Perceptual Image Quality Metrics Concept in Continuous Scanning 2D

We illustrate the potential of this approach for image quality optimization for a suite of ... To improve the image quality of still pictures, video, ...
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Perceptual Image Quality Metrics Concept in Continuous Scanning 2D LA-ICP-MS Bioimaging Johannes T. van Elteren, Martin Šala, and Vid Simon Šelih Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b00751 • Publication Date (Web): 31 Mar 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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Analytical Chemistry

Perceptual Image Quality Metrics Concept in Continuous Scanning 2D LA-ICP-MS Bioimaging Johannes T. van Elteren,* Martin Šala and Vid S. Šelih Department of Analytical Chemistry, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia ABSTRACT: This work focuses on the structural similarity (SSIM) index as a tool for optimization of the perceived visual image quality obtainable by continuous scanning 2D LA-ICP-MS bioimaging, but also other mass spec imaging techniques may benefit from this approach. This index quantifies the differences between a distorted image and a reference image based on parameters associated with luminance, contrast and noise. Since reference images are not normally available, a protocol was developed to virtually apply distortion-related information introduced by the LA-ICP-MS imaging system to a reference image of one’s choice. Distortion-related information in the form of blur and noise was experimentally retrieved from line scans across a laser milled knife edge on custom-prepared gelatin standards (mimicking proteinaceous biomatrices). Distorted images were generated via computational procedures developed earlier, warranting objective image quality assessment via the SSIM indices. We illustrate the potential of this approach for image quality optimization for a suite of LA-ICP-MS imaging conditions.

The phrase perceptual image quality metrics may seem fancy but in daily life we get constantly confronted with image quality and how to improve it. To improve the image quality of still pictures, video, computer graphics, animation, visual data, etc., an objective image quality assessment strategy is needed, in general a measure that reflects the perceived quality by the human visual system (HVS). Rose1 already proposed an image quality model in the 1940s based on simple criteria for evaluation of imaging devices, stating that a signal can be visually distinguished from the background noise with 100 % certainty for a signal-to-noise ratio (SNR) ≥ 5. The human eye is very sensitive to weak signals and is able to detect them when the contrast is large enough to overcome the random image noise.2 Although the Rose model has been embraced by the medical field for evaluation of clinically acquired images, the model has limited validity in LA-ICP-MS imaging due to the fact that Rose considered the detectability of a flat-topped, sharp-edged signal in a uniform background.3 This is something that cannot be easily realized by LA-ICP-MS scanning as a result of blur generated through the physical size of the laser beam and via dispersion in the LA-ICP-MS interface.4 More accurate image quality metrics have been developed over the years with the advance of digital images. In contrast to the no-reference (NR) Rose model, full-reference (FR) assessment techniques compare the distorted image with the reference image, the most commonly applied ones being mean square error (MSE), peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index.5,6 MSE and PSNR are pixel difference-based techniques whereas the SSIM index is a correlation-based technique. Since its introduction in 2004 by Wang et al.,7 the SSIM index has received a great deal of attention in multifarious fields. The SSIM index improves the traditional algorithms MSE and PSNR by considering structural information in the image quality evaluation through loss of correlation, contrast degradation and luminance distortion.8

In 2D LA-ICP-MS imaging one normally generates a distorted element map but has no insight into the reference element map, unless specific resolution targets are used with known elemental distribution. These resolution targets are usually associated with simple monochrome (binary) patterns such as lines,9–12 squares13 or periodic gratings14,15 to evaluate or quantify the spatial resolution. However, real-life LA-ICPMS imaging for optimum perceptual visual image quality is also associated with parameters such as contrast, noise, structural information, etc. that are critically related to the instrumental specifications and operational conditions that determine the image quality, next to the elemental concentration and distribution characteristics of the sample. As the human eye is able to effectively “smooth” an image, minute variations in an image may still result in visually distinguishable artefacts. This work proposes an approach to quantify and optimize the perceptual image quality in continuous scanning 2D LAICP-MS bioimaging based on the SSIM index and by applying earlier developed computational protocols to simulate the distortion generated in the LA-ICP-MS imaging process.4,14,16 These computational protocols are based on the introduction of blur and noise, extracted from the edge spread function ensuing from experimental LA line scans across a knife edge,17 laser milled on a custom-prepared gelatin standard with known elemental concentration.18 We demonstrate that distorted images generated in this way, from a reference image of one’s choice, allow for objective image quality assessment via the computed SSIM indices, and as such offer a straightforward way to select the optimal LA-ICP-MS conditions for best image quality. EXPERIMENTAL AND MODELING LA-ICP-MS Instrument for Milling and Imaging. The instrument for LA milling and LA-ICP-MS imaging comprised a laser ablation system (193 nm ArF*; Analyte G2,

