Title: Compressive Sensing via Convolutional Factor Analysis,
Abstract: We solve the compressive sensing problem via convolutional factor analysis,
where the convolutional dictionaries are learned {\em in situ} from the
compressed measurements. An alternating direction method of multipliers (ADMM)
paradigm for compressive sensing inversion based on convolutional factor
analysis is developed. The proposed algorithm provides reconstructed images as
well as features, which can be directly used for recognition ($e.g.$,
classification) tasks. When a deep (multilayer) model is constructed, a
stochastic unpooling process is employed to build a generative model. During
reconstruction and testing, we project the upper layer dictionary to the data
level and only a single layer deconvolution is required. We demonstrate that
using $\sim30\%$ (relative to pixel numbers) compressed measurements, the
proposed model achieves the classification accuracy comparable to the original
data on MNIST. We also observe that when the compressed measurements are very
limited ($e.g.$, $<10\%$), the upper layer dictionary can provide better
reconstruction results than the bottom layer.