We describe a multifunction nonlinear optical processor that can perform various types of operations such as image deconvolution and nonlinear correlation. This processor is joint power spectrum based and does not use any filters. In this technique both the input signal and the processing function are displayed side by side at the input plane of the processor. The joint power spectrum of the input signals is thresholded with varying nonlinearity to produce the specific operation. In image deconvolution the joint power spectrum is modified and hard clip thresholded to remove the amplitude distortion effects and to restore the correct phase of the original image. An amplitude mask averaged over an ensemble of images is assigned to the thresholded power spectrum to provide the amplitude magnitude of the restored image. In optical correlation, the Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. We show that various types of correlation signals can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, a phase-only correlation signal is produced by selecting the appropriate nonlinearity. An analysis of the nonlinear processor for image deconvolution is presented. Computer simulation of the proposed technique for a linearly smeared image is provided.