms to restrict theFSC to the needle region, thus reducing the influence of thebackground (i.e. vacuum). The resolution estimate was determined

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238 233

at a threshold of 0.3. The algorithm implemented in Bsoft is de-scribed in details in [49].

The quality of the reconstructions was also assessed by calcu-lating the peak signal-to-noise ratio (PSNR). This was estimatedusing the SNR plugin provided by the Biomedical Image Group,EPFL, Switzerland (http://bigwww.epfl.ch/sage/soft/snr/). The de-finition of PSNR is given in (Eq. (3)), where r is the reference imageand t is the test image. For the analysis here, r is the reconstructionfrom a fully sampled dataset and t is the reconstruction obtainedfrom datasets with angular undersampling. The higher the PSNR,the higher the fidelity of the reconstruction. A perfect recoverywould lead to a PSNR value of infinity.

⎡

⎣⎢⎢⎢

⎤

⎦⎥⎥⎥

r x y

r x y t x yPSNR 10 log

max ,

, ,3n n

n n10

2

1. 0

10

1 2x y

x y= ⋅ ( ( ))

⋅ ∑ ∑ [ ( ) − ( )] ( )− −

3. Results

3.1. Isotropic ET reconstructions

Fig. 1(a) displays a voxel projection of a WBP reconstruction,where high fidelity 3D structural information is evident, un-corrupted by missing wedge or truncation artefacts. This can beappreciated in the yz and xy orthoslices (b and c) highlighting thepresence of synaptic vesicles with a uniform shape and mi-tochondria with resolved double membranes (inset in (c)). Cross-sectional slices (d) through an excitatory synapse and (e) a mi-tochondrion further illustrate the isotropic retrieval of features

Fig. 1. ADF-STEM tomography of a needle-shaped sample, from a portion of the nuclconstruction from an ADF-STEM tilt series (�90°:1°:þ90°), showing an excitatory synap(where the z direction is parallel to the electron beam at 0̊ sample tilt) highlight some oIsotropic 3D resolution is achieved, as confirmed by the uniform shape of the synaptic vescolor in this figure legend, the reader is referred to the web version of this article.)

with the absence of missing wedge artefacts (slices through theentire 3D reconstruction of the needle, in xy and xz planes, areshown in the movie S6).

In addition, segmentation can be performed more readily androbustly than on reconstructions from limited angle datasets. Toillustrate this, Fig. 2 shows results of automated thresholding usingthe Bernsen method [50] to segment the synaptic vesicle shown inFig. 2(a). When projections spanning the full tilt range are avail-able, the vesicle is reliably segmented with uniform visibility ofthe membranes. If, however, the tilt range is artifically reduced tomimic the restricted tilt range of a conventional slab-like section,the missing wedge of information induces blurring and elongation.Automated segmentation routines then fail to retrieve membraneswhose normals lie in the missing wedge. The continuity of thevesicle is then lost, and manual segmentation with prior knowl-edge about the expected shape would be necessary to attempt tolabel such features – a challenging and subjective task.

Missing wedge artefacts are especially pronounced when seek-ing to image objects that have elongated features perpendicular tothe optic axis. In this case, the features are partially or completelylost due to important Fourier components lying in the missingwedge. This can be appreciated in Fig. 2 by noting how the hor-izontal portion of the postsynaptic membrane (indicated in redinset) becomes faint as the tilt range is reduced. Similar critical lossof information has been demonstrated previously, e.g. concerningCdTe tetrapods [51], block copolymers with cylindrical micro-domains [52], and actin filament networks [24]. Dual-axis tomo-graphy partially, but not entirely, reduces these artefacts [26,51,52].Full tilt range on-axis tomography of such structures within aneedle-shaped specimen, however, completely eliminates them.

eus accumbens shell of a rat brain. (a) Voxel projection rendering of the 3D re-se (*) and a mitochondrion (**). (b) yz, (c) xy and (d,e) xz slices through the needlef the features indicated in (a). The yellow inset in (c) shows resolved lipid bilayers.icles in all three orthogonal directions (b–d). (For interpretation of the references to

Fig. 2. Cross-sectional slices through the reconstructed synapse region obtained from a tilt series with 1° increment and deliberately introduced restricted tilt ranges.(a) Isotropic resolution is achieved with full tilt range on-axis ET. (b–d) Artefacts such as elongation and blurring of a synaptic vesicle (yellow insets) and the reduced contrastof a region of the postsynaptic membrane (red insets) are observed on reconstructions obtained from limited angular ranges of 160°, 140° and 120°, respectively. Localthresholding by Bernsen method (top right insets) successfully segments the full tilt range reconstruction (a), but fails to retrieve the complete synaptic vesicle in the case oflimited angle tomography (b–d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238234

To further illustrate the improvements, a region of the needlecontaining the mitochondrion, with both vertical and horizontalcristae, was selected for additional analysis. Fig. 3 shows a cross-sectional slice from a reconstruction with no missing wedge, andreconstructions using a restricted angular range of 760°. Theanisotropic degradation caused by a limited tilt range is shown bysimulating two different missing wedge directions (see Fig. S3).Horizontal membranes are absent when the missing wedge di-rection is vertical (Fig. 3(b)), vertical membranes are absent whenit is horizontal (Fig. 3(c)), while the reconstruction from the full tiltseries (no missing wedge) retrieves all features (Fig. 3(a)). More-over, closely spaced features that are clearly separated in a full tiltrange reconstruction are erroneously merged in the limited anglereconstructions; see for example the falsely merged features in-dicated by the vertical arrows in the insets of the top images inFig. 3(b,c).