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Teledyne Photon Machines Inc., Bozeman, MT) with twovolume ablation cell (HelEx II; He carrier gas flow rate, cup = 0.5 L min-1, cell = 0.3 L min-1); for imaging the LA unit was interfaced with an ICP-MS instrument (Agilent 7900, Agilent Technologies, Santa Clara, CA; Ar makeup gas was added before the ICP torch (0.8 L min-1) and MS operation was in time-resolved mode, measuring one point per mass, acquiring the mass of 52Cr. Fabrication of Gelatinous Knife Edge Cr-Standard. A microhomogeneous 10 % (m/v) gelatin standard containing 20 mg kg-1 Cr was prepared based on a recently published paper,18 followed by laser milling of a custom knife edge. In summary, this procedure uses a porcine skin gelatin, type A, with bloom strength 300, prepared under strictly regulated drying/setting conditions by adding a Cr(VI) solution to an aqueous gelatin solution at 55 °C, followed by thorough mixing, degassing and depositing of ca. 20 µL of the mixture onto a glass microscope slide. The Petri dish-covered slide is then dried for 1 h in a mechanical convection oven at 100 °C, yielding a circular deposit with a diameter of ca. 5 mm and a height of ca. 50 µm. The knife edge is formed by removal of part of the circular deposit to create a perfectly straight edge by laser milling to a depth of the glass support under the following milling conditions: beam diameter, 80 µm (square mask); scan speed, 400 µm s-1; fluence, 0.4 J cm-2; repetition rate, 20 Hz. The SEM image of the milled knife edge in Figure 1 shows a very high level of smoothness, without serious fraying, what should make retrieval of the edge spread function with beam size diameters between 10 and 50 µm (round mask) very accurate. The milled away area of the gelatin standard, in essence exposing the glass microscope slide, contained negligible amounts of Cr compared to the gelatinous Cr-standard area this is an essential condition to accurately retrieve the edge spread function when line scanning the knife edge. Background correction due to the Cr gas blank was still found to be necessary for the LA-ICP-MS setup used.

Figure 1. SEM image of a laser milled gelatinous knife edge Cr-standard, and tracks made by 50 and 10 µm laser beams (round mask) on the standard according to conditions 1 and 7 in Table 1, respectively. LA-ICP-MS Imaging of Gelatinous Knife Edge CrStandard. For elemental imaging of the gelatinous Crstandard the knife edge was traversed in perpendicular fashion to the line scan direction (focused on the Cr-standard area), using seven different LA-ICP-MS conditions presented in Table 1, yielding differently pixelated Cr images with various levels of blur and noise, but all pertaining to equal mapping

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times. Conditions were chosen in such a way that square pixels were obtained, i.e. beam diameter (BD, µm) = scanning speed (SS, µm s-1) × acquisition time (AT, s), and pulses that overlap five times per crater, i.e., beam diameter (BD, µm) × repetition rate (RR, Hz) / scanning speed (SS, µm s-1) = 5. Since only one element is measured the acquisition time (AT, s) equals the dwell time (DT, s), in this case the dwell time for 52 Cr, but for more elements the sum of the dwell times, plus the settling times for the respective elements, should equal the acquisition time.19 Elemental concentrations in the gelatinous standard are preferably chosen in such a way that enough counts per pixel are recorded (say more than 1,000) to reduce the noise level and enable easy retrieval of distortion-related parameters. Table 1. LA-ICP-MS conditions for “perpendicular” line scanning of the gelatinous knife edge Cr-standard (20 mg kg-1) to retrieve the blur- and noise-related information; the dwell time DT is in this case similar to the acquisition time AT as only one element is measured. In all seven experiments the pixel dimensions are equal to the beam diameter, pulses overlap five times per crater and the criteria for identical mapping times are satisfied. Exp. No.

