Another common complaint about MEM is that the answer is biased, i.e., that the ensemble average of the estimated noise is not zero. This is true; it is the price paid by any method which does not try to fit exactly to the data as `CLEAN' does. Bias in an estimator is both common and acceptable, as it usually leads to smaller variance. Cornwell (1980) has estimated the magnitude of the bias, and has shown that it is much less than the noise for pixels having signal-to-noise ratio much greater than one. In fact, with good u,v coverage, for bright pixels the effect of noise on an MEM image is similar to that on a dirty image. The effect of bias can be substantially reduced by using a reasonable default, such as a previous MEM image smoothed with a Gaussian; then only the highest spatial frequencies are biased. The effect of bias can also be eliminated by adding back the residuals, after ensuring a similar flux scale via convolution of the MEM image with a Gaussian (as outlined above).
1996 November 4