Fast Holographic Deconvolution

Transcription

1 Precision image-domain deconvolution for radio astronomy Ian Sullivan University of Washington 4/19/2013

2 Precision imaging Modern imaging algorithms grid visibility data using sophisticated beam models Frequency and polarization dependence Non-uniform arrays use the measured beam pattern of each antenna Direction-dependence Time variability

3 Source: Morales & Wyithe 2010 Recall (from Miguel s talk):

4 Visibility-domain subtraction (A-projection) Features: Sources are fit in the image domain Precise model visibilities are generated from the detected sources Model visibilities are subtracted from the data Residual visibilities are gridded and Fourier transformed

5 Visibility-domain subtraction (A-projection) Software Holography / forward modeling Features: Sources are fit in the image domain A precise u-v plane model is generated from the detected sources u-v model is integrated over the beam pattern to form visibilities, re-gridded, and Fourier transformed The dirty model image is subtracted from the data

6 Visibility-domain subtraction (A-projection) Software Holography / forward modeling (FHD) Key features: Degridding and gridding are pre-computed as a (complex) matrix H(u,u) contains all direction-, polarization-, and antenna-dependent beam effects

7 Model u-v Dirty u-v Dirty image (xpb 2 ) Ian Sullivan On center 2 o 5 o 10 o 20 o The Holographic Mapping Function

8 HEALPix mosaicing Standard w-projection increases K pix for long integrations Instead, resample snapshot images to HEALPix (mapping can be pre-computed and applied quickly) Combine single-polarization snapshots and weights in the holographic frame (xpb 2 ) Correct combined single-polarization maps by the combined weights and add/subtract to form Stokes maps Detect peaks in Stokes I map and update sky model Apply HMF to sky model for each snapshot

9 Jy Dirty image Stokes I

10 Jy Restored image Stokes I

11 Jy Residual image Stokes I

12 Back of the envelope cost comparison T A ~ N comp N vis K pix Grid and de-grid with different precision Note: ignoring here the cost of the Fourier transform and fitting components in the image T SH ~ 2 N comp N vis K pix Grid and de-grid N comp times with same precision N vis = N pix = N comp = K pix = T FHD ~ N vis K pix 2 + N comp N pix K pix 2 Build HMF (and grid once) Apply HMF N comp times

13 Advantages and Limitations FHD is most useful for: Compact array layouts (N vis >> N pix ) Large numbers of antennas Stable instruments Any situation with many overlapping visibilities High time resolution Continuum imaging with high frequency resolution Disk I/O limited systems

14 Advantages and Limitations FHD is at a disadvantage: If anything changes during processing Calibration Beam model Flagging Field of view To mitigate aliasing, must image 2 the desired FOV For minimum-redundancy array layouts Memory-limited systems

15 Conclusions FHD can achieve the same precision as visibilitydomain deconvolution Exact computational cost trade-off between FHD and A-projection is unclear for current instruments FHD changes the traditional cost scaling for deconvolution, and will be increasingly competitive for new large arrays Much greater computational intensity vs I/O The HMF can stay in memory once built Well suited to GPU implementation

16 The first 128T MWA data is coming out! One 2 minute snapshot observation: 101 working tiles 30.7 MHz bandwidth Dual polarization Size of visibilities on disk: 8.6GB ~ 1.65 resolution 51 sources > 100 sigma 2686 sources > 10 sigma

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18 Future work More than can be listed Wide-band effects Ionosphere Extended / diffuse sources Feed back residuals to improve beam model Automatic generation of 3D power spectrum Analyze more data! Southern sky survey Galactic plane Targeted long-integrations (EOR )

19 Jy Residual image Stokes Q

20 The Murchison Widefield Array (MWA) The Murchison Widefield Array (MWA) 128 Tiles of cm crossed dipole antennas 3km maximum baseline Located in the Murchison desert of Western Australia

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22 Dirty Image Jy Ian Sullivan 1100 deg 2 snapshot centered on Pictor A 5 minutes of data from the 32-tile MWA prototype

23 Restored Image Jy Pictor A snapshot

24 Source Image Jy Pictor A snapshot

25 Residual Image Jy Pictor A snapshot

26 Stokes Q Residual Image Ian Sullivan Jy Pictor A snapshot

27 Implementation 1. Calculate HMF and grid visibilities to u-v plane 2. FFT gridded visibilities to image domain 3a. Convert to HEALPix for long integrations 3. Convert from instrumental polarizations to Stokes 4. Calculate brightest component and update u-v model 5. Apply HMF to full model 6. Subtract dirty model from gridded visibilities 7. Repeat from step 2

28 Building the HMF 1. Define image resolution and FOV Image must be at least 2x larger than FOV 2. Define individual beam model (gridding kernel) for every visibility Kernel size limited to the physical aperture 3. Calculate the set of pixels within the kernel for each visibility 4. Group all visibilities gridded to exactly the same pixels 5. For each pixel, calculate the kernel value for every visibility, times the vector of kernel values for every pixel within the kernel If visibilities are grouped, this can be done efficiently as matrix multiplication 6. Combine any entries that map between the same pair of pixels 7. Convert matrix entries to a sparse storage format