-- UrvashiRV - 2010-08-19

Current Status of Imaging Algorithms in CASA

This page contains a list of existing and planned imaging algorithms for CASA, based on the current code-design.

EVLA Memo 139 "Plan for Imaging Algorithm Research and Development",S.Bhatnager, July 2009, describes the current research plan in more detail. The ARDG DevelopmentList contains another list of planned algorithms.

Introduction :

Iterative image reconstruction in CASA is divided into two parts - Major and Minor cycles. A chi-square minimization process is followed by alternating Major and Minor cycles until convergence is achieved. Convergence is usually defined as the peak of the residual image crossing below a user-specified threshold.

  • Imaging (Major Cycle) : Construct an image from a list of visibilities and apply direction-dependent corrections via gridding convolution functions. Predict model visibilities from a model image, applying various direction-dependent effects during de-gridding.

  • Deconvolution (Minor Cycle) : Reconstruct the sky brightness distribution (dirty image -> clean/model/component/restored image)

Imaging Algorithms (Major Cycle)

Input kiss Calibrated/corrected visibilities, and the current model image (initially empty).
*Output
: Normalized residual image in units of Jy/beam, Point-Spread-Function (PSF) with unit peak.
  • Standard 2D Imaging :

Imaging weights and weighted visibilities are first resampled onto a regular uv-grid (convolutional resampling) using a prolate-spheroidal function as the gridding convolution function (GCF). The result is then Fourier-inverted and grid-corrected to remove the image-domain effect of the GCF. The PSF and residual image are then normalized by the sum-of-weights.
  • Imaging with direction-dependent corrections :

Older methods use standard imaging along with image-domain operations to correct for direction-dependent effects. Newer methods apply direction-dependent,time-variable and baseline-dependent corrections during gridding in the visibility-domain, by choosing/computing the appropriate GCF to use along with the imaging-weights.

W-term :

For wide-field imaging, sky curvature and non-coplanar baselines result in a non-zero w-term. Standard 2D imaging applied to such data will produce artifacts around sources away from the phase center. There are three methods to correct the w-term effect.

  • Image-plane faceting : Multiple image-domain facets are created by gridding the visibilities multiple times for different phase-reference centers. These facets are deconvolved separately using their own PSFs. Model images from all facets are used to predict a single set of model visibilities, from which a new set of residual-image facets are computed. One disadvantage of this method is that emission that crosses facet boundaries will not be deconvolved accurately. (Ref : Cornwell & Perley 1992, 1999).
  • UV-domain faceting : Visibilities are gridded multiple times onto the same uv-grid, each time with a different phase-reference center. One single dirty/residual image is constructed from the resulting grid and deconvolved using a single PSF. Unlike in image-domain faceting, this deconvolution is not affected by emission that crosses facet boundaries. (Ref : Sault et al, 1999)

  • W-projection : Visibilities with non-zero w-values are gridded using using a GCF given by the Fourier transform of the Fresnel EM-wave propagator across a distance of w wavelengths. In practice, GCFs are computed for a finite set of w-values (wprojplanes) and applied during gridding. W-projection is roughly an order of magnitude faster than faceted imaging because it grids each visibility only once. (Ref: )

Primary-Beam :

The aperture-illumination-function (AIF) of each antenna results in a direction-dependent complex gain that can vary with time and is usually different for each antenna. The resulting antenna power pattern is called the primary beam. There are two methods to correct for the effect of the primary beam.

  • Image-domain PB-correction : A simple method of correcting the effect of the primary beam is a post-deconvolution image-domain division of the model image by an estimate of the average primary beam. This method ignores primary-beam variations across baselines and time, and is therefore approximate, limiting the imaging dynamic-range within the main lobe of the beam to about 10^5.

  • A-projection : Time and baseline-dependent corrections are applied during gridding, by computing GCFs for each baseline as the convolution of the complex conjugates of two antenna aperture illumination functions. An additional image-domain normalization step is required, and can result in either a flat-sky or flat-noise image. The advantage of this method is that known time and baseline variability can be accounted for, both during gridding as well as de-gridding. (Ref:).

