Improving retinal image resolution with iterative weighted shift-and-add

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1 Improving retinal image resolution with iterative weighted shift-and-add Nizan Meitav 1 and Erez N. Ribak 1 Department of Physics, Technion Israel Institute of Technology, Haifa 32000, Israel High-resolution retinal imaging requires dilating the pupil, and therefore exposing more aberrations that blur the image. We developed an image processing technique that takes advantage of the natural movement of the eye to average out some of the high order aberrations, and to oversample the retina. This method was implemented on a long sequence of retinal images of subjects with normal vision. We were able to resolve structures of the size of single cells in the living human retina. The improvement of resolution is independent of the acquisition method, as long as the image is not warped during scanning. Consequently even better results can be expected by implementing this technique on higher-resolution images. OCIS codes: , , Introduction High-resolution imaging of the retina has significant importance for science: physics and optics, biology and medicine. On the one hand the ability to resolve micron scale structures in the retina can help better understand the bio-physical and vision processes of the retina [1,2] and on the other hand it can provide early diagnosis of retinal diseases. However, for improving resolution, the pupil has to be dilated, and as a consequence primary and high-order aberrations are added to the ocular optics, resulting in a blurry image and suffering from low signal to noise ratio (SNR). There exist computational imaging algorithms that are able to super-resolve sets of images [3-6]. Due to the level and complexity of the aberrations in the eye, they cannot improve the image significantly, since they are based on deconvolution of the aberration operator from the high resolution image, but the time dependence of this operator is not trivial. In the past decade a major boost in retinal imaging was achieved by adaptive optics (AO) techniques, i.e. using a feedback mechanism for correcting the aberrated wave front emanating from the eye, thus giving an excellent lateral resolution [1,2,7]. Other techniques that are recently used for obtaining even higher resolution imaging are confocal scanning laser ophthalmology (SLO) and optical coherence tomography (OCT), in some cases combined with AO [8-12]. 1 These methods provide combined depth and lateral information by scanning in at least one direction. The above-mentioned methods gave an adequate solution for high resolution imaging, but in order to make them widespread some obstacles had to be overcome. One hurdle is their sensitivity to the eye's movements. These movements, or saccades, produce smearing and warping during the imaging process, especially in scanning systems such as SLO and OCT. These effects can be reduced through tracking mechanisms or by sophisticated image processing [13-16]. Due to light source coherence, OCT and SLO can also be riddled with speckles. The limited field of view might require the patching together of many small sections. Other hurdles in the way of the technology are (a) partial corrections of the ocular aberrations, (b) high cost and complexity, as well as (c) for clinical applications, lack of information about diseases at early appearance, until now only recognizable at advanced, extended stages. Here we present an image processing algorithm for resolution enhancement of retinal images. Our aim is to improve the image resolution, rather than correct motion distortion. This is done by dual step accurate summation of a large number of frames (>200), weighted with respect to their correlation value with a reference frame. The correlation weight and sub-pixel shift values are found after normalization of the frames, which seeks to flatten the local background.

