Convolutional Gaussian Mixture Models with Application to Compressive Sensing

Gaussian mixture models (GMM) have been used to statistically represent patches in an image. Extending from small patches to an entire image, we propose a convolutional Gaussian mixture models (convGMM) to model the statistics of an entire image and apply it for compressive sensing (CS). We present the algorithm details for learning a convGMM from training images by maximizing the marginal log-likelihood estimation (MMLE). The learned convGMM is used to perform model-based compressive sensing, using the convGMM as a model of the underlying image. In addition, a key feature of our method is that all of the training and reconstruction process could be fast and efficient calculated in the frequency-domain by 2-dimensional fast Fourier transforms (2d-FFTs). The performance of the convGMM on CS is demonstrated on several image sets.