Extending the Quantum Entropy to Multidimensional Signal Processing

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising operation, this new definition of entropy can be implemented to compare the performance analysis of filtering methods. In the second part, we apply the concept of pure state in quantum formalism to generalize the maximum entropy method for narrowband and farfield source localization problem. Several computer simulation results are illustrated to demonstrate the effectiveness of the proposed techniques. Keywords—Von Neumann entropy, Filtering, array, DoA, Maximum Entropy Method.