The technique of maximizing sharpness metrics has been used to estimate and compensate for aberrations with adaptive optics, to correct phase errors in synthetic-aperture radar, and to restore images. The largest class of sharpness metrics is the sum over a nonlinear point transformation of the image intensity. How the second derivative of the point nonlinearity varies with image intensity determines the effects of various metrics on the imagery. Some metrics emphasize making shadows darker, and other emphasize making bright points brighter. One can determine the image content needed to pick the best metric by computing the statistics of the image autocorrelation or of the Fourier magnitude, either of which is independent of the phase error. Computationally efficient, closed-form expressions for the gradient make possible efficient search algorithms to maximize sharpness.

Telescopes and imaging interferometers with sparsely filled apertures can be lighter weight and less expensive than conventional filled-aperture telescopes. However, their greatly reduced MTF's cause significant blurring and loss of contrast in the collected imagery. Image reconstruction algorithms can correct the blurring completely when the signal-to-noise ratio (SNR) is high, but only partially when the SNR is low. This paper compares both linear (Wiener) and nonlinear (iterative maximum likelihood) algorithms for image reconstruction under a variety of circumstances. These include high and low SNR, Gaussian noise and Poisson-noise dominated, and a variety of aperture configurations and degrees of sparsity. The quality metric employed to compare algorithms is image utility as quantified by the National Imagery Interpretability Rating Scale (NIIRS). On balance, a linear reconstruction algorithm with a power-law power-spectrum estimate performed best.

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This case report demonstrates the unpredictable nature of autologous fat grafting. Clinicians should be aware of this potential complication of fat hypertrophy after autologous fat grafting.