Analysis of the wavelet-matched filtering in a four-wave mixing arrangement

In image processing, the wavelet transform is useful to enhance the local features of images, so that, the correlation of a target with a reference signal can be improved by wavelet filtering. The wavelet filtering operation and correlation can be photorefractively performed if a crystal is used as a dynamic holographic recording medium. In particular, the sillenite family of photorefractive crystals have a high photosensitivity and high carrier mobility which allow a fast response that makes them attractive for real-time image processing and optical phase conjugation. We analyze a real-time wavelet-matched optical correlator using phase conjugation in a four-wave mixing arrangement. The robustness of the correlator to the noise due the finite crystal depth is improved using a proper wavelet filter.