We present a theory of optimum coherence recovery applicable in computation-limited environments. We describe approaches for implementing coherence recovery employing two-dimensional Fourier transform acousto-optic architectures which afford very high throughput signal searches. The optimum one parameter, second order approximation to a small portion of a sinusoidally chirped sinusoid is a quadratic time transformation. The algorithm exploits the coincidence that the product of two chirps of nearly equal acceleration generates a Fourier kernel with an additional temporal phase which can exactly compensate a quadratically shifted sinusoid. Since for a large variety of functions the quadratic approximation is near optimum, such devices may have wide applicability for coherence recovery. A family of quadratic transformations may be applied, using a high throughput acousto-optic device, to effect recovery of an unknown periodicity in near real time. Alternatively, the technique may be employed to determine precisely the difference in time derivatives of frequency between two chirped signals. We describe our technique for implementing the coherence recovery algorithm in a prototype one-dimensional time-integrating Fourier processor. We have demonstrated analytically that the algorithm is realizable in a high bandwidth, two-dimensional hybrid (space-and time-integrating) system. High performance analog devices which effect coherence recovery have immediate relevance for detection of weak signals from electronic sources with phase modulation or sources undergoing acceleration, e.g., for gravitational wave experiments, and radio and X-ray searches for binary millisecond pulsars.