Non-negative least-squares (NNLS), introduced by Lawson & Hanson (1974), also solves the basic matrix equation algebraically, but subject to the added constraint that S contains no negative elements. In principle, the algorithm has the merit that, given sufficient time, it will satisfy well-defined termination conditions, and thus requires no arbitrary cutoff parameter. This makes it a `hands-off' algorithm whose output is not susceptible to mis-tuning by unfortunate choice of the input parameters. In practice, however, the computation time and memory usage can be impossibly large if the number of non-zero pixels exceeds about 6000-8000.
The point source model output by NNLS is again smoothed with a Gaussian beam and added to any residual emission when making the final image.
NNLS distinguishes itself on bright, compact sources that neither `CLEAN' nor MEM can process adequately. Briggs showed that on such sources, both CLEAN and MEM produce artifacts that resemble calibration errors and that limit dynamic range. NNLS has no difficulty imaging such sources. It also has no difficulty with sharp edges, such as those of planets or of strong shocks, and can be very advantageous in producing models for self-calibration for both types of sources. Briggs (1995) showed that NNLS deconvolution can reach the thermal noise limit in VLBA images for which `CLEAN' produces demonstrably worse solutions.
NNLS is therefore a powerful deconvolution algorithm for making high dynamic range images of compact sources for which strong finite support constraints are applicable.
1996 November 4