BD (µm)

SS (µm s-1)

DT (s)

RR (Hz)

RS

1 2 3 4 5 6 7

50 40 25 20 15 12 10

100 125 200 250 333 416 500

0.5 0.32 0.125 0.08 0.045 0.0288 0.02

10 16 40 62 111 173 250

25.0 16.4 6.25 3.97 2.25 1.43 1.00

BD = Beam Diameter; SS = Scan Speed; DT = Dwell Time; RR = Repetition Rate; RS = Relative Sensitivity.

Figure 2. Reference image (6,000×8,000 µm2) based on a photograph of Albert Einstein; we virtually mapped the whole image and calculated MS-SSIM indices based on distorted images scaled up to the size of the original reference image. The blue square denotes the area of the image that will be shown in later images to be able to easier distinguish visual dissimilarities between images. Numerical Calculations and Data Processing. To evaluate the image quality assessment strategy developed in this work, distorted images were generated from a reference image based on an 8-bit (256 grayscale values; black = 0 and white = 255) photograph (Figure 2) of Albert Einstein 1879 - 1955 (Turner,

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Analytical Chemistry

Figure 3. Extraction of blur (LSFi) and noise (ASTD,i and qi) parameters from experimental line scans on a knife edge composed of gelatin, admixed with i elemental standards. The LSFi was constructed from the derivative of the ESFi, after averaging and (percentile filter) smoothing of the line scans. Experimental LA-ICP-MS conditions for the knife edge scan: beam diameter, 15 µm; scan speed, 333 µm s-1; acquisition time (= dwell time), 0.045 s; repetition rate, 111 Hz; element measured, 52Cr. Blur and noise parameters extracted were used for virtual imaging of the radial stars in Figure 4. O.J., photographer, ca. 1947, Library of Congress). For this purpose we assumed that the “sample” photograph consisted of a gelatin matrix (mimicking of biological tissues) with a maximum Cr concentration of 20 mg kg-1. After extraction of blur- and noise-related information from LA-ICP-MS scans across a gelatinous knife edge standard with a Cr concentration of 20 mg kg-1, earlier developed convolution and noise addition protocols were applied to generate the distorted images.4,14,16 Images constructed from csv files were saved in (lossless) 8-bit PNG format. All numerical calculations regarding convolution and noise addition were performed in GNU Octave 4.0.017;20 further data and image processing was performed in ImageJ 1.491821 with special attention to plugins for registration and image quality. RESULTS AND DISCUSSION Extraction of Blur- and Noise-Related Information from LA-ICP-MS Knife Edge Scans. Image distortion by blur is caused by the physical size of the laser sampling beam traversing the artefact and impaired washout/transfer of aerosol particles in the LA cell/interface, respectively, leading to phenomena such as “halo effects” and “smearing”.14 Fast response cells developed primarily for LA-ICP-MS imaging in single pulse mode22 may be used to good effect in continuous scanning mode as well, thereby circumventing to a great extent the “smearing” phenomenon.23 Nevertheless, blur due to “halo effects” still remains and can only be resolved by performing oversampling combined with post-processing via signal and image deconvolution approaches11,24 although this approach is still in its infancy. Noise as a result of fluctuations in the primary laser output (Flicker or proportional noise) and counting statistics in the detector (Poisson or shot noise) further reduce the lateral resolution and distort the image. Figure 3 illustrates how blur- and noise-related information can be extracted from LA-ICP-MS line scans across a knife edge standard. To retrieve the edge spread function the scan lines for each element i are averaged, followed by computation of the first derivative; after normalization the line spread func-

tion (LSFi) containing all the blur-related information is obtained. In case the line spread function would have been a vertical line without any thickness, implying a LA-ICP-MS imaging system with infinitely small laser beam and no dispersion in the ablation cell and/or interface, the imaged knife edge would have been blur-free. The levels of Flicker and Poisson noise can be extracted from the average signal (ASTD,i, counts) and standard deviation (SDSTD,i, counts) per pixel on the knife edge standard for each element i, under the assumption of negligible contribution of the gas blank and glass support (in the Supporting Information, SI-1, a more extensive version for correction of these parameters is given). The following equation gives the relationship between these variables to facilitate retrieval of the noise-related information: ,  ,,  ,,  

(1)



