David G. Sheppard

Iterative multiframe superresolution algorithms for atmospheric-turbulence-degraded imagery

The subject of interest is the superresolution of atmospheric-turbulence-degraded, short-exposure imagery, where superresolution refers to the removal of blur caused by a diffraction-limited optical system along with recovery of some object spatial-frequency components outside the optical passband. Photon-limited space object images are of particular interest. Two strategies based on multiple exposures are explored. The first is known as deconvolution from wave-front sensing, where estimates of the optical transfer function (OTF) associated with each exposure are derived from wave-front-sensor data. New multiframe superresolution algorithms are presented that are based on Bayesian maximum a posteriori and maximum-likelihood formulations. The second strategy is known as blind deconvolution, in which the OTF associated with each frame is unknown and must be estimated. A new multiframe blind deconvolution algorithm is presented that is based on a Bayesian maximum-likelihood formulation with strict constraints incorporated by using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wave-front sensing are used to demonstrate the superresolution performance of the algorithms.

Lapped nonlinear interpolative vector quantization and image super-resolution

This paper presents an improved version of an algorithm designed to perform image restoration via nonlinear interpolative vector quantization (NLIVQ). The improvement results from using lapped blocks during the encoding process. The algorithm is trained on original and diffraction-limited image pairs. The discrete cosine transform is used in the codebook design process to control complexity. Simulation results are presented which demonstrate improvements over the non-lapped algorithm in both observed image quality and peak signal-to-noise ratio. In addition, the nonlinearity of the algorithm is shown to produce super-resolution in the restored images.

A vector quantizer for image restoration

An algorithm based on nonlinear interpolative vector quantization (NLIVQ) is presented which accomplishes image restoration concurrently with image compression. The algorithm is applied to the problem of deblurring noise-free diffraction-limited images by training with a large set of blurred and original image pairs. Simulation results demonstrate a quantitative improvement in images processed by the algorithm, as measured by image peak signal-to-noise ratio (PSNR), as well as a significant improvement in perceived image quality. A theoretical formulation of the algorithm is presented along with a discussion of implementation, training and simulation results.

Comparison of image reconstruction algorithms using adaptive optics instrumentation

We present preliminary results from a comparison of image estimation and recovery algorithms developed for use with advanced telescope instrumentation and adaptive optics systems. Our study will quantitatively compare the potential of these techniques to boost the resolution of imagery obtained with undersampled or low-bandwidth adaptive optics; example applications are optical observations with IR- optimized AO, AO observations in server turbulence, and AO observations with dim guidestars. We will compare the algorithms in terms of morphological and relative radiometric accuracy as well as computational efficiency. Here, we present qualitative comments on image results for two levels each of seeing, object brightness, and AO compensation/wavefront sensing.

Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery

Algorithms for image recovery with super-resolution from sequences of short-exposure images are presented. Both deconvolution from wavefront sensing (DWFS) and blind deconvolution are explored. A multiframe algorithm is presented for DWFS which is based on maximum a posteriori (MAP) formulation. A multiframe blind deconvolution algorithm is presented based on a maximum likelihood formulation with strict constraints incorporated using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wavefront sensing are used to demonstrate the super-resolution performance of the algorithms.

Multiframe Poisson map deconvolution of astronomical images

Two multiframe formulations of Hunts Poisson maximum a posteriori (MAP) image restoration algorithm (Hunt and Sementilli, 1992; and Hunt 1995) are presented as a means to restore an astronomical object from multiple short-exposure images. This work anticipates accurate wavefront sensor estimates of the optical transfer function of the atmosphere and telescope combination. Theoretical discussion of the algorithms is presented with simulation results. These results indicate that the multiframe algorithms produce significantly better restorations than single frame algorithms. Additionally, our studies demonstrate that the multiframe algorithms presented accomplish super-resolution.

Removal of image defocus and motion blur effects with a nonlinear interpolative vector quantizer

In this paper, results are presented which demonstrate the removal of image defocus and motion blur effects using an algorithm based on nonlinear interpolative vector quantization (NLIVQ). The algorithm is trained on original and diffraction-limited image pairs which are representative of the class of images of interest. The discrete cosine transform is used in the code-book design process to control complexity. Imagery processed with this algorithm demonstrate both qualitative and quantitative improvements (as measured by the peak signal-to-noise-ratio before and after processing).

Super-resolution of imagery acquired through turbulent atmosphere

The resolution of images is determined by the processes of diffraction. Recently, practical algorithms have emerged that are capable of recovering spatial frequency detail that lies beyond the diffraction limit of an image sensor. In this presentation we shall briefly review some of the aspects of super-resolution algorithms and then discuss the extension of same to images obtained through a turbulent atmosphere. We will present a multiframe super-resolution algorithm that achieves reconstruction of diffraction-limited detail by using multiple speckle image frames and wavefront sensor data on the instantaneous point-spread-function. Examples of simulations of the algorithm will be given, along with a discussion of how the algorithm can be integrated with existing blind deconvolution algorithms to relax the requirements for wavefront sensing.

Blur identification from vector quantizer encoder distortion

A method is presented for image blur identification from vector quantizer (VQ) encoder distortion. The method requires a set of training images produced by each member of a set of candidate blur functions. Each of these sets is then used to train a VQ encoder. Given an image degraded by an unknown blur function, the blur function can be identified by choosing from among the candidates the one corresponding to the VQ encoder with the lowest encoder distortion. Two training methods are investigated: the generalized Lloyd algorithm and a non-iterative discrete cosine transform (DCT)-based approach.

Resolution limits for shadow imaging of geosynchronous satellites: analytic and simulated approaches

Shadow imaging is a technique to obtain highly resolved silhouettes of resident space objects (RSOs) which would otherwise be unattainable using conventional terrestrial based imaging approaches. This is done by post processing the measured irradiance pattern (shadow) cast onto the Earth as the RSO occults a star. The research presented here focuses on recent developments in shadow imaging of geosynchronous (GEO) satellites with near stationary orbits approximately 36,000 km from the Earth. The fundamental resolution limits of shadow imaging are quantified analytically as a function of spectral bin width of the collected light. A set of simulated imagery is shown to agree with analytically derived resolution limits.