Mathematical Approaches to Image Deconvolution Editor Ludwig Schwardt

Attendees • • • Ludwig Schwardt Anna Scaife Sarod Yatawatta Stefan Wijnholds Amir Leshem

Relevant talks • Least Squares All-Sky Imaging With A LOFAR Station (Stefan Wijnholds) •

Inventory • Compressed sensing – Ludwig Schwardt (SKA SA) – Anna Scaife (Cambridge), Yves

Inventory • Multi-scale – Shapelets (Sarod Yatawatta, Astron) – ASP-Clean (Sanjay Bhatnagar, NRAO) –

Inventory • Model fitting – Smear fitting (Rob Reid, NRAO) – Parametric imaging (Amir

Inventory • Prior information – Automatic CLEAN windows (Bill Cotton, NRAO) – Soft boxes

Unresolved issues • Source representation – Choice of basis functions / parameterization – Interoperability

Unresolved Issues • Mosaic weighting issues (especially multibeam) • Error recognition (this is the

Relevance to SKA • Compressed sensing – Less compelling for SKA due to large

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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 • 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)

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

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

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, L 2, SVD) (Stefan Wijnholds, Miguel Morales)

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

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

Unresolved Issues • Mosaic weighting issues (especially multibeam) • 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

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