Point Spread Function Parameters Research Articles

Improved prior for adaptive optics point spread function estimation from science images: Application for deconvolution

Context. Access to knowledge of the point spread function (PSF) of adaptive optics(AO)-assisted observations is still a major limitation when processing AO data. This limitation is particularly important when image analysis requires the use of deconvolution methods. As the PSF is a complex and time-varying function, reference PSFs acquired on calibration stars before or after the scientific observation can be too different from the actual PSF of the observation to be used for deconvolution, and lead to artefacts in the final image. Aims. We improved the existing PSF-estimation method based on the so-called marginal approach by enhancing the object prior in order to make it more robust and suitable for observations of resolved extended objects. Methods. Our process is based on a two-step blind deconvolution approach from the literature. The first step consists of PSF estimation from the science image. For this, we made use of an analytical PSF model, whose parameters are estimated based on a marginal algorithm. This PSF was then used for deconvolution. In this study, we first investigated the requirements in terms of PSF parameter knowledge to obtain an accurate and yet resilient deconvolution process using simulations. We show that current marginal algorithms do not provide the required level of accuracy, especially in the presence of small objects. Therefore, we modified the marginal algorithm by providing a new model for object description, leading to an improved estimation of the required PSF parameters. Results. Our method fulfills the deconvolution requirement with realistic system configurations and different classes of Solar System objects in simulations. Finally, we validate our method by performing blind deconvolution with SPHERE/ZIMPOL observations of the Kleopatra asteroid.

AutoDeconJ: a GPU-accelerated ImageJ plugin for 3D light-field deconvolution with optimal iteration numbers predicting.

Light-field microscopy (LFM) is a compact solution to high-speed 3D fluorescence imaging. Usually, we need to do 3D deconvolution to the captured raw data. Although there are deep neural network methods that can accelerate the reconstruction process, the model is not universally applicable for all system parameters. Here, we develop AutoDeconJ, a GPU-accelerated ImageJ plugin for 4.4× faster and more accurate deconvolution of LFM data. We further propose an image quality metric for the deconvolution process, aiding in automatically determining the optimal number of iterations with higher reconstruction accuracy and fewer artifacts. Our proposed method outperforms state-of-the-art light-field deconvolution methods in reconstruction time and optimal iteration numbers prediction capability. It shows better universality of different light-field point spread function (PSF) parameters than the deep learning method. The fast, accurate and general reconstruction performance for different PSF parameters suggests its potential for mass 3D reconstruction of LFM data. The codes, the documentation and example data are available on an open source at: https://github.com/Onetism/AutoDeconJ.git. Supplementary data are available at Bioinformatics online.

The impact of scleral contact lenses correction of keratoconus on wave-front and accommodation parameters

