Computation of Posterior Cramer-Rao Bounds for Deep Learning Networks

Abstract

One of the key advantages of deep learning over traditional automatic target recognition (ATR) is its features can be directly selected by the network and do not necessary need, like the ATR, the designer input parametric constraints to carry out its operation. However, this advantage has its pitfall; because the network considers too many features the possibility to develop Cramer-Rao lower bounds that take into account size of an input image, its key scattering centers and its signal-to-noise ratio (SNR), and also the depth, width, weight and bias matrices from different layers of the network, is limited. In this paper, state space matrices that capture the features of an input image, the state vector and output observation matrix that allow computation of the noise covariance matrices together with the network parameters and weight matrices are used to develop Cramer-Rao bounds from an input image that is fed to a multiple-layer deep learning network. The proposed bounds are computed from a 5-layer deep learning network that is trained and tested on MSTAR data collected at HH polarization by a 0.596 GHz radar bandwidth at fifteen- and seventeen-degree depression angles, respectively.