2 Low weight is given to frames that suffer from uneven lighting. Images that were captured during eye movement, and therefore came out blurred, are weighted out by this method. To test this method, we applied it to retinal images obtained by a rather simple setup. The illumination was based on light-emitting diodes (LEDs) with longitudinal coherence < 7 µm and lateral coherence < 2 µm, to avoid speckle. We produced magnified images, where the fairly large field of view (as compared to SLO images), of ~ mm 2, allows further tiling of fewer images, and with a greater overlap of these images. Imaging in a multi-frame mode, instead of single flash mode, enabled us to use much less illumination power with greater comfort to the subjects. The novelty in the suggested method is the ability to significantly improve the resolution of an ensemble of poor quality retinal images, by making use of the variation in the high order aberrations caused by the eyes' saccades [3-6]. The final resolution allows detection of single cells in the retina outside the fovea, up to the periphery where low-order aberrations dominate. Although tested on a simple optical setup with medium quality images, the image processing method does not depend on the acquisition method. Consequently, this method can also be implemented on other imaging techniques such as adaptive optics to increase their resolution even further. In other cases, the suggested method can only be applied after initial analysis, such as after correction of warping or following AO deconvolution. One of the reasons for the resolution improvement is derived from the fact that the point spread function (PSF) of a diffraction-limited optical apparatus consists of the Fraunhofer diffraction pattern of the exit pupil [17]: (, ) = ( ) ( )exp [ / + (, )] 1 2 λ PSF ξ t z P r ik r ξ z w r t d r 2 where ξ = (u, v) are the image plane coordinates, r = (x, y) are exit pupil plane coordinates, the pupil function P (r) is unity existing only inside the projected aperture and z is the distance from the exit pupil to the image plane. Without aberrations, the wave front w (r, t) = 0, but in their presence it is the local phase error. Since w (r, t) is a function of the position in the exit pupil and time, small changes in the eye's regard will change the PSF and give quite a different PSF at each frame [18]. The temporal PSF variations are a result of (1) imaging through a different section of the cor- Fig 1. Averaging of high order aberrations is exemplified with point spread functions from three frames (left). By accurately shifting and summing the frames, weighted according to quality, the central peak is increased while the variable side-lobes average out (right). nea, (2) thinning and break-up of the tear film, and (3) cardiopulmonary effects on the eye. (Accommodation effects were minimized since we paralyzed the crystalline lens muscles.) As a result of these PSF variations, the zeros of the modulation transfer function shift their positions, providing information at all spatial frequencies. Fig. 1 illustrates the change in the PSF in several frames (left). By registering a large number of frames accurately, we can average out some of the high order aberrations and obtain better PSF compared to the PSF of each single frame. In other words, we take advantage of the eye s natural movement in order to level out some of its high order aberrations and obtain better resolution. That said, this method cannot eliminate w (r, t) completely, but rather even out its high frequency components, which have significant role in deteriorating the image quality when the pupil is large [19]. This is somewhat akin to stellar speckle interferometry where averaging over different realizations of the atmosphere improves the final image [20], and is used in the infra-red, where the number of speckles is small [21]. However, and unlike in the case of stellar speckles interferometry, in which the aberrations are more random in nature, in this case the averaged PSF would be that resulting from the main aberration component of the eye. Also, unlike stellar shift-and-add [20], we do not have a reference point source to deconvolve the final image from. However, further improvement can be gained by removal of the average wave front, provided we measure it [22]. In addition to averaging over aberrations, the improvement in the resolution also results from oversampling of the PSF. The structure of the sampling impulse function can be described by the following convolution: s x, y = f i, j p x i, y j ( ) ( ) ( ) i j 2

3 where s (x, y) is the impulse image data, f (i, j) is the image data at each sampling vertex and p(x, y) is the PSF, over-sampled by the detector pixels. Since the eye moves between frames in random non-integer intervals, each frame produces different sampled information. Knowing these displacements, and adding the frames in sub-pixel accuracy, allows denser sampling of the PSF. That finer sampling enables a highresolution reconstruction of the image [23-25]. 2. Image processing technique In order to increase the SNR and to average out some of the aberrations, we added a large number of frames, shifted at sub-pixel accuracy from the same retinal region. The method was based on two iterations (Fig. 2). As a preliminary step, all the frames were normalized by subtraction of the average value of the frame and dividing the resulting image by the standard deviation of the frame. This normalization help reduce the effect of different illumination levels in different frames, in addition of giving a low weight to frames with non uniform light level. We tried more complex normalizations [26,27], but the results were similar. Fig. 2. Weighted shift-and-add through Fourier crosscorrelation. The dashed line marks the second iteration. In the first iteration, a region of interest (ROI) was selected from a reference image. The ROI was chosen in a section without blood vessels, since they are dilated periodically by breathing and heartbeats thus cannot be used as a repeatable reference. Then the ROI image was cross-correlated with each of the other frames in the Fourier domain, using the crosscorrelation theorem [28]: * { } { } { } F r g = F r F g (3) where r is the reference ROI, g is the current frame, the asterisk symbolizes the complex conjugate and is the correlation operator. Afterwards the result was inverse transformed to the image plane, giving the cross-correlated image. The maximum value and the 3 Fig. 3. SNR improvement with more frames, for two different subjects. Adding more than 200 frames did not improve the signal to noise significantly. coordinates of the each cross correlations were found at sub-pixel accuracy by using a two-dimensional parabolic fit [29]. Having the cross correlation value and coordinates in a sub-pixel precision, it was possible to shift and add the frames weighted by their crosscorrelation value, but without the preliminary normalization. The images were registered in sub-pixel scale using linear interpolation. In the second iteration, the same algorithm was used, but the ROI was now taken from the final image of the first iteration, producing a matched filter for the next cross-correlations [20]. By virtue of the second ROI having finer details than the raw one, better correlation is possible with the set of frames. Thus the effective PSF became narrower, although it is difficult to quantify that measure. It is only in the Fourier domain that it is possible to see higher frequencies rising above the noise level. Since this method is based on cross correlations, images taken while the eye was not fixated on the target, moved, or was blinking had low correlation, and were automatically disqualified or given a very low weight. We found out that without the preliminary normalization of the frames, the results of this method were poor. This was also true when using only one iteration instead of two, hence using the final image of the first iteration as a matched filter is crucial. The use of Fourier cross-correlation implies that the image had periodic infinite domain. In order to remove this difficulty we disqualified frames having cross-correlation coordinates that are within the range of 20% from the frame edges (the ROI position is chosen to be far from this region). One should keep in