Purpose: to evaluate the wave-front and accommodation changes in various stages of keratoconus corrected by scleral contact lenses.Material and methods. 20 patients (39 eyes) aged 18–37 with keratoconus of various stages (8 eyes with stage I, 3 eyes with stage II, 12 eyes stage II/III and 16 eyes with stage III wore OneFit or OneFitMed scleral lenses, made of hard gas-permeable material Contamac (Great Britain) with Dk 100 and mean thickness of 200–220 μm. All patients were examined using refractometry before and after cycloplegia, tested for uncorrected and best corrected visual acuity, relative accommodation reserve (RAR), binocular and monocular accommodation response (with Grand Seiko Binocular Open Field Autorefkeratometer WR-5100K, Japan) for full spectacle correction and scleral contact lens correction. 17 patients (34 eyes) were tested for corneal aberrations with OPD Scan III aberrometer (Nidek) without correction and with scleral contact lenses.Results. Patients with keratoconus demonstrated a manifest form of refraction -5.26 ± 0.45 D (by sphere equivalent) and a cycloplegic refraction of -4.75 ± 0.33 D. Uncorrected visual acuity averaged 0.26 ± 0.05, increasing with full spectacled correction to 0.54 ± 0.07 and with scleral contact lenses correction to 0.95 ± 0.08. Keratoconus patients demonstrated binocular accommodative response (BAR) of +4.5 to -6.12 D averaging -1.43 ± 0.34 D with full spectacled correction diopters and of -0.5 to -8.13 D averaging - 2.83 ± 0.23 D with scleral contact lenses, р ≤ 0.01. We could not measure the BAR in 3 patients with keratoconus stage III. Monocular accommodative response (MAR)with a full correction with glasses averaged -0.98 ± 0.33 D (from + 6.0 to -5.0 D) with full spectacled correction and -2.41 ± 0.27 D (from +1.25 to -5.5 D) with scleral contact lenses, р ≤ 0.02. At the same time monocular accommodative response of 4 patients with keratoconus of the third stage of disease was not available to assess. So, accommodative response significant increased with scleral contact lenses. Positive relative accommodation with a full correction with glasses averaged 1.50 ± 0.35 D, with scleral contact lenses – 2.25 ± 0.29 D, р ≤ 0.01. The level of all aberrations, from lower to higher orders was significantly increased. With scleral contact lenses that correct the shape of the anterior surface of the cornea, the level of all corneal aberrations dropped to nearly normal values, while the coefficient of asphericity dropped below normal values, and the point spread function parameter (PSF) increased by fifteen times (to reach 0.06).Conclusions. Patients with keratoconus demonstrated a generally lower objective accommodative response as compared to normal values, but with the scleral lenses it increases to the normal level. Scleral contact lenses normalize corneal aberrations and increase the quality of vision. All of the above justifies the recommendation to use scleral contact lenses for optical correction of keratoconus to increase the vision, the accommodation response and visual comfort, including that of near-visual work.

Impact of point-spread function reconstruction on dynamic and static 18F-DOPA PET/CT quantitative parameters in glioma.

Quantification of dynamic and static parameters extracted from 3,4-dihydroxy-6-[18F]-fluoro-L-phenylalanine (18F-DOPA, FDOPA) positron emission tomography (PET)/computed tomography (CT) plays a critical role for glioma assessment. The objective of the present study was to investigate the impact of point-spread function (PSF) reconstruction on these quantitative parameters. Fourteen patients with untreated gliomas and investigated with FDOPA PET/CT were analyzed. The distribution of the 14 cases was as follows: 6 astrocytomas-isocitrate dehydrogenase-mutant; 2 oligodendrogliomas/1p19q-codeleted-isocitrate dehydrogenase-mutant; and 6 isocitrate dehydrogenase-wild-type glioblastomas. A 0-20-min dynamic images (8×15, 2×30, 2×60, and 3×300 s post-injection) and a 0-20-min static image were reconstructed with and without PSF. Tumoral volumes-of-interest were generated on all of the PET series and the background volumes-of-interest were generated on the 0-20-min static image with and without PSF. Static parameters (SUVmax and SUVmean) of the tumoral and the background volumes-of-interest and kinetic parameters (K1 and k2) of the tumoral volumes-of-interest extracted from using full kinetic analysis were provided. PSF and non-PSF quantitative parameters values were compared. Thirty-three tumor volumes-of-interest and 14 background volumes-of-interest were analyzed. PSF images provided higher tumor SUVmax than non-PSF images for 23/33 VOIs [median SUVmax =3.0 (range, 1.4-10.2) with PSF vs. 2.7 (range, 1.4-9.1) without PSF; P<0.001] and higher tumor SUVmean for 13/33 volumes-of-interest [median SUVmean =2.0 (range, 0.8-7.6) with PSF vs. 2.0 (range, 0.8-7.4) without PSF; P=0.002]. K1 and k2 were significantly lower with PSF than without PSF [respectively median K1 =0.077 mL/ccm/min (range, 0.043-0.445 mL/ccm/min) with PSF vs. 0.101 mL/ccm/min (range, 0.055-0.578 mL/ccm/min) without PSF; P<0.001 and median k2 =0.070 min-1 (range, 0.025-0.146 min-1) with PSF vs. 0.081 min-1 (range, 0.027-0.180 min-1) without PSF; P<0.001]. Background SUVmax and SUVmean were statistically unaffected [respectively median SUVmax =1.7 (range, 1.3-2.0) with PSF vs. 1.7 (range, 1.3-1.9) without PSF; P=0.346 and median SUVmean =1.5 (range, 1.0-1.8) with PSF vs. 1.5 (range, 1.0-1.7) without PSF; P=0.371]. The present study confirms that PSF significantly increases tumor activity concentrations measured on PET images. PSF algorithms for quantitative PET/CT analysis should be used with caution, especially for quantification of kinetic parameters.

