<title>Maximum-likelihood estimation technique for the registration of coherent speckle images in the presence of noise</title>

Abstract

The recovered object in speckle imaging is generally an accumulated average of instantaneous speckled image frames. Misregistration of individual frames with respect to each other degrades image quality by blurring the average resultant image. In particular, atmospheric perturbations can cause random tilts in the phase of the detected speckle pattern, which tilts in turn induce random translations in each reconstructed image. Various techniques have been proposed to deal with this registration problem. We present here a maximum likelihood estimator to estimate and correct for the random tilts when each speckle frame is further corrupted by shot noise. The noise is modeled as a Poisson-distributed random variable. Results of this correction technique are compared with the performance of previous registration routines. INTRODUCTIONIn previous work,' we reported on a correlation-based technique for registering speckle images. This technique was unusual in that it used only data to register successive frames to images that had been roughly centered first. The procedure involved determining the rough outline, or shape, of the recovered object and obtaining a binary image of this recovery. Each of these binary images was then correlated to one another and the tilts between them removed.In this present work, we report a different technique for registering speckle images that is based on a multiframe maximum likelihood estimation (MLE) algorithm. First proposed by Schulz2 to form object estimates from turbulence-degraded images, the multi-frame MLE algorithm was adapted specifically for our application.In forming estimates of either object functions or point spread functions, the MLE technique not only uses the data at hand, but also permits the observer' s biases, in the form of prior knowledge, to be built into the estimate. In such a way, the probability law thus generated becomes precisely tailored to the particular problem. As a result, MLE represents one of the most powerful tools available for reconstructing images degraded by random atmospheric perturbations.We will show in this paper that the results from the MLE algorithm and our previous correlation-based technique are very similar. We believe that this result derives from the fact that the correlation technique uses significant a priori knowledge about the image. When this same prior knowledge is included in the MLE algorithm, a significant improvement in registration performance can be achieved in some, but not all, cases.In section 2, we describe the MLE technique and compare it briefly to the correlation-based technique and discuss the use of a sharpness criteria as a performance metric. In section 3, we discuss the results of a simulation using the MLE algorithm to register 25 coherent speckle images and we compare it to the results of our previous technique. Finally, we present our conclusions in section 4.