Efficient patch-based approach for compressive depth imaging.

We present efficient camera hardware and algorithms to capture images with extended depth of field. The camera moves its focal plane via a liquid lens and modulates the scene at different focal planes by shifting a fixed binary mask, with synchronization achieved by using the same triangular wave to control the focal plane and the pizeoelectronic translator that shifts the mask. Efficient algorithms are developed to reconstruct the all-in-focus image and the depth map from a single coded exposure, and various sparsity priors are investigated to enhance the reconstruction, including group sparsity, tree structure, and dictionary learning. The algorithms naturally admit a parallel computational structure due to the independent patch-level operations. Experimental results on both simulation and real datasets demonstrate the efficacy of the new hardware and the inversion algorithms.

Spectral-temporal compressive imaging.

This Letter presents a compressive camera that integrates mechanical translation and spectral dispersion to compress a multi-spectral, high-speed scene onto a monochrome, video-rate detector. Experimental reconstructions of 17 spectral channels and 11 temporal channels from a single measurement are reported for a megapixel-scale monochrome camera.

Coded aperture compressive temporal imaging.

We use mechanical translation of a coded aperture for code division multiple access compression of video. We discuss the compressed video's temporal resolution and present experimental results for reconstructions of > 10 frames of temporal data per coded snapshot.

Compressive sensing by learning a Gaussian mixture model from measurements.

Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.

Video compressive sensing using Gaussian mixture models.

A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.