Point Spread Function Estimation Research Articles

Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur.

Blind-deconvolution microscopy, the simultaneous estimation of the specimen function and the point-spread function (PSF) of the microscope, is an underdetermined problem with nonunique solutions that are usually avoided by enforcing constraints on the specimen function and the PSF. We derived a maximum-likelihood-based method for blind deconvolution in which we assume a mathematical model for the PSF that depends on a small number of parameters (e.g., less than 20). The algorithm then estimates the unknown parameters together with the specimen function. The mathematical model ensures that all the constraints of the PSF are satisfied, and the maximum-likelihood approach ensures that the specimen is nonnegative. The method successfully estimates the PSF and removes out-of-focus blur. The PSF estimation is robust to aberrations in the PSF and to noise in the image.

Reconstruction of turbulence-degraded images using the vector Wiener filter

Adaptive optics and speckle imaging are common methods for improving Fourier domain signal-to-noise ratio (SNR) in astronomical images. These techniques may benefit from linear processing to decon- volve blurring due to the attenuation of high spatial frequencies in the compensated images. Typical linear deconvolution methods require an explicit estimate of the random atmospheric-optical system point spread function or optical transfer function (OTF). In addition, a priori knowledge of the object class and noise are not used in an optimal manner. We apply a vector Wiener filter to photon-limited images degraded by atmo- spheric turbulence to demonstrate the potential advantages of optimal deconvolution processing. This filter incorporates model-based informa- tion about object, OTF, and noise. To our knowledge, this is the first application of complete OTF correlation statistics to the reconstruction of turbulence-degraded images. Computer simulation of binary star images show the vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for non-wide-sense sta- tionary objects. Much of this performance improvement can be attributed to variance reduction in the noisy Fourier data at spatial frequencies where the mean OTF is severely attenuated. However, vector Wiener filter performance is substantially degraded with respect to both mean square error and mean square phase error at spatial frequencies where the OTF SNR is less than unity. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)01009-5)

Out-of-focus blur estimation and restoration fordigital auto-focusingsystem

A fully digital auto-focusing system based on point-spread function (PSF) estimation is proposed. To increase accuracy in estimating the PSF of the defocused image, the input image is subdivided, and the step responses of edge-containing subimages are averaged. The PSF, which results from out-of-focus blur, is estimated by differentiating the averaged step response along the appropriately estimated edge direction under the assumption that an image usually contains a piece-wise linear boundary between an object and background. By using the estimated PSF, the corresponding image restoration filter is realised, based on the constrained least squares approach.

Generation of arbitrarily focused images by using multiple differently focused images

We propose a novel method of arbitrarily focused image generation using multiple differently focused images. First, we describe our previously proposed select and merge method for all focused image acquisition. We can get good results by using this method but it is not easy to extend this method for generating arbitrarily focused images. Then, based on the assumption that depth of a scene changes stepwise, we derive a formula for reconstruction between the desired arbitrarily focused image and multiple acquired images; we can reconstruct the arbitrarily focused image by iterative use of the formula. We also introduce coarse-to-fine estimation of point spread functions (PSFs) of the acquired images. We reconstruct arbitrarily focused images for a natural scene. In other words, we simulate virtual cameras and generate images focused on arbitrary depths. © 1998 SPIE and IS&T. [S1017-9909(98)02201-6]

Generation of a restored image from a video sequence recorded under turbulence effects

Turbulence conditions affect video images in two ways. They cause local blur, and they distort the geometry of the scene. A video sequence of a still scene recorded under turbulence appears to contain local random motion of small neighborhoods in the images. The blur is an accumulated result of the imaging point spread function and the local motion. The geometric distortion is due to the fact that small neighborhoods move in different directions. The restoration scheme reported takes care of the geometric distortion as well as the blur. The geometric distortion is reduced by averaging the gray levels of relatively long (a few hundred images) video segments. The averaging reduces the geometric distortion, but it increases the blur. The second stage is the estimation of the global point spread function. The blur in the average image is a combination of the effects of the imaging system transfer function, the turbulence, and the averaging of the sequence. The global nonisotropic point spread function is estimated based on edge responses in the average image. A Wiener filter is used for the restoration of the image. The presented experimental results are superior to the results obtained by a previously proposed majority-vote technique.

Estimation of the adaptive optics long-exposure point-spread function using control loop data

Astronomical images obtained with adaptive optics systems can be enhanced by using image restoration techniques. However, this usually requires an accurate knowledge of the system point-spread function (PSF) which is variable in time. We present a method to estimate the PSF related to each image, using data from the adaptive optics control computer, namely, the wave-front sensor measurements and the commands to the deformable mirror, accumulated in synchronization with the acquisition. This method requires no extra observing time and has been successfully tested on PUEO, the Canada–France–Hawaii Telescope adaptive optics system. With this system, accurate PSF estimations could be achieved for guide stars of magnitude 13 or brighter.