High-fidelity structured illumination microscopy by point-spread-function engineering

Structured illumination microscopy (SIM) has become a widely used tool for insight into biomedical challenges due to its rapid, long-term, and super-resolution (SR) imaging. However, artifacts that often appear in SIM images have long brought into question its fidelity, and might cause misinterpretation of biological structures. We present HiFi-SIM, a high-fidelity SIM reconstruction algorithm, by engineering the effective point spread function (PSF) into an ideal form. HiFi-SIM can effectively reduce commonly seen artifacts without loss of fine structures and improve the axial sectioning for samples with strong background. In particular, HiFi-SIM is not sensitive to the commonly used PSF and reconstruction parameters; hence, it lowers the requirements for dedicated PSF calibration and complicated parameter adjustment, thus promoting SIM as a daily imaging tool.

A GPU-accelerated fully 3D OSEM image reconstruction for a high-resolution small animal PET scanner using dual-ended readout detectors

In this work, a GPU-accelerated fully 3D ordered-subset expectation maximization (OSEM) image reconstruction with point spread function (PSF) modeling was developed for a small animal PET scanner with a long axial field of view (FOV). Dual-ended readout detectors that provided high depth of interaction (DOI) resolution were used for the small animal PET scanner to simultaneously achieve uniform high spatial resolution and high sensitivity. First, we developed a novel sinogram generation method, in which the dimension of the sinogram was determined first and then an event was assigned to a few neighboring sinogram elements by using weights that are inversely proportional to the distance from the measured line of response (LOR) to the LOR of the sinogram elements. System geometric symmetry, precomputation of LOR-driven ray-tracing and texture memory were applied to accelerate the GPU-based reconstruction. We developed a spatially variant PSF model where the PSF parameters were obtained by using point source images measured at 18 positions in the FOV and a spatial invariant PSF model where the PSF parameters were obtained by using only one image measured at the center FOV. The performance of the image reconstruction method was evaluated by using simulated phantom data as well as phantom and in-vivo mouse data acquired on the scanner. The results showed that the proposed reconstruction method provided better spatial resolution, a higher contrast recovery coefficient and lower noise than the OSEM reconstruction and was more than 1000 times faster than the CPU-based reconstruction. The spatially variant PSF model did not result in any spatial resolution improvement compared to the spatial invariant PSF model, and thus, the latter that is much easier to implement in image reconstruction and can be used in a small animal PET scanner using detectors with very high DOI resolution. A whole body 18F-FDG mouse image with high resolution and a high contrast to noise ratio was obtained by using the proposed reconstruction method.

Iterative approach for parametric PSF estimation

In this paper a parametric point spread function (PSF) estimation method is presented. This method can be employed for estimating the parameters of linear motion blur vector. The proposed method works on single image and estimates angle and length of motion blur vector to generate required PSF for deblurring. This method is based on step-by-step estimation of motion blur vector. In the first approximation the blind method considers short length vectors in all directions and deblurs image with PSF of these candidate vectors. The quality of deblurred image is assessed by a no-reference quality measurement metric which is proposed in this paper. The proposed no-reference image quality metric evaluates degradation in sharpness of edges and the amount of resulted artifact caused by saturated pixels, in the deblurred image. Those motion vectors that caused unacceptable deblurring results are omitted in the next iteration. The approximation is improved by increasing the length of the remaining vectors and the same process continues iteratively. The process goes on until only one vector remains as the estimation for motion blur vector. Experimental results show that in estimation of motion blur vectors, the length estimation error is less than one pixel in 85% of the cases and angle estimation error in 95% of the cases is less than one degree. Comparing with a conventional method indicates that the proposed method shows more than four times improvement in length estimation and 10% improvement in angle estimation. Moreover, the proposed method has comparatively lower computational load than other conventional deblurring methods.