4 mind that since we use a relatively large field of view images (with respect to SLO) only few frames are disqualified by this condition. We also zero-padded each of the frames before shifting them. To avoid edge periodicity in the Fourier domain, the ROI was circularly shaped. We estimated the number of frames required for our retinal camera (Section 3), by first measuring the noise (or clutter) level. Noise was assumed to be all artifacts finer than 2 µm, as obtained by a high-pass filter with no transition range. A corresponding low pass filter (top hat) produced the signal in the same retinal segment ( µm 2 size). While Poisson and detector noise have a flat spectrum, it is difficult to assume much about the image and clutter content. An extra-foveal segment was taken where the smallest structures expected were bigger than 3 µm, thus our estimation of 2 µm cut off between signal and noise is quite reasonable [30]. The diffraction limit was also ~2 µm. The two results were combined to give the SNR as a function of the number of frames. We used hundreds of frames to see where the SNR would level off. Fig. 3 shows that summation of more than ~200 frames did not increase the SNR significantly. On the other hand, a longer series of frames caused discomfort for the subject. Thus we settled on sets of 250 frames for each retinal area, of which some bad frames had to be ignored during image processing. This takes approximately 16 seconds at 15 frames per second, at 16 bit resolution. In order to check the validity of the algorithm we ran two tests. First this method was applied on a set of frames consisting of a single retinal image (acquired by the setup described below) shifted various times in an integer random number of pixels. In a second test, a set of 100 frames was measured of the artificial eye described below, with µm graphite granules simulating retinal features (Fig. 4). During this measurement the eye was moved at random directions in order to simulate the movement of the biological eye. Since in both of these simple tests shifting was succssful, we could assume that the method was valid, and could be used on real retinal data. 3. Optical system In order check the efficiency of the shift and add algorithm, we built a rather simple imaging system with a relatively wide field-of-view (Fig 5). To avoid back reflection from the cornea into the retinal camera, a green LED (520 nm) was used with a central stop, forming an annular light pattern, which was focused on the pupil and crystalline lens and defocused on the retina. The second part of the system is the pupil imaging section, used for setting the subject s eye at the central position. A lens formed the pupil image on the corresponding camera. The small monitor showing the pupil doubled as a fixation target. This way the subjects could position their heads and help in controlling the corneal reflection. The third part of the apparatus was the imaging leg, consisting of two lenses. The first one formed a magnified secondary image in front of the other lens, which in turn formed a further magnified image onto the retinal camera. Even though a narrow bandwidth light source was used, all lenses were achromatic, as they are better corrected. The focus was set by moving the retinal camera along the optical axis. Since the retinal layers are mostly transparent it was difficult to know which retinal layer was in focus, so we focused on surface blood vessels, then further ~100 µm into the retina. Since the analysis method was based on regions of in- Fig. 4. One frame (left) and 100 added frames (right). Notice the improvement in contrast and detail and the drop in noise. Fig. 5. High-resolution retinal camera. The fixation target for the other eye (not shown) was the monitor of the pupil camera. 4

5 terest without blood vessels, we found out that finer features could only show in processed images obtained from maximum number of added frames. In order to calibrate the magnification of the camera, we built a water-filled artificial eye [31], with a length adjustable as in emmetropic eyes (Fig. 6). A resolution target made of 8 µm silicon pillars and a 4 µm gap between them was placed at its retina. It was easily resolved at the scale of 1.2 µm/pixel, to be compared with the 2 µm diffraction limit of a dilated human eye. The fundus (retinal) camera was designed for flood illumination, multi-frame mode instead of a flash shot mode, which is common with most fundus cameras [32]. Therefore a low power illumination was possible (~50 µw), well below the permitted standards (e.g. IEC 825-1). Subjects did not suffer any saturation or after-image. All measurements were done after pupil dilation and accommodation paralysis. Fig. 6. The artificial eye (left), the magnified image of the resolution target with 12 µm period (center), and through the artificial eye (right). Due to the incidence angle only the horizontal lines were visible. Fig. 7. A single retinal frame (a), compared to the final image (b).the image is across, with its right side at 14 0 nasal eccentricity. Blood vessel boundaries are not sharp due to averaging over many heart beats. Scale bar, 100 µm; image area mm 2 ( pixels). The rectangles are magnified region of interest in Fig 8. Fig 8. A magnified region of interest of one frame (left), after registration and summation of 240 frames (center), and after a one-time application of a high pass filter (blocking features over 20 µm) to reduce the background fluctuations (right). Scale bar: 25 µm, images size µm 2 (1.2 µm/pixel). Similar results were obtained at various eccentricities ( ). 5