 ∙ , , where F and P denote the association with Flicker and Poisson noise, respectively.14 Flicker noise (SDSTD,i,F) is proportional to the signal intensity (q⋅ASTD,i with q a factor between 0 and 1), whereas Poisson noise (SDSTD,i,P) is related to the square root of the signal intensity (√ASTD,i). Written in relative standard deviation form we obtain RSDSTD,i,F = 100⋅q (%) and RSDSTD,i,P = 100/√ASTD,i (%). In the Supporting Information, SI2, these fundamental principles of noise for 2D LA-ICP-MS imaging are illustrated; it can be seen that for low count numbers, Poisson noise (RSDP) becomes the dominant source of noise,25 whereas Flicker noise (RSDF) is constant, although the absolute noise level increases proportionally to the number count. Construction of Distorted Image using Blur- and NoiseRelated Information. Figure 4 shows how a binary (radial star) image (Oi) is distorted4 based on applying the distortionrelated parameters for blur (LSFi) and noise (ASTD,i and q) as extracted from LA-ICP-MS scans (Figure 3) on the knife edge standard for each element i.4,14 In the first step, image Oi,

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Figure 4. Virtual imaging of a binary radial star image Oi using input data related to blur and noise as extracted from an experimental LA-ICP-MS scan on a knife edge composed of gelatin (Figure 3), admixed with i elemental standards, to yield the blurred image I1,i and the subsequent noise-added image I2,i. The blue trace below the radial star images represents the 8-bit grayscale values, indicating that the two levels of the binary image Oi are 10 and 100 % of the grayscale, when traversing the yellow horizontal line on the radial star images. Experimental LA-ICP-MS conditions for the knife edge scan: beam diameter, 15 µm; scan speed, 333 µm s-1; acquisition time (= dwell time), 0.045 s; repetition rate, 111 Hz; element measured, 52Cr. Blur and noise parameters were retrieved from Figure 3 for virtual imaging of the radial stars. appropriately pixelated with a pixel size BD × SS × AT or BD2 for “square” pixels (both in µm2), undergoes blurring via discrete-time convolution with line spread function LSFi for each element i: ,  ⊗ 

structure (s[x,y]) in the respective reference (x = Oi) and distorted (y = I2,i) images (after the images have been divided into blocks of size 8×8) via the block means (µx and µy), the block standard deviations (σx and σy) and the block covariance value (σx,y) using the following equation:7

(2) , 

with ⊗ denoting the convolution operator. In the second step, blurred image I1,i is subjected to addition of Flicker and Poisson noise based on Eq. (1). Normally, Flicker noise is added to an image whereas Poisson noise is applied; however, it has been shown26 that a very close Poisson noise approximation can be obtained using a Gaussian distribution by adapting the variance of the Gaussian noise to the pixel values, i.e. Poisson(λ) = Gaussian(µ=λ, σ2=λ), thus not only Gaussian (normal) distributed Flicker noise but also Poisson noise can be added to an image (see the Supporting Information, SI-3, for more details). The blurred/noise-added (star) image I2,i in Figure 4 shows all the characteristics of continuous scanning 2D LA-ICP-MS bioimaging, viz. “halo effects”, “smearing” and noise, leading to loss of contrast and deteriorated spatial resolution. Image Quality Assessment of Distorted Image Based on the SSIM Index. The SSIM index compares the differences between a reference image (Oi) and a distorted image (I2,i), in this case distortion of the (radial star) image generated in Figure 4 via virtual ablation, using the blur- and noise-related parameters retrieved from the knife edge scans. The SSIM index compares the luminance (l[x,y]), contrast (c[x,y]) and

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(3)

with c1 and c2 constants to avoid instability; SSIM(x,y) comprises the individual contributions of l[x,y], c[x,y] and s[x,y].7 An upgraded multi-scale version of the SSIM index,27 i.e. the MS-SSIM index, applies a smooth windowing approach by sliding a window, pixel-by-pixel, across the whole image space and averaging of all N windows:  % 

 &

' ∑& )*)

(4)

Since the LA-ICP-MS imaging procedure translates the image laterally, in the scan direction, registering of the reference and distorted images via a translation action is required prior to computation of the MS-SSIM index. Both registration and MS-SSIM index computations are performed in ImageJ, using the plugins “register virtual stack slices” and “MS-SSIM index”, respectively. Since the distorted image is smaller than the virtually ablated original image, it was upscaled to the original image size without interpolation, i.e. merely by replication of pixels. The MS-SSIM index and its individual com-

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Analytical Chemistry ponents computed for comparison of the reference image (Oi) with the distorted (radial star) image (I2,i) in Figure 4 are as follows: l = 0.98804, c = 0.82267, s = 0.95955 and MS-SSIM index = 0.80840. This implies that the structure component, represented by blur and noise, contributes most to distortion of the (radial star) image under the LA-ICP-MS imaging conditions applied and elemental concentrations presumed. Also for the images constructed in the next section the image structure is the predominant source of distortion.

