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Mathematical Approaches to Image Deconvolution

Mathematical Approaches to Image Deconvolution. Editor: Ludwig Schwardt Presenter: Ludwig Schwardt. Attendees. Ludwig Schwardt Anna Scaife Sarod Yatawatta Stefan Wijnholds Amir Leshem Urvashi Rau Sanjay Bhatnagar Rob Reid Panos Lampropoulos Steve Myers. Relevant talks.

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Mathematical Approaches to Image Deconvolution

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  1. Mathematical Approaches to Image Deconvolution Editor: Ludwig Schwardt Presenter: Ludwig Schwardt

  2. Attendees • Ludwig Schwardt • Anna Scaife • Sarod Yatawatta • Stefan Wijnholds • Amir Leshem • Urvashi Rau • Sanjay Bhatnagar • Rob Reid • Panos Lampropoulos • Steve Myers

  3. Relevant talks • Least Squares All-Sky Imaging With A LOFAR Station (Stefan Wijnholds) • Back to the future with Shapelets (Sarod Yatawatta) • Parametric imaging and calibration techniques (Amir Leshem) • Image reconstruction using compressed sensing (Anna Scaife) • Compressed Sensing: Extending CLEAN and NNLS (Ludwig Schwardt) • Widefield Low-frequency Imaging Techniques and Application to EOR Power Spectrum Measurement (Steve Myers)

  4. Inventory • Compressed sensing • Ludwig Schwardt (SKA SA) • Anna Scaife (Cambridge), Yves Wiaux (EPFL), Laurent Jacques (EPFL) • Amir Leshem (Delft)

  5. Inventory • Multi-scale • Shapelets (Sarod Yatawatta, Astron) • ASP-Clean (Sanjay Bhatnagar, NRAO) • MS-MFS extension (Urvashi Rau, NRAO) • Spherical wavelets (Anna Scaife, Cambridge)

  6. Inventory • Model fitting • Smear fitting (Rob Reid, NRAO) • Parametric imaging (Amir Leshem, Delft) • Global (statistical) methods • Maximum entropy (Steve Gull, Cambridge) (Sutton, Illinois) • Maximum likelihood / a posteriori • Linear least-squares (OMM, L2, SVD) (Stefan Wijnholds, Miguel Morales)

  7. Inventory • Prior information • Automatic CLEAN windows (Bill Cotton, NRAO) • Soft boxes (Steve Myers, NRAO)

  8. Unresolved issues • Source representation • Choice of basis functions / parameterization • Interoperability of different representations • Including prior information • Avoiding user interaction (CLEAN boxes) • Stopping criteria • Cooperation with self-cal • Optimal gridding

  9. Unresolved Issues • Mosaic weighting issues (especially multi-beam) • Error recognition (this is the final chance!) • Error estimates (uncertainty) for user • Availability of algorithms in standard packages • Computational issues (also numerical accuracy) • Test problems to illustrate performance

  10. Relevance to SKA • Compressed sensing • Less compelling for SKA due to large number of visibilities and dense continuum • Could reduce human interaction • Useful in specific cases (spectral lines, large image size compared to visibilities) • Continuum subtraction an issue • Efficient numerical algorithms

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