6 4. Results Fig. 9. Left: Intensity histogram of Fig. 8a. Right: average of ten sequential frames showing the same statistics. Both histograms exclude the possibility of speckle statistics. The minimal value of each frame was deducted before calculating the histograms. 6 Fig 10. The averaged radial power spectrum for one frame (dashed red line) and for the final image (continuous blue line). The data were taken from a µm 2 region of interest, without the use of any filter. A typical comparison between a single retinal image and the final one is shown in Fig frames were registered to produce an improved image. While in Fig. 7a it is almost impossible to identify any structure in the image, in Fig. 7b the dynamic range is much better and the structures in the image are much clearer (we scaled linearly all images to obtain maximal contrast, here and later). Fig. 8 is a magnified region of interest, taken from the rectangles at Fig 7, chosen where no blood vessels are present, as they dilate with the pulse and cannot provide a repeatable reference. Once again the fine structure is much clearer after image processing, mostly due to averaging of the high order aberrations caused by saccades between frames (Fig 8b.). The SNR has also improved thanks to image registration and summation. A circular high-pass filter (without any transition range) was used to diminish the background fluctuations. As a result, only features' spacing smaller than 20 µm are visible, improving the image contrast (Fig. 8c.). We wish to stress that this is the only place we use a filter anywhere in this work (i.e. all the processed data hereafter will be as in Fig. 8b.) Since the illumination source used was not coherent temporally or spatially, there was no risk that the fine structure in the image resulted from a speckle pattern. Indeed instead of having an exponential intensity distribution due to speckle in each retinal frame, we obtained a Gaussian distribution (Fig. 9) [33]. Fig. 10 shows the radial mean (averaging over the angles at a constant radius) of the power spectrum for a µm 2 section of the retina. The averaged radial intensity power spectrum for a single frame is almost constant, i.e. the signal and the noise are almost inseparable, while at the final image the spectrum is decreasing at high frequencies. Moreover at around cycles/deg there are peaks in the intensity that are probably related to the arrangement of the local cells. In all the images that were taken and processed by this method we were able to resolve these microscopic structures, as in Fig. 8. In line with previous in-vivo studies [1,2,7-16], the fine structure in the data presented here (ours or others ) will be loosely termed cones, although the only safe identification can sometimes be made by differential bleaching. Still, our data were obtained using incoherent light, where cones are the first visible and resolved items in the transparent retina. The radial average of the power spectrum was repeated for µm 2 segments. The results of nine adjacent segments (i.e. total µm 2 square) were averaged in order to get the average power spectrum of a larger area. When plotting the results, the x- axis was transformed into distance (period) units instead of spatial frequencies units, for the readers convenience. The power spectrum of each segment was normalized by dividing each spectrum by its highest value (which excludes the origin). Fig. 11 shows the results of this analysis for three different eccentricities and two different subjects. These results are showing that the distance between cells is increasing with eccentricity (at the shown eccentricities), since at low eccentricity the peaks of the graphs tend to smaller periods. By comparing the cells spacing with ex-vivo measurement of cones' nearest neighbors we found similar increase of the mean distances at each eccentricity (3