Figure 5. Line spread functions (LSFs) extracted from line scans across a laser milled knife edge on a custom-prepared gelatin standard with 20 mg kg-1 Cr; the experiment numbers (Table 1) are shown above the respective LSFs. For reasons of clarity the LSFs are shifted horizontally so that the full profiles are visible. Markers are associated with the experimental measurements and the lines through the markers are best curve fits using an asymmetric double sigmoidal function. Table 2. Noise-related information extracted from the LAICP-MS scanned gelatinous knife edge Cr-standard (20 mg kg-1).

*

Exp. No.

ASTD (cpp*)

SDSTD (cpp*)

q

RSDSTD,F (%)

RSDSTD,P (%)

1 2 3 4 5 6 7

13676 8691 3376 2131 1253 773 565

542 203 65 75 45 49 38

0.039 0.021 0.009 0.028 0.022 0.053 0.054

3.9 2.1 0.9 2.8 2.2 5.3 5.4

0.9 1.1 1.7 2.2 2.8 3.6 4.2

, counts per pixel

Optimization of Image Quality for a Suite of LA-ICPMS Imaging Conditions. Selection of the optimal operating conditions for minimal image degradation and maximal sample throughput is critically dependent on the response (time) of the LA-ICP-MS system and the sensitivity of the ICP-MS, both instrumentally fixed parameters. To demonstrate the power of the above developed image quality assessment procedure for optimization of the LA-ICP-MS imaging conditions, seven different conditions were selected (Table 1), from small beam/high speed to large beam/low speed, but all satisfying the criteria for identical mapping times (160 min per map), square pixels and pulses that overlap five times per crater. Although construction of distorted image I2,i is based on

application of the distortion-related parameters LSFi, ASTD,i and q, extracted from a knife edge standard with a Cr concentration of 20 mg kg-1, we can assume that LSFi and q are independent of the Cr concentration. This implies that for other Cr concentrations, data may simply be deduced via the equation given in the Supporting Information, SI-3, by adjusting the count number through the average signal ASTD,i. Extraction of the blur- and noise-related information for the LA-ICP-MS conditions given in Table 1 yields the Cr-LSFs as shown in Figure 5 and ASTD and q values, and associated Flicker (RSDSTD,F) and Poisson (RSDSTD,P) noise, as reported in Table 2. From Figure 5 and Table 2 it can be seen that the smallest beam size (10 µm) is prone to yield the blurriest image due to the “widest” LSF and also the noisiest image due to the lowest count number ASTD. The largest beam size (50 µm) should yield a less blurry image and minimal noise compared to the smallest beam size. However, the “sweet spot” for best image quality can only be evaluated after subjecting a suitable reference image to virtual ablation with these experimentally generated blur- and noise-related parameters, and subsequent comparison of the perceived image quality of the distorted images, either visually or via their MS-SSIM indices. Figure 6 shows the distorted images generated from the reference image (6,000×8,000 µm2) of Albert Einstein (Figure 2), assuming that the matrix composition is associated with a maximum Cr concentration of 20 mg kg-1 (for comparison the distorted images have been scaled up to the original reference image size without interpolation). It is obvious that the subjective, visual “sweet spot” for best image quality is somewhere around LA-ICP-MS conditions 3 or 4 (image pixel size: 25×25 µm2 or 20×20 µm2). This is confirmed by the objective MSSSIM indices (shown on the left-hand side of each individual distorted image in Figure 6) which are maximal for these particular conditions (ca. 0.78). These conditions seem to have the right balance between pixel size, noise and blur for best perceive image quality. Larger pixels (conditions 1 and 2), with similar noise (Table 2) but higher blur levels (∵ larger physical beam sizes), have a lower perceived image quality; the same is true for smaller pixels (conditions 5-7) with higher noise (Table 2) and higher blur (∵ higher scan speeds) levels. As mentioned above, distorted images can also be constructed for other (maximum) Cr concentrations then 20 mg kg-1, simply by adjusting the count number ASTD. The figures shown in the Supporting Information, SI-4, give the distorted images generated for ASTD values associated with (maximum) Cr concentrations of 0.2, 1 and 500 mg kg-1. It can be seen that (ultra)low Cr concentrations ≤ 0.2 mg kg-1 as result of decreasing counts per pixel (ASTD,i) and inherent progressive Poisson noise (RSDSTD,i,P = 100/√ASTD,i) are the main cause of image quality degradation. Flicker noise (RSDSTD,i,F = 100⋅q) can be regarded as constant, independent of ASTD,i (see also the Supporting Information, SI-2). The higher (maximum) Cr concentrations of 1, and especially 20 and 500 mg kg-1 are less affected by these problems as clearly illustrated in Figure 7 where the MS-SSIM indices are plotted as a function of the pixel size. Higher concentrations seem to have nearly identical perceived image quality, with a clear maximum at LA-ICP-MS conditions related to pixel sizes of 20-25 µm (square), whereas the perceived image quality at lower concentrations is essentially noise-limited, implying that for best quality under these conditions large pixel sizes are required.