Sub-pixel non-parametric PSF estimation for image enhancement

Applying standard resolution enhancement and sub-pixel measurement techniques to an imaging system is problematic when the system characteristics are not known. The importance of precise system characterisation is often underestimated in resolution enhancement and sub-pixel measurement. The methods presented allow accurate sub-pixel measurements of system characteristics to be made with minimal assumptions. The non-parametric technique developed accurately characterises the properties of an imaging system. This is demonstrated by measuring the point spread function (PSF), along with static and dynamic distortions, for a high precision thermal imaging system to sub-pixel accuracy. The PSF is estimated to ±0.1 of a pixel and imaging system errors to the order of ±0.1 of a pixel are identified. The improved precision of PSF estimation is shown to benefit resolution enhancement. A novel feature of the method used to estimate the PSF (and to enhance the image) is that the estimation of the spatially invariant sub-pixel PSF and of geometric distortion are performed independently.

Iterative restoration of fast‐moving objects in dynamic image sequences

If a point on an object passes over two or more photoreceptors during image acquisition, a blur will occur. Under these conditions, an object or scene is said to move fast relative to the camera's ability to capture the motion. In this work, we consider the iterative restoration of images blurred by distinct, fast moving objects in the frames of a (video) image sequence. Even in the simplest case of fast object motion, the degradation is spatially variant with respect to the image scene. Rather than segmenting the image into regions where the degradation can be considered space invariant, we allow the blur to vary at each pixel and perform iterative restoration. Our approach requires complete knowledge of the blur point spread function (PSF) to restore the scene. The blur of fast moving object in a single frame is under specified. With the appropriate assumptions, an estimate of the blur PSF can be specified to within a constant scaling factor using motion information provided by a displacement vector field (DVF). A robust iterative restoration approach is followed which allows for the incorporation of prior knowledge of the scene structure into the algorithm to facilitate the restoration of difficult scenes. A bilinear approximation to the continuous PSF derived from the motion estimate is proposed to obtain results for real and synthetic sequences. We found this approach suitable for restoring motion degradations in a wide range of digital video applications. The results of this work reinforced the well known flexibility of the iterative approach to restoration and its application as an off-line image sequence restoration method.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Estimation of point-spread functions and modulation-transfer functions of optical devices by statistical properties of randomly distributed surfaces

The point-spread function a(PSF) and the modulation-transfer function (MTF) are important tools to characterize the information transfer through optical devices. They give useful information about the resolution. Several methods have already been achieved to calculate the PSF and the MTF from theoretical aspects of wave propagation or from experimental results. I present a novel way of estimating these two functions. It deals with statistical considerations for a randomly distributed surface involving a statistical determination of the PSF and the MTF. Indeed, in this case the theoretical shape of the autocorrelation function of such surface profiles is known. It is a decaying exponential function α[exp(-β|x|)]. Comparingthe theoretical autocorrelation-function profile with the experimental one and deconvolving in Fourier space leads to an estimation of the MTF of the imaging device. Applying the inverse Fourier transform to the MTF involves the computation of the PSF, assuming that the latter has no imaginary part and is symmetrical. The two-dimensional images are regarded as an iteration of one-dimensional ones according to the orthogonal direction. The MTF's and PSF's are therefore one-dimensional. Different results are presented. The first result proceeds from investigation with scanning near-field microscopy and illustrates the method step by step. The tunneling effect is detected assuming that the information transfer is linear. The last result concerns an optical profilometer, and the influence of the microscope objective is studied.

Estimation of SPOT P-mode point spread function and derivation of a deconvolution filter

The integrating effect of the point spread function of a satellite remote sensing system significantly affects the signature from a single cover class if the surrounding cover is dissimilar and also reduces the spatial resolution of the output data. Digital SPOT P-Mode data acquired over linear ground edge and impulse features were analysed to determined the SPOT system's line spread function. This was integrated to give the normalised point spread function, and then inverted to derive an equation to estimate the true ground response by deconvolution of the observed response. The paper describes the procedures used in determining the point spread function, and applies the result to a number of urban features. A significant improvement in the image quality resulted.

Statistical estimation of point spread function applied to scanning near-field optical microscopy

Scanning near-field optical microscopy is a newly-born type of microscopy whose typical resolution reaches a few nanometres. One important step of the characterisation of such an optical device is the measurement of its point spread function (PSF). Up to now, only theoretical considerations about the PSF or results of simulations have been reported. The method used to estimate the PSF consists of determining the theoretical power spectrum of the surface profile corresponding to an experimental one. Using a known profile (randomly distributed) whose theoretical power spectrum can be calculated, allows in Fourier space the deconvolution of the measured profile and the PSF. It yields the estimation of the statistical PSF. The main advantage of this method is that the estimated PSF is experimental and describes the capabilities of such devices easily although the result is statistical.

