Sunday, 8 April 2007

Maximum Entropy Method

A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called the all-poles model or autoregressive model. For images with more than a million pixels, maximum entropy is faster than the CLEAN algorithm.

MEM is commonly employed in astronomical synthesis imaging. In this application, the resolution depends on the signal-to-noise ratio, which must be specified. Therefore, resolution is image dependent and varies across the map. MEM is also biased, since the ensemble average of the estimated noise is nonzero. However, this bias is much smaller than the noise for pixels with a SNR>>1. It can yield super-resolution, which can usually be trusted to an order of magnitude in solid angle.

Two definitions of "entropy" normalized to the flux in the image are



where M_k is a "default image" and I_k is the smoothed image. Several unnormalized entropy measures (Cornwell 1982, p. 3) are given by






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