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Figure 6. Image distortion associated with seven different LA-ICP-MS conditions based on virtual imaging of the “Albert Einstein” image in Figure 2, assuming a gelatinous composition with a maximum concentration level associated with 20 mg kg-1 Cr. CONCLUSIONS Although bioimaging by LA-ICP-MS yields 2D images with quantitative elemental distribution information, the perceptual visual image quality is associated with parameters such as contrast, spatial resolution and noise in the image. These parameters are critically dependent on the instrumental specifications and operational conditions, next to the elemental concentration and distribution characteristics of the sample.

Figure 7. MS-SSIM indices calculated from comparing the “Albert Einstein” reference image (Figure 2) with the distorted images (Figure 6 and figures in the Supporting Information, SI-4) for four different (maximum) Cr concentrations, and based on virtual LA-ICP-MS imaging using blur- and noiserelated information extracted from experimental line scans on a knife edge Cr-standard of 20 mg kg-1; for the other concentrations simple extrapolation has been applied via pixel count numbers.

However, the perceptual visual image quality is normally an a posteriori measure associated with certain LA-ICP-MS conditions that may not be optimal for the best image quality. Since LA-ICP-MS is in essence a destructive technique, for unique samples we strive for an a priori measure according to human perception that allows us to optimize the LA-ICP-MS conditions before ablation. A plethora of other “destructive” imaging techniques associated with laser beams (LIBS, MALDI, LAESI, etc.) or ion/proton beams (DART, DESI, SIMS, FIB-SEM EDS, PIXE, etc.) may also benefit from this approach. Unfortunately, suitable reference images with known elemental distribution are unavailable, except for a few simple resolution targets, forcing us to use an intermediate approach in which virtual LA-ICP-MS imaging is performed based on experimentally retrieved parameters. These parameters are associated with blur and noise and were extracted from line scans on a laser milled gelatinous knife edge Cr-standard, yielding the edge spread (and subsequent line spread) function and the Flicker and Poisson noise for a specific Cr concentration. Using these parameters in earlier developed computational protocols one can generate a distorted image from a reference image of one’s choice. We have shown that the perceived image quality of these distorted images can be objectively calculated based on a perceptual model of human vision using the structural similarity (SSIM) index. Hence, this index offers a new, objective strategy to optimize the LA-ICP-MS conditions for highest possible image quality in 2D elemental bioimaging as illustrated for

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Analytical Chemistry seven different LA-ICP-MS conditions, all pertaining to equal mapping times. Incorporation of this strategy in already existing software for simulation of the LA-ICP-MS output16 may aid in a higher perceived image quality in a given time and faster mapping times for the same image quality, without destroying unique samples.

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(12) ASSOCIATED CONTENT Supporting Information SI-1, extraction of noise-related information from LA-ICP-MS knife edge scans; SI-2, fundamentals of noise in LA-ICP-MS imaging demonstrated for five standards; SI-3, mathematical addition of noise to a blurred image; SI-4, image distortion associated with seven different LA-ICP-MS conditions based on virtual imaging of the “Albert Einstein” image at three Cr concentrations. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This research was financed by the Slovenian Research Agency (program P1-0034 and bilateral project N1-0060). The authors are indebted to Dr. Gregor Kapun (National Institute of Chemistry, Ljubljana, Slovenia) for his assistance with SEM imaging.

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