Learning Dependent Dictionary Representation with Efficient Multiplicative Gaussian Process

In dictionary learning for analysis of images, spatial correlation from extracted patches can be leveraged to improve characterization power. We propose a Bayesian framework for dictionary learning, where spatial location dependencies are captured by imposing a multiplicative Gaussian process prior on the latent units representing binary activations. Data augmentation and Kronecker methods allow for efficient Markov chain Monte Carlo sampling. We further extend our model with a sigmoid belief network, linking Gaussian processes and high-level latent binary units to capture inter-dictionary dependencies, while yielding additional computational savings. Applications to image denoising, inpainting and depth-information restoration demonstrate that the proposed model outperforms traditional Bayesian dictionary learning approaches.