A rather large class of problems involving the determination of an object function from observation is linear-inversion problems for which unique solutions exist but that have the property that any signal-processing algorithm designed to approximate the exact solution too precisely is unstable. This is because the problems are ill posed. The precision attainable in a class of such problems is treated here abstractly in terms of a concept called a linear-precision gauge, which essentially involves an ordered family of linear estimators. Fundamental properties of linear-precision gauges are demonstrated and discussed. A major portion of the paper is given over to applying the linear-precision gauge concept and results to Fourier imaging problems that can occur, for example, in radar and tomography.
© 1984 Optical Society of America
Original Manuscript: June 13, 1983
Manuscript Accepted: September 26, 1983
Published: February 1, 1984
Lawrence S. Joyce and William L. Root, "Precision bounds in superresolution processing," J. Opt. Soc. Am. A 1, 149-168 (1984)