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