Single-frame blind deconvolution by means of frame segmentation

For restoration of an image degraded with a shift-invariant point-spread function (PSF), partial images segmented from the degraded image are blind deconvolved in parallel for estimation of the common PSF in each partial image. An object function is reconstructed by deconvolution of the whole image with the PSF. A technique for calibrating contamination caused by the segmentation is developed. Results for a computer-generated image and an atmospherically degraded solar image are presented.

Image identification and restoration in the subband domain

When faced with a large support point spread function (PSF), the iterative expectation-maximization (EM) algorithm, which is often used for PSF identification, is very sensitive to the initial PSF estimate. To deal with this problem, the authors propose to do EM image identification and restoration in the subband domain. After the image is first divided into subbands, the EM algorithm is applied to each subband separately. Since the PSF can be taken to have smaller support in each subband, these subbands should be less of a problem with the EM model identification. They also introduce an adaptive subband EM method for use in the upper frequency subbands.

Accurate Measurement of the Geometry for a Full-Disk Solar Image and Estimation of the Observational Point Spread Function

view Abstract Citations (19) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Accurate Measurement of the Geometry for a Full-Disk Solar Image and Estimation of the Observational Point Spread Function Toner, C. G. ; Jefferies, S. M. Abstract We present a new method for accurately determining the geometry for full-disk solar intensity images that is insensitive to changes in the observational point spread function. The method exploits the zero-crossing properties of the Fourier transform of an observed image to recover the image's true dimensions and to reconstruct an azimuthally averaged estimate for the point spread function. Simulations show that the undistorted image dimensions can be reproduced to better than 0.01 of a resolution element, and that the point spread function can be recovered to within 5% at low spatial frequencies and 15% at high spatial frequencies. Preliminary tests with real data confirm the results from the simulations and show the method to be robust. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173207 Bibcode: 1993ApJ...415..852T Keywords: SUN: FUNDAMENTAL PARAMETERS; SUN: OSCILLATIONS; TECHNIQUES: INTERFEROMETRIC full text sources ADS |

Blur identification by residual spectral matching

The estimation of the point spread function (PSF) for blur identification, often a necessary first step in the restoration of real images, method is presented. The PSF estimate is chosen from a collection of candidate PSFs, which may be constructed using a parametric model or from experimental measurements. The PSF estimate is selected to provide the best match between the restoration residual power spectrum and its expected value, derived under the assumption that the candidate PSF is equal to the true PSF. Several distance measures were studied to determine which one provides the best match. The a priori knowledge required is the noise variance and the original image spectrum. The estimation of these statistics is discussed, and the sensitivity of the method to the estimates is examined analytically and by simulations. The method successfully identified blurs in both synthetically and optically blurred images.

Point spread function estimation and correction for digitized film radiography

Point spread function estimation and correction for digitized film radiography

Development and validation of a Monte Carlo simulation of photon transport in an Anger camera

The geometric component of the point spread function (PSF) of a gamma camera collimator can be determined analytically, and the penetration component can be calculated readily by numerical ray-tracing. A Monte Carlo simulation of photon transport which includes collimator scatter is developed. The simulation was implemented with an array processor which propagates up to 1024 photons in parallel, allowing accurate estimates of the total radial PSF in less than a day. The simulation was tested by imaging monoenergetic point sources of Tc-99m, Cr-51, and Sr-85 (140, 320, and 514 keV, respectively) on a General Electric Star Cam with low-energy, general-purpose, and medium-energy collimators. Comparisons of measured and simulated PSFs demonstrate the validity of the model and the significance of collimator scatter in the degradation of image quality.

A tomographic image of mantle structure beneath Southern California

We determined the variations in seismic structure beneath southern California by using a tomographic method of inversion on teleseismic P delays recorded with the Southern California Array. The algorithm employed was a modified form of an Algebraic Reconstruction Technique (ART) used in medical X‐ray imaging. Deconvolution with an empirically estimated point spread function was also used to help in focusing the image.The inversion reveals two prominent features beneath the region. The first is a thin, vertical wedge directly beneath the Transverse Ranges that is 2‐3% faster than the surrounding region. This feature deepens to the east, attaining a maximum depth of about 250 km beneath the San Bernardino Mountains. The second feature is a major zone of low velocity material that is 2‐4% slow under the Salton Trough rift valley, extending to a depth of about 125 km. Two possible explanations for the spatial association of the Transverse Ranges with the velocity anomaly below are lithospheric subduction or small‐scale sublithospheric convection in the region of the Big Bend of the San Andreas Fault. The low velocity anomaly beneath the Salton Trough is consistent with convective upwelling there.

Study of Target Edge Response Viewed Through Atmospheric Turbulence over Water

Photographed edge response of a quadrant target made through atmospheric turbulence at a range of 1.6 km 10.7 m above water was found to fit an error function form quite accurately. A theoretical estimate of the intensity point spread function based upon a parabolic approximation to the wave structure function for a point source is consistent with the data. Assuming the validity of the approximation, thermal values of C(n) give turbulence inner scales in the millimeter range.