Researchers have shown that aberrations in incoherent optical systems can be corrected through the use of an image-sharpness criterion . An analogous image-sharpness criterion is defined for the case of speckled imagery derived from coherent imaging of diffuse objects. By appealing to a multiplicative noise model we show that this speckled-image sharpness criterion is a random variable with an expected value proportional to the sharpness criterion for the associated incoherent image. Thus, aberration correction can be accomplished by maximizing the speckled-image sharpness criterion. A variety of computer simulation experiments designed to test the performance of the image-sharpness criterion applied to speckled imagery are presented. These experiments model the problem of imaging moving targets with synthetic aperture radar (SAR). Target motion introduces one-dimensional (azimuthal) phase aberrations in SAR Fourier data producing a one-dimensional blur in the image. These aberrations can be represented as a linear sum of orthogonal polynomials and the coefficients of such a representation serve as optimization parameters. The sharpness criterion is maximized with respect to the aberration parameters through the use of a conjugate-gradient algorithm. The problem of entrapment by local minima can be overcome by using multiple initial estimates. We demonstrate that quadratic, cubic, and quartic polynomial coefficients are successfully sensed through this technique. The method is shown to succeed for both extended images and point-like images that more closely resemble SAR images of cultural targets.