Coupled Convolutional Neural Network With Adaptive Response Function Learning for Unsupervised Hyperspectral Super Resolution

Due to the limitations of hyperspectral imaging systems, hyperspectral imagery (HSI) often suffers from poor spatial resolution, thus hampering many applications of the imagery. Hyperspectral super-resolution refers to fusing HSI and MSI to generate an image with both high spatial and high spectral resolutions. Recently, several new methods have been proposed to solve this fusion problem, and most of these methods assume that the prior information of the Point Spread Function (PSF) and Spectral Response Function (SRF) are known. However, in practice, this information is often limited or unavailable. In this work, an unsupervised deep learning-based fusion method - HyCoNet - that can solve the problems in HSI-MSI fusion without the prior PSF and SRF information is proposed. HyCoNet consists of three coupled autoencoder nets in which the HSI and MSI are unmixed into endmembers and abundances based on the linear unmixing model. Two special convolutional layers are designed to act as a bridge that coordinates with the three autoencoder nets, and the PSF and SRF parameters are learned adaptively in the two convolution layers during the training process. Furthermore, driven by the joint loss function, the proposed method is straightforward and easily implemented in an end-to-end training manner. The experiments performed in the study demonstrate that the proposed method performs well and produces robust results for different datasets and arbitrary PSFs and SRFs.

Blind deconvolution in astronomy with adaptive optics: the parametric marginal approach

ABSTRACT One of the major limitations of using adaptive optics (AO) to correct image post-processing is the lack of knowledge about the system’s point spread function (PSF). The PSF is not always available as direct imaging on isolated point-like objects, such as stars. The use of AO telemetry to predict the PSF also suffers from serious limitations and requires complex and yet not fully operational algorithms. A very attractive solution is to estimate the PSF directly from the scientific images themselves, using blind or myopic post-processing approaches. We demonstrate that such approaches suffer from severe limitations when a joint restitution of object and PSF parameters is performed. As an alternative, here we propose a marginalized PSF identification that overcomes this limitation. In this case, the PSF is used for image post-processing. Here we focus on deconvolution, a post-processing technique to restore the object, given the image and the PSF. We show that the PSF estimated by marginalization provides good-quality deconvolution. The full process of marginalized PSF estimation and deconvolution constitutes a successful blind deconvolution technique. It is tested on simulated data to measure its performance. It is also tested on experimental AO images of the asteroid 4-Vesta taken by the Spectro-Polarimetric High-contrast Exoplanet Research (SPHERE)/Zurich Imaging Polarimeter (Zimpol) on the Very Large Telescope to demonstrate application to on-sky data.

Reconstruction of the ground-layer adaptive-optics point spread function for MUSE wide field mode observations

Context. Here we describe a simple, efficient, and most importantly fully operational point-spread-function (PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) wide field mode. Aims. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data. Methods. The PSFR approach is based on a Fourier description of the GLAO correction to which the specific instrumental effects of MUSE wide field mode (pixel size, internal aberrations, etc.) have been added. It was first thoroughly validated with full end-to-end simulations. Sensitivity to the main atmospheric and AO system parameters was analysed and the code was re-optimised to account for the sensitivity found. Finally, the optimised algorithm was tested and commissioned using more than one year of on-sky MUSE data. Results. We demonstrate with an on-sky data analysis that our algorithm meets all the requirements imposed by the MUSE scientists, namely an accuracy better than a few percent on the critical PSF parameters including full width at half maximum and global PSF shape through the kurtosis parameter of a Moffat function. Conclusions. The PSFR algorithm is publicly available and is used routinely to assess the MUSE image quality for each observation. It can be included in any post-processing activity which requires knowledge of the PSF.

Spatially-Variant CNN-based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy.

Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with highresolution microscopes leads to unsharp image regions and makes depth localization and quantitative image interpretation difficult. Here, we present a method that improves the resolution of light microscopy images of such objects by locally estimating image distortion while jointly estimating object distance to the focal plane. Specifically, we estimate the parameters of a spatiallyvariant Point Spread Function (PSF) model using a Convolutional Neural Network (CNN), which does not require instrument- or object-specific calibration. Our method recovers PSF parameters from the image itself with up to a squared Pearson correlation coefficient of 0.99 in ideal conditions, while remaining robust to object rotation, illumination variations, or photon noise. When the recovered PSFs are used with a spatially-variant and regularized Richardson-Lucy (RL) deconvolution algorithm, we observed up to 2.1 dB better Signal-to-Noise Ratio (SNR) compared to other Blind Deconvolution (BD) techniques. Following microscope-specific calibration, we further demonstrate that the recovered PSF model parameters permit estimating surface depth with a precision of 2 micrometers and over an extended range when using engineered PSFs. Our method opens up multiple possibilities for enhancing images of non-flat objects with minimal need for a priori knowledge about the optical setup.

Physics-based model of the adaptive-optics-corrected point spread function

Context.Adaptive optics (AO) systems greatly increase the resolution of large telescopes, but produce complex point spread function (PSF) shapes, varying in time and across the field of view. The PSF must be accurately known since it provides crucial information about optical systems for design, characterization, diagnostics, and image post-processing.Aims.We develop here a model of the AO long-exposure PSF, adapted to various seeing conditions and any AO system. This model is made to match accurately both the core of the PSF and its turbulent halo.Methods.The PSF model we develop is based on a parsimonious parameterization of the phase power spectral density, with only five parameters to describe circularly symmetric PSFs and seven parameters for asymmetrical ones. Moreover, one of the parameters is the Fried parameterr0of the turbulence’s strength. This physical parameter is an asset in the PSF model since it can be correlated with external measurements of ther0, such as phase slopes from the AO real time computer (RTC) or site seeing monitoring.Results.We fit our model against end-to-end simulated PSFs using the OOMAO tool, and against on-sky PSFs from the SPHERE/ZIMPOL imager and the MUSE integral field spectrometer working in AO narrow-field mode. Our model matches the shape of the AO PSF both in the core and the halo, with a relative error smaller than 1% for simulated and experimental data. We also show that we retrieve ther0parameter with sub-centimeter precision on simulated data. For ZIMPOL data, we show a correlation of 97% between ourr0estimation and the RTC estimation. Finally, MUSE allows us to test the spectral dependency of the fittedr0parameter. It follows the theoreticalλ6/5evolution with a standard deviation of 0.3 cm. Evolution of other PSF parameters, such as residual phase variance or aliasing, is also discussed.

Closing the gap between Earth-based and interplanetary mission observations: Vesta seen by VLT/SPHERE

Context. Over the past decades, several interplanetary missions have studied small bodies in situ, leading to major advances in our understanding of their geological and geophysical properties. These missions, however, have had a limited number of targets. Among them, the NASA Dawn mission has characterised in detail the topography and albedo variegation across the surface of asteroid (4) Vesta down to a spatial resolution of ~20 m pixel−1 scale. Aims. Here our aim was to determine how much topographic and albedo information can be retrieved from the ground with VLT/SPHERE in the case of Vesta, having a former space mission (Dawn) providing us with the ground truth that can be used as a benchmark. Methods. We observed Vesta with VLT/SPHERE/ZIMPOL as part of our ESO large programme (ID 199.C-0074) at six different epochs, and deconvolved the collected images with a parametric point spread function (PSF). We then compared our images with synthetic views of Vesta generated from the 3D shape model of the Dawn mission, on which we projected Vesta’s albedo information. Results. We show that the deconvolution of the VLT/SPHERE images with a parametric PSF allows the retrieval of the main topographic and albedo features present across the surface of Vesta down to a spatial resolution of ~20–30 km. Contour extraction shows an accuracy of ~1 pixel (3.6 mas). The present study provides the very first quantitative estimate of the accuracy of ground-based adaptive-optics imaging observations of asteroid surfaces. Conclusions. In the case of Vesta, the upcoming generation of 30–40 m telescopes (ELT, TMT, GMT) should in principle be able to resolve all of the main features present across its surface, including the troughs and the north–south crater dichotomy, provided that they operate at the diffraction limit.