Pointing-offset correction :

An antenna pointing offset results in a phase-gradient across the aperture illumination function. Ignoring pointing errors of the order of 20 arcsec can limit the imaging dynamic range to 10^5. A known pointing-offset can be corrected during gridding by augmenting the A-projection GCF with a phase-gradient calculated to cancel that due to the pointing offset. Note that the EVLA beam-squint is a polarization-dependent pointing offset, and can also be corrected in this way.

Mosaics :

Data from multiple pointings can be combined during gridding to form one single large image.Three methods are currently implemented.

  • Linear Deconvolution : Each pointing is deconvolved and the final deconvolved images are stitched together. Heuristics and weights are used to improve the accuracy of deconvolution of emission present in multiple (overlapping) pointings.

  • Joint Deconvolution : Dirty/residual images are constructed separately for each pointing, and then weighted and stitched together before deconvolution. The advantage of this method is that deconvolution proceeds on one single image, eliminating the problem of deconvolving emission present in multiple pointings. However, the PSF used during deconvolution will be approximate.

  • Mosaic Imaging : Data from each pointing is gridded using a GCF augmented with a phase-gradient (across the spatial-frequency plane) corresponding to the difference between the phase-reference center of the pointing and of the final image. This can be thought of as an intentional pointing-offset. Since this method uses all the visibilities at once and produces one dirty image and one PSF, it has better imaging fidelity (and performance) than linear or joint deconvolution.

Deconvolution Algorithms (Minor Cycle)

*Input kiss Dirty/residual image, PSF
*Output kiss Model/component/restored image.

  • CLEAN :
Model the sky brightness distribution as a collection of point sources. Iteratively pick out the location and amplitude of flux-components and subtract the contribution of these components from the current residual image (Clean-iterations). Variants : Clark/Hogbom/Cotton-Schwab

  • MS-Clean :
Model the sky brightness distribution as a collection of 'blobs' (inverted,truncated paraboloids) of different scale sizes (preset by the user). Use an approximation to a linear least squares approach within Clean-iterations to solve for best-fit flux components.

  • MSMFS-Clean :
Model the wide-band sky brightness distribution as a collection of blobs of different scale sizes, whose amplitudes follow a polynomial in frequency. Use a linear-least squares approach within Clean-iterations to solve for best-fit spectral and spatial parameters.

  • MEM :
Model the sky brightness distribution as a collection of point-sources. Use a prior image along with an entropy-based penalty function to bias the solution of pixel amplitudes.

Combinations of Major and Minor cycle possible in CASA, and the resulting functionality :

The goal of the current algorithm-development effort in CASA is to provide the ability to match any or all imaging modes (Major cycles with direction-dependent corrections) with any Minor-cycle deconvolution algorithm. The end-goal is to enable "Wide-Field Wide-Band Full-Stokes Imaging of emission at multiple spatial scales".
Wide-Field Imaging :
Existing :
  • Primary-beam : Image-domain corrections, A-projection with Clean, MS-Clean, MEM (all with Cotton-Schwab Major/Minor cycles)
  • Mosaics : Linear, Joint, gridded-mosaic with Clean, MS-Clean, MEM (all with Cotton-Schwab Major/Minor cycles)
  • w-term : image and uv-faceting, w-projection with Clean, MS-Clean, MEM (all with Cotton-Schwab Major/Minor cycles)
In progress :
  • Use A-projection, w-projection and gridded-mosaicing simultaneously.
Multi-Scale Deconvolution :
Existing :
  • MS-Clean with standard gridding and all direction-dependent-correction methods.
In progress :
  • ASP-Clean algorithm.
Wide-Band Imaging :
Existing :
  • MS-MFS-Clean with standard gridding (wide-band narrow-field imaging).
In progress :
  • Combine MS-MFS with A-projection, w-projection, and gridded-mosaicing (wide-band wide-field imaging)
Full-Stokes Imaging :
Existing :
  • Clean, MS-Clean, MEM separately for Stokes I,Q,U,V, with standard gridding, w-projection, and mosaic-gridding.
In progress :
  • Correction of full-Stokes PB effects (full-Stokes A-projection),
  • MS-MFS for Stokes Q,U,V.
  • Faraday Rotation Synthesis (Ref : )
Topic revision: r2 - 2010-08-19, UrvashiRV
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