Automatic Estimation of Modulation Transfer Functions

The modulation transfer function (MTF) is widely used to characterise the performance of optical systems. Measuring it is costly and it is thus rarely available for a given lens specimen. Instead, MTFs based on simulations or, at best, MTFs measured on other specimens of the same lens are used. Fortunately, images recorded through an optical system contain ample information about its MTF, only that it is confounded with the statistics of the images. This work presents a method to estimate the MTF of camera lens systems directly from photographs, without the need for expensive equipment. We use a custom grid display to accurately measure the point response of lenses to acquire ground truth training data. We then use the same lenses to record natural images and employ a data-driven supervised learning approach using a convolutional neural network to estimate the MTF on small image patches, aggregating the information into MTF charts over the entire field of view. It generalises to unseen lenses and can be applied for single photographs, with the performance improving if multiple photographs are available

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones

The unidentified TeV source (TeVJ2032+4130) and surrounding field: Final HEGRA IACT-System results

The unidentified TeV source in Cygnus is now confirmed by follow-up observations from 2002 with the HEGRA stereoscopic system of Cherenkov Telescopes. Using all data (1999 to 2002) we confirm this new source as steady in flux over the four years of data taking, extended with radius 6.2 arcmin (+-1.2 arcmin (stat) +-0.9 arcmin (sys)) and exhibiting a hard spectrum with photon index -1.9. It is located in the direction of the dense OB stellar association, Cygnus OB2. Its integral flux above energies E>1 TeV amounts to \~5% of the Crab assuming a Gaussian profile for the intrinsic source morphology. There is no obvious counterpart at radio, optical nor X-ray energies, leaving TeVJ2032+4130 presently unidentified. Observational parameters of this source are updated here and some astrophysical discussion is provided. Also included are upper limits for a number of other interesting sources in the FoV, including the famous microquasar Cygnus X-3.Comment: 7 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic

Scaling Relations and Overabundance of Massive Clusters at z>~1 from Weak-Lensing Studies with HST

We present weak gravitational lensing analysis of 22 high-redshift (z >~1) clusters based on Hubble Space Telescope images. Most clusters in our sample provide significant lensing signals and are well detected in their reconstructed two-dimensional mass maps. Combining the current results and our previous weak-lensing studies of five other high-z clusters, we compare gravitational lensing masses of these clusters with other observables. We revisit the question whether the presence of the most massive clusters in our sample is in tension with the current LambdaCDM structure formation paradigm. We find that the lensing masses are tightly correlated with the gas temperatures and establish, for the first time, the lensing mass-temperature relation at z >~ 1. For the power law slope of the M-TX relation (M propto T^{\alpha}), we obtain \alpha=1.54 +/- 0.23. This is consistent with the theoretical self-similar prediction \alpha=3/2 and with the results previously reported in the literature for much lower redshift samples. However, our normalization is lower than the previous results by 20-30%, indicating that the normalization in the M-TX relation might evolve. After correcting for Eddington bias and updating the discovery area with a more conservative choice, we find that the existence of the most massive clusters in our sample still provides a tension with the current Lambda CDM model. The combined probability of finding the four most massive clusters in this sample after marginalization over current cosmological parameters is less than 1%.Comment: ApJ in press. See http://www.supernova.lbl.gov for additional information pertaining to the HST Cluster SN Surve