Learning based restoration of Gaussian blurred images using weighted geometric moments and cascaded digital filters

Image moments such as zernike, tchebichef and geometric moments have been widely used in image processing applications. They have useful properties to detect edges. In this paper, we present how one of the moment families, in particular geometric moments (GM) can be utilized in estimating the sigma and size of the Gaussian point spread function (PSF) that degrades the images. With the knowledge of how edges vary in the presence of Gaussian blur, a method that uses low order geometric moments is proposed to estimate the PSF parameter. This is achieved by using the difference of the GMs of the original and the reblurred images as feature vectors to train extreme learning machine (ELM) to estimate the PSF parameters respectively. Further, a novel method that uses a cascaded digital filters operating as subtractors is proposed to transform the image from geometric moment domain to spatial domain. The effectiveness of the proposed method of estimating the PSF parameters is examined using cross database validation. The results show that the proposed method in most of the cases performs better than the three existing methods when examined in terms of the visual quality evaluated using structural similarity (SSIM) index.

Optimal combination of anti-scatter grids and software correction for CBCT imaging.

Cone beam computed tomography (CBCT) has been widely adopted in clinical practice for image-guided radiotherapy. Soft tissue contrast and Hounsfield units are impaired to the presence of scattered radiation. In our previous work, we proposed a high selectivity anti-scatter grid (ASG) as a possible solution to the problem. An alternative approach is the application of iterative scatter correction using deconvolution with scatter point spread function (PSF). The purpose of this work was to compare the performance of ASGs with different selectivity with and without the iterative and uniform scatter corrections in terms of CBCT image quality. A secondary objective of this study was to develop a novel measurement approach to measure the scatter point spread functions. The scatter PSF was modeled as a sum of two bivariate Gaussian functions. The PSF parameters were estimated from a series of transmission measurements through polystyrene slabs of varying thickness with lead partial beam-blocker for three different ASG designs ranging from low (5.6), medium (9), and high (11) selectivity. The scatter correction scheme is based on iterative convolution of the current estimate of the primary with the scatter PSF until the root mean square deviation (RMSD) of the measured projection and the sum of the estimate of primary and scatter falls below a predefined threshold. The image quality was evaluated with the CIRS CBCT Image Quality and Electron Density phantom in a head and neck and pelvis configuration and the CIRS Virtual Male Human Patient. The image quality was quantified by the contrast-to-noise ratio (CNR) relative to the uncorrected scans and the root mean square deviation of the average gray values for different regions with respect to the nominal Hounsfield units and the mean difference of the reconstructed HU between the planning CT and CBCTs of the virtual human phantom. For the head and neck phantom, the CNR increased with more advanced scatter correction algorithm and the ASG selectivity, reaching 3.9, 3.7, 3.5, and 3.1 for the high, medium, light, and with no grid configuration, respectively, combined with the iterative software correction. The same is true for the pelvis phantom with CNR improvement reaching 1.5 for the heavy and medium grid, 1.3 for the light grid, and 1.1 on its own. The HU RMSD for the head and neck phantom was 22HU, 13HU, 12HU, and 6HU for iterative correction without the grid, with the light grid, medium grid and the heavy grid, respectively. For same correction strategies, the values for the pelvis phantom where 170, 120, 34, and 27HU. The average difference with the PCT of the virtual human phantom was 59±48HU and 63±59HU with scans reconstructed with the iterative correction and two higher selectivity grids. Visual inspection revealed similar trends for a head-and-neck and prostate cancer patient. The best scatter mitigation strategy was found to be a combination of a grid with selectivity larger than 9, combined with iterative scatter estimation. None of the investigated grids required increasing the imaging dose. The PSF determined using proposed method leads to image quality improvements results for all but one of the investigated scenarios.

