On Capacity of Automatic Target Recognition Systems Under the Constraint of PCA-Encoding

Limiting capabilities of practical recognition systems are determined by a variety of factors that include source encoding techniques, quality of images, complexity of underlying objects and their projections. Given a source encoding technique, the remaining factors are characteristics of a recognition channel. In this work, we evaluate recognition capacity of a PCA-based automatic target recognition system. The encoded data are modeled to be Gaussian distributed with zero mean and estimated variances. We analyze both the case of a single encoded image and the case of encoded correlated multiple frames. For this case, we propose a model that is orientation and elevation angle dependent. The fit of proposed models is verified using statistical tests. Similar to the communication channel, the recognition channel capacity is the best achievable recognition rate in practice. Given a value of capacity and the length of encoded image (assume large), we can predict the number of distinct target classes that can be stored in a target library and be identified with probability of error close to zero. In this work, the constrained recognition capacity is evaluated as a function of the asymptotic signal-to-noise ratio.