7 to 13 µm at nasally) [34]. Moreover the 1 0 graphs give mean distance of ~ µm, is also in good agreement with in-vivo measurement at the same retinal area [7,35]. In addition, for eccentricities over 1 0 there are small peaks at ~4.5 to 7 µm. Those peaks are probably caused by minimally-distanced cones, which are at almost constant distance across most of the retina (6-8 µm) [34]. One of the signs of resolved cones is due to their close packing, which produces hexagonal power spectra. We computed the power spectra of the µm 2 section taken from Fig. 7 before and after image processing (Fig. 12). While in the single frame power spectra the hexagon shape is vague, it is clearer in the power spectrum of the processed image. Fig 12. A Fourier spectrum (log scale) of a small section of the retina in one frame (top) and in 240 frames (bottom). The hexagonal pattern, caused by the spatial arrangement of the cells, is somewhat clearer on the processed image (unfiltered data). Fig 11. Average radial power spectrum at eccentrcities of 1 0 (blue solid line), 7 0 (red dashed) and 14 0 or 16 0 (black dash-dot) for two different subjects, along the nasal horizontal meridian. Each of the graphs is an average of nine adjecnt µm 2 segments taken from final images of this method (without the use of any filter). At 1 0 eccentricity, where the cells are highly dense, the power spectrum has peaks at a smaller period (higher frequencies). At higher eccentricities, where the cones density is decreasing, the highest peaks are shifted to greater distances (lower frequencies). 7 The spatial frequency of the hexagon perimeters corresponds to ~4 µm distance between cells, which is smaller than expected from close packed cones at this eccentricity. Yet agreement with the ex-vivo measurement of minimal distance of cones (6-8 µm across most of the retina [34]) is achieved by looking at the peak in the corresponding (black dotted) graph in Fig. 11 (bottom), yielding minimal distance of 5.5 µm. Moreover, by using a method for measuring the mean size of hexagonally arranged cells we found that the mean size in this eccentricity is 7.4 µm [36]. Since less than 50% of the cones are arranged in hexagonal symmetry at the center and peripheral regions of the retina [1,36], the power spectrum of the processed image was somewhat low in contrast. Similar images were obtained for various eccentricities ( ) for three different subjects at three different wavelengths

8 (420 nm, 520nm and 680 nm). Further analysis of the hexagonal packing of cells, using the final images of this method as an input, is provided elsewhere [36]. 5. Discussion In this work we demonstrated a processing method that enables resolution enhancement of retinal images. First, it takes advantage of the natural movement of the eye to average out some of the high order monochromatic aberrations, which reduce the image quality when the pupil is dilated [19]. In addition, the saccades move the same scene by random displacements that are, obviously, of a random fraction of the PSF. This permits denser sampling than the PSF and consequently better resolution [23-25], as well as relatively high SNR. In practice, the method is based on double registration process. First it stacks more than 200 frames to produce a matched filter. Then it uses the matched filter to register the frames again with a better precision. The efficiency of this method has been demonstrated on a rather simple optical setup without active correction of monochromatic aberrations (except for a onetime focus), on subjects with weak low-order aberrations or hard contact lenses. In spite of the basic setup, a much better image was gained using this data analysis, to a point that single cells can be distinguished. By using a low coherent light source we can rule out the possibility of speckles, and indeed the intensity statistics prove this (Fig. 9). Moreover, the agreement in the mean and minimal cells' spacing with other invivo and ex-vivo measurements [7,34,35,37] indicates that the image are of real cells and not artifacts. An estimation of the PSF of the method is not straightforward, as it depends on the ocular aberrations of the subject. By examining the power spectrum at high density areas of cones we can estimate the maximum resolving limit of this method to vary between 3 and 3.5 µm. This excludes cones in the vicinity of the fovea. Other methods, such as blind deconvolution [38] allow better estimation (and thus deconvolution) of the PSF. The capability to resolve single cells near the center and at peripheral areas of the retina could help better understand vision processes starting from single photoreceptor cells. We can also learn about the contribution of their spatial arrangement to the human peripheral vision [1,36-44]. Even when implemented on this optical setup, this method can also be used as a 8 medical early detection tool, since it affords a simple, non invasive, low cost measurement at relatively low illumination power. Fig. 13 is an example of a pathology found with this method using two nonoverlapping sets of 100 frames. It also shows the reliability of the method, starting from two randomly chosen initial ROIs outside the pathology (even if nearby) and arriving at almost exactly the same final image. Through compensation of primary and high order aberrations, imaging methods based on adaptive optics can produce better images compared with our basic setup. That said, our goal in this work was not to develop a high quality fundus camera but rather to develop a processing method to enhance the resolution of a given set of images, independent of their origin. As the acquisition of the long series of images does not depend on the optical system, the same data analysis can be performed on AO-assisted fundus images (with or without unwarped SLO or OCT), to further improve the results. Fig. 13. A pathology repeats nearly perfectly in two mutually exclusive sets, processed each from 100 different frames, with different ROIs. Scale bar, 100 µm. Images size mm 2 ( pixels).

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