Snapshot compressive imaging (SCI) is a promising technique for capturing high-speed video at low bandwidth and low power, typically by compressing multiple frames into a single measurement. However, similar to traditional CMOS image sensor based imaging systems, SCI also faces challenges in low-lighting photon-limited and low-signal-to-noise-ratio image conditions. In this paper, we propose a novel Compressive Denoising Autoencoder (CompDAE) using the STFormer architecture as the backbone, to explicitly model noise characteristics and provide computer vision functionalities such as edge detection and depth estimation directly from compressed sensing measurements, while accounting for realistic low-photon conditions. We evaluate the effectiveness of CompDAE across various datasets and demonstrated significant improvements in task performance compared to conventional RGB-based methods. In the case of ultra-low-lighting (APC $\leq$ 20) while conventional methods failed, the proposed algorithm can still maintain competitive performance.

We consider design of linear projection measurements for a vector Poisson signal model.

We propose a natural optimization problem for signal recovery under this model and develop a new greedy algorithm called SpaRCS to solve it. SpaRCS inherits a number of desirable properties from the state-of-the-art CoSaMP and ADMiRA algorithms, including exponential convergence and efficient implementation. Simulation results with video compressive sensing, hyperspectral imaging, and robust matrix completion data sets demonstrate both the accuracy and efficacy of the algorithm.

Image-based anomaly detection systems are of vital importance in various manufacturing applications. The resolution and acquisition rate of such systems is increasing significantly in recent years under the fast development of image sensing technology. This enables the detection of tiny defects in real-time. However, such a high resolution and acquisition rate of image data not only slows down the speed of image processing algorithms but also increases data storage and transmission cost. To tackle this problem, we propose a fast and data-efficient method with theoretical performance guarantee that is suitable for sparse anomaly detection in images with a smooth background (smooth plus sparse signal). The proposed method, named Compressed Smooth Sparse Decomposition (CSSD), is a one-step method that unifies the compressive image acquisition and decomposition-based image processing techniques. To further enhance its performance in a high-dimensional scenario, a Kronecker Compressed Smooth Sparse Decomposition (KronCSSD) method is proposed. Compared to traditional smooth and sparse decomposition algorithms, significant transmission cost reduction and computational speed boost can be achieved with negligible performance loss. Simulation examples and several case studies in various applications illustrate the effectiveness of the proposed framework.

We consider the problem of recovering a matrix $\mathbf{M}$ that is the sum of a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from a small set of linear measurements of the form $\mathbf{y} \mathcal{A}(\mathbf{M}) \mathcal{A}({\bf L} {\bf S})$. We propose a natural optimization problem for signal recovery under this model and develop a new greedy algorithm called SpaRCS to solve it. SpaRCS inherits a number of desirable properties from the state-of-the-art CoSaMP and ADMiRA algorithms, including exponential convergence and efficient implementation. Simulation results with video compressive sensing, hyperspectral imaging, and robust matrix completion data sets demonstrate both the accuracy and efficacy of the algorithm. Papers published at the Neural Information Processing Systems Conference.

Finding compact representation of videos is an essential component in almost every problem related to video processing or understanding. In this paper, we propose a generative model to learn compact latent codes that can efficiently represent and reconstruct a video sequence from its missing or under-sampled measurements. We use a generative network that is trained to map a compact code into an image. We first demonstrate that if a video sequence belongs to the range of the pretrained generative network, then we can recover it by estimating the underlying compact latent codes. Then we demonstrate that even if the video sequence does not belong to the range of a pretrained network, we can still recover the true video sequence by jointly updating the latent codes and the weights of the generative network. To avoid overfitting in our model, we regularize the recovery problem by imposing low-rank and similarity constraints on the latent codes of the neighboring frames in the video sequence. We use our methods to recover a variety of videos from compressive measurements at different compression rates. We also demonstrate that we can generate missing frames in a video sequence by interpolating the latent codes of the observed frames in the low-dimensional space.

We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an $n$-$\ell_1$ cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from compressive measurements. Our method processes a data vector of the stream per time instance from a small number of measurements in contrast to conventional batch RPCA, which needs to access full data. The $n$-$\ell_1$ cluster-weighted minimization leverages the sparse components along with their correlations with multiple previously-recovered sparse vectors. Moreover, the proposed minimization can exploit the structures of sparse components via clustering and re-weighting iteratively. The method outperforms the existing methods for both numerical data and actual video data.

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA with prior information for recursively separating a sequences of frames into sparse and low-rank components from a small set of measurements. In contrast to conventional batch-based PCA, which processes all the frames directly, the proposed method processes measurements taken from each frame. Moreover, this method can efficiently incorporate multiple prior information, namely previous reconstructed frames, to improve the separation and thereafter, update the prior information for the next frame. We utilize multiple prior information by solving $n\text{-}\ell_{1}$ minimization for incorporating the previous sparse components and using incremental singular value decomposition ($\mathrm{SVD}$) for exploiting the previous low-rank components. We also establish theoretical bounds on the number of measurements required to guarantee successful separation under assumptions of static or slowly-changing low-rank components. Using numerical experiments, we evaluate our bounds and the performance of the proposed algorithm. In addition, we apply the proposed algorithm to online video foreground and background separation from compressive measurements. Experimental results show that the proposed method outperforms the existing methods.

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matrices consisting of i.i.d. zero-mean entries and finite first four moments. In contrast to previous works, we make no structural assumptions about the underlying covariance matrix such as being low-rank. In fact, our analysis is based on a non-Bayesian data setting which requires no distributional assumptions on the set of data samples. Furthermore, inspired by the generality of the projection matrices, we propose an approach to covariance estimation that utilizes sparse Rademacher matrices. Therefore, our algorithm can be used to estimate the covariance matrix in applications with limited memory and computation power at the acquisition devices. Experimental results demonstrate that our approach allows for accurate estimation of the sample covariance matrix on several real-world data sets, including video data.

We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the number of vectors is large. This result is achieved by a simple algorithm that computes the eigenvectors of an estimate of the covariance matrix. The main insight is to exploit an averaging effect that arises from applying a different random projection to each vector. We provide a number of simulations confirming our theoretical results.