3.2. CS-ET for 3D cellular imaging

In this work, we took advantage of the availability of a full tiltrange experimental dataset to explore compressed sensing (CS)reconstruction approaches, with the aim to improve the fidelity ofthe reconstructions and reduce the total dose without loss ofstructural information. WBP reconstructions from datasets with a

full tilt range but a large tilt increment suffer from severe artefactsand low SNR. Fig. 4 shows orthoslices through the mitochondrion,obtained from a full-range tilt series and with different degrees ofundersampling. Streaking artefacts (also called ‘fanning’ artefacts)are visible in tomograms obtained with 45 (Fig. 4(c)) and 26 pro-jections (Fig. 4(d)), and make the segmentation challenging. Re-constructions from 180 or 90 projections (corresponding to 1° and2° increments, respectively) are visually very similar (Fig. 4(a) and(b), respectively), suggesting that a 2° increment is sufficient whenthe full tilt range is available. This can be appreciated in the auto-mated segmentation of the selected box in Fig. 4(a): the continuityof the membranes is well preserved when datasets with 1° and 2°increments are available, but lost for higher undersampling.

As shown in Fig. 4(a,b) and (e,f), for highly sampled datasets,CS-ET appears to perform similarly to WBP. However, as thenumber of projections is reduced, the inner membranes in the CS-ET reconstructions remain visible and are less affected by streakingartefacts compared to the WBP reconstructions. Moreover, auto-mated segmentation of CS-ET data yielded much improved resultscompared to WBP on the reconstructions from 26 or 45 projec-tions (see insets in Fig. 4(c,d) and (g,h)).

The fidelity of the CS-ET reconstructions can be quantifiedusing the peak-signal-to-noise-ratio (PSNR), with the fully sam-pled reconstruction as a reference (Fig. 5) [53]. Although this is

Fig. 3. The anisotropic effect of the missing wedge direction on feature visibility. Yellow arrows indicate key linear features that are retrieved, while red ones indicate thosethat are not successfully reconstructed according to the orientation of the missing wedge. (a) Isotropic recovery of all lines from the full tilt range acquisition. (b) Orthoslicesthrough the reconstructed mitochondrion where only a 760° portion of the full tilt series has been used, and with the missing wedge (MW) in the z direction. Features lyingpreferentially in the x direction are faint or absent. (c) Orthoslices of a reconstruction with the same tilt range as (b), but the missing wedge of the tilt series lying in the xdirection. Features lying preferentially in the z direction are faint or absent. Additionally, the inset in (c) (top row) highlights features being falsely merged by the blurringinduced by the missing wedge. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238 235

only one of many possible measures of the reconstruction fidelity,it suffices to reinforce the trends clearly visible in Fig. 4: for highlysampled datasets, WBP and CS-ET have a similar PSNR, but as thenumber of projections is reduced, CS-ET consistently achieves vi-sually interpretable reconstructions with high PSNR values. This iskey to permitting reliable segmentation, even when just 26 pro-jections are used for reconstruction.

A reduced number of projections, and therefore total dose, im-plies that using CS-ET type reconstruction algorithms it is nowpossible to characterize samples that have previously been con-sidered too beam sensitive for ET. Interestingly also, spreading thedose over fewer projections may lead to higher fidelity re-constructions using regularization techniques. More generally, inthe context of further reconstruction algorithm development, thefull tilt range datasets possible using a needle sample can be used toempirically evaluate advanced reconstruction algorithms and thelimits in which further post-processing can be robustly applied,such as automated labeling and template matching methods.

4. Discussion

Accurate 3D cellular density maps obtained by ET are critical forsuccessful docking of macromolecular structures derived from

higher resolution imaging techniques, such as single particleanalysis, X-ray crystallography or nuclear magnetic resonance [54].The needle-like geometry offers a way to generate faithful cellularlandscapes with isotropic resolution. The constant thicknessthroughout the tilt series implies that fields of view of a few mi-crons are accessible, potentially including whole cells and orga-nelles. A resolution of 6.3 nm was estimated by Fourier shell cor-relation (Fig. S4), which could be improved by exploring otherimaging conditions for the same sample thickness [10]. Ultimately,there is almost always a compromise between field of view andresolution, according to the Crowther criterion [3]. ET of needle-shaped specimen may be considered as a complementary techni-que to FIB-SEM tomography, which can image larger volumes butwhose spatial resolution is highly anisotropic. Each slice imaged inthe FIB-SEM process has a lateral resolution governed by the SEMoptics and sample interaction; typically 3–4 nm [34], with thepossibility to reach 1 nm [32]. However, slice thicknesses of (atbest) 5–10 nm lead to a depth resolution of 10–20 nm (accordingto Nyquist criterion).

