Massively Parallel Spatially-Variant Maximum Likelihood Image Restoration

A. F. Boden, D. C. Redding

Jet Propulsion Laboratory, California Institute of Technology

R. J. Hanisch, J. Mo

Space Telescope Science Institute

Abstract:

1. Introduction

Herein we report on our ongoing research in the restoration of HST images with spatially-variant point-spread function (SV-PSF) models. This research is embodied in a prototype restoration code MPRL---Massively Parallel Richardson-Lucy algorithm (Richardson 1972; Lucy 1974)---scheduled to be released to the astronomy community in mid-1996. This development is motivated by the primary mirror (PM) fabrication error and attendant spherical aberration in the Hubble Space Telescope (HST) Optical Telescope Assembly (OTA). We find considerable advantage by employing high-fidelity models of the HST optics to enhance our knowledge of the instrument PSF for individual observation conditions (COMP---Redding 1993; Redding 1995). This high-fidelity model can then be used to predict the instrument point-spread function (PSF) at arbitrary field points in the image. Restoration of HST imagery, and in particular images from the primary imaging instrument, WFPC2, proved to be particularly challenging because WFPC2's PSF was both large in its spatial extent, and spatially-varying across the focal planes of the instrument. These two effects exacerbate both the complexity of and time required for restoration calculations, so most restoration techniques must compromise the spatial variability of the PSF model to achieve tractable runtimes (Hanisch 1995).

2. Concurrent Spatially-Variant Maximum Likelihood Restoration

2.1. Spatially-Variant Point-Spread Function

The efficacy of any deconvolutional restoration technique is eventually limited by the fidelity of the PSF. In principle the PSF for any optical system is continuously spatially varying across the focal plane. In particular, WF/PC-1 and WFPC2 exhibit a strong spatial variation of their PSF; the PM spherical aberration introduces a strong phase gradient across the instrument apertures, and multiple internal obscurations complicate the phase distribution with field angle within the focal plane (MacKenty 1992; Burrows 1995). In practice we are often limited in the number and coverage of the reference PSFs for a particular image. We therefore have implemented an interpolative PSF model that computes the PSF for an arbitrary image location based on a (possibly irregular) grid of reference PSFs and a bilinear interpolation scheme (Press 1986). This method assures continuity in our model of the PSF across the focal plane with a sparse sampling of reference data. In testing with computationally-estimated PSFs we observe this interpolation model to the follow the simulated PSF faithfully using only a modest number of reference PSFs.

We find a great deal of value in employing physical optics models to aid our analysis of individual datasets. We are using the COMP software to refine our estimates of the overall optical prescription of the HST and camera/detector, and can eliminate some of the uncertainty in the PSF owing to time variability if we have reasonably well-exposed field stars in the field of view of the target observation.

2.2. Concurrency in the Richardson-Lucy Method

Several groups have studied the application of concurrent computing techniques to provide spatially-variant PSF models (SV-PSF) and thereby improve restoration performance on HST data (Cobb 1993; Faisal 1995; Boden 1995). Concurrency in the Richardson-Lucy (R-L) method is accomplished most simply by a systematic division of the image to be restored (Trussel 1978). Only pixel values that are within the support of the PSF are interdependent. Thus an arbitrary division of the image into segments with appropriate overlapping guard bands allows each segment to be processed independently. In practice the minimum segment size is on the order of the PSF diameter---this is driven by the surrounding guard band which is a PSF radius in size.

To realize this concurrency our R-L implementation uses the popular public-domain Parallel Virtual Machine (PVM) communications package (Geist 1994). PVM allowed us to implement a R-L restoration engine, and spawn a large number of these engines each restoring separate image sections on a heterogeneous set of UNIX workstations. Because PVM has implementations on MPP multicomputers, the same code is directly portable to machines such as the Intel Paragon and Cray T3D.

3. Results

Star Cluster Simulation Test Case

A standard test case for HST image restoration is a set of synthetic Wide Field 2 (WF2) exposures of a simulated star cluster. There are versions of these synthetic observations corresponding to both WF/PC-1 (pre-repair) and WFPC2 (post-repair). Deconvolutions on this synthetic testcase conclusively demonstrate the value of SV-PSF restoration in both WF/PC-1 and WFPC2 data (for brevity we refer the reader to Boden 1995 for detailed performance information on this testcase).

HH 47

Herbig-Haro (HH) objects are bipolar outflow jets produced in the protostellar accretion processes. A particularly compelling example of the HH phenomenon is the HH 46/47 complex (Reipurth 1991). Restorations of recent WFPC2 imagery by Reipurth et al. of HH 47 are interesting in that they improve spatial resolution and dynamic range in areas of sufficient S/N, and these improvements further constrain the hydrodynamic modeling of this source. HH 47 also represents a particularly challenging target for restoration in that the object covers a full WF chip (approx. 1 1), requiring a full-field SV-PSF restoration. Figure 1 shows contour plots of the bow shock high-excitation region HH 47a. The MPRL restoration exhibit higher dynamic range (contrast between bright pixels and the smooth background enhanced by about 45%) and morphological detail than the original data. The added resolution aids in comparing the HH 47 data to hydrodynamic simulation of the source. This restoration was used in the NASA press release and scientific publication of this data (Heathcote 1995).

  
Figure 1: Contour Plots of SII HH 46/47 Imagery Before and After Restoration. Left: contour plot of the bow shock emission region HH 47a (Reipurth 1991) in the WFPC2 WF SII imagery of Reipurth et al. (Heathcote 1995) (size is 15 X 15). Right: the same region after SV-PSF restoration with MPRL. The dynamic range and spatial resolution are considerably higher in the restored version; the restoration was used in the NASA press release and scientific publication of this data.
Figure 1: (left) PS 37 Kb, Figure 1: (right) PS 45 Kb

Acknowledgments:

The work described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology and the Space Telescope Science Institute under contracts with the National Aeronautics and Space Administration.

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