Spectral method for estimating the point-spread function in the task of eliminating image distortions

This paper gives a further development of a method for estimating the parameters of the point-spread function (PSF), based on the Fourier spectrum of a distorted image. This method makes it possible to estimate the PSF parameters: the angle θ and magnitude Δ of the image smearing, as well as the size ρ or σ of the image-defocusing spot. This is important for enhancing the image-reconstruction accuracy. The spectrum of a smeared image is compressed in the smearing direction, and this makes it possible to estimate θ and Δ. The spectrum of a defocused image is also compressed more strongly, the larger the defocusing spot. New, more accurate estimates of the defocusing parameters are derived, ρ using the Bessel function and σ using the three-sigma rule, and the smearing parameters θ and Δ are estimated using the Nyquist frequency. Numerical examples of the use of this technique are given. The technique thus developed can be used to enhance the accuracy with which smeared and defocused images are restored by mathematically processing them.

Shack-Hartmann-based objective straylight assessment of the human eye in an increased scattering angle range.

Objective measurement of straylight in the human eye with a Shack–Hartmann (SH) wavefront aberrometer is limited in imaging angle. We propose a measurement principle and a point spread function (PSF) reconstruction algorithm to overcome this limitation. In our optical setup, a variable stop replaces the stop conventionally used to suppress reflections and scatter in SH aberrometers. We record images with 21 diameters of the stop. From each SH image, the average intensity of the pupil is computed and normalized. The intensities represent integral values of the PSF. We reconstruct the PSF, which is the derivative of the intensities with respect to the visual angle. A modified Stiles Holladay approximation is fitted to the reconstructed PSF, resulting in a straylight parameter. A proof-of-principle study was carried out on eight healthy young volunteers. Scatter filters were positioned in front of the volunteers’ eyes to simulate straylight. The straylight parameter was compared to the C-Quant measurements and the filter values. The PSF parameter shows strong correlation with the density of the filters and a linear relation to the C-Quant straylight parameter. Our measurement and reconstruction techniques allow for objective straylight analysis of visual angles up to 4 deg.

Mallows’ statistics CL: A novel criterion for parametric PSF estimation

Considering blind image deconvolution as a statistical estimation problem, we propose an unbiased estimator of the prediction error – Mallows’ statistics CL – as a novel criterion for estimating a point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of smoother filterings (with frequency-dependent regularization term). We then perform non-blind deconvolution using the popular BM3D algorithm. The CL-based framework is exemplified with a number of parametric PSF’s, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel.The experimental results show that the CL-minimization yields highly accurate estimates of the PSF parameters, which also result in a negligible loss of visual quality, compared to that obtained with the exact PSF. The highly competitive results demonstrate the great potential of developing more powerful blind deconvolution algorithms based on the CL-estimator.

Enhancing resolution of single-pixel imaging system

In this paper, we propose a subpixel-shifted method to overcome the limitations on the resolution of an image obtained from single-pixel imaging system. In the proposed method, modulation system is moved by sub-integer low grid units, and new information contained in each shifted low grid area can be exploited to obtain a high-resolution image. The front and back modulation single-pixel imaging systems are analyzed. Based on the shifted and point spread function parameters, this method using compressed sensing algorithm can overcome the limitative resolution generated by the modulation system pixel size and transmission effect to get high-resolution image. Finally, the machining experiment results prove the effective of the proposed method.

SURE-Type Functionals as Criteria for Parametric PSF Estimation

Point spread function (PSF) estimation plays an important role in blind image deconvolution. This paper proposes two novel criteria for parametric PSF estimation, based on Stein's unbiased risk estimate (SURE), namely, prediction-SURE and its variant. We theoretically prove the SURE-type functionals incorporating exact (complementary) smoother filtering as the valid criteria for PSF estimation. We also provide the theoretical error analysis for the regularizer approximations, by which we show that the proposed frequency-adaptive regularization term yields more accurate PSF estimate than others. In particular, the proposed SURE-variant enables us to avoid estimation of noise variance, which is a key advantage over the traditional SURE-like functional. Finally, we propose an efficient algorithm for the minimizations of the criteria. Not limited to the examples we show in this paper, the proposed SURE-based framework has a great potential for other imaging applications, provided the parametric PSF form is available.