Identifying a region of interest for ET is a challenge in biologyand usually involves correlative light and electron microscopy, andthe screening of many slab-like sections [55]. A similar challenge isfaced when preparing needle samples. One approach to identify a

Fig. 4. Orthoslices through the mitochondrion, reconstructed from a full tilt range acquisition with different degrees of undersampling. The number of projections used isshown on the images. Top row images (a–d) are WBP reconstructions while the bottom row (e–h) show those obtained with CS-ET. For a qualitative comparison of WBP andCS-ET, automated local thresholding by the Bernsen method was applied to the boxed region in (a) (insets). For highly undersampled datasets, the continuity of themembranes is better preserved in the CS-ET reconstructions.

Fig. 5. PSNR for WBP and CS-ET reconstructions as a function of the number ofprojections spanning the full 180° tilt range. The fully sampled (1° increment) re-constructions were used as references.

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238236

buried region of interest would be to follow the correlative TEMand FIB-SEM approach suggested by Hernandez-Saz et al. [56]: athick section can be prepared by FIB-SEM and marked with fea-tures that are visible both in TEM and SEM. The region of interestis then identified by TEM and a needle is subsequently milled byFIB-SEM.

As seen in movie S5, and after comparison of the first and lastimage acquired in the tilt series, little shrinkage (o2%) and beamdamage was observed, even though the dose was not optimizedin this particular experiment. This may be attributed to the con-ductive Gaþ layer acting as a protective and stabilizing shell, andsuggests that higher doses could be employed on FIB-preparedsamples, both at room temperature and in cryogenic conditions[33,57]. The advantages of a similar metallic layer in close proximity

to a biological specimen were reported recently by Russo et al. [58]using gold support films for cryo-microscopy.

Finally, while WBP is the most widely used algorithm in bio-logical ET, we show that CS is capable of producing high fidelityreconstructions even when applied to datasets with significantangular undersampling (i.e. large tilt increment). Further under-sampling may be achievable by spatial low-dose acquisition stra-tegies using the scanning mode. Since CS-ET resolution is depen-dent on fine scale sampling of the projections [59], one approachto speed up the acquisition is to scan the beam to acquire data atonly selected (e.g. randomly chosen) pixel positions while keepinga large frame size (say 2048�2048), and use inpainting algo-rithms to retrieve the full frame [53,60]. In particular, as recentlyshown by some of the authors [60], a dose reduction of 10� ispossible when pixel subsampling is combined with angular sub-sampling and CS reconstruction. We believe this undersamplingapproach will prove to be advantageous for ET experiments inboth life sciences and materials science. In general, using CS ap-proaches and prior knowledge, acquiring relatively few data points(pixels in each image and/or number of projections in a tilt series)but each with relatively high SNR may lead to an improved re-construction compared to the conventional dose fractionationapproach. Most interestingly, templates of macromolecular struc-tures could be used as prior knowledge, effectively performing thereconstruction and docking simultaneously, compared to theclassical post-processing steps of denoising followed by templatematching.

5. Conclusions

In summary, we have shown how needle-shaped specimensoffer a new approach for ET of biological structures without missingwedge artefacts. High fidelity 3D reconstructions with an order ofmagnitude reduction in dose are now achievable using a needlesample geometry combined with CS reconstruction.

Z. Saghi et al. / Ultramicroscopy 160 (2016) 230–238 237

Acknowledgments

R. Marotta is gratefully acknowledged for providing the biologicalsample and giving constructive comments on the manuscript. Wethank J.J. Fernandez for his assistance in the resolution estimation byFSC, and B. Butz for his help with the TEM measurements. The re-search leading to these results has received funding from the Eur-opean Union Seventh Framework Programme under Grant Agreement312483-ESTEEM2 (Integrated Infrastructure Initiative–I3), as well asfrom the European Research Council under the European Union’s Se-venth Framework Programme (FP/2007-2013)/ERC grant agreement291522-3DIMAGE. B.W. and E.S. acknowledge financial support fromthe Deutsche Forschungsgemeinschaft (DFG) within the framework ofthe SPP 1570 as well as through the Cluster of Excellence “Engineeringof Advanced Materials” at the Friedrich-Alexander-Universität Erlan-gen-Nürnberg. G.D. and C.D. acknowledge funding from the ERC underGrant no. 259619 PHOTO EM. B.W. acknowledges the ResearchTraining Group “Disperse Systems for Electronic Applications” (DFGGEPRIS GRK 1161). R.L. acknowledges a Junior Research Fellowshipfrom Clare College, University of Cambridge.

All data accompanying this publication are directly availablewithin the publication.

Appendix A. Supplementary material

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.ultramic.2015.10.021.

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