Sparsity-based techniques have been popular for reconstructing images and videos from limited or corrupted measurements. Methods such as dictionary or transform learning have been demonstrated to be useful in applications such as denoising, inpainting, and medical image reconstruction. In this work, we propose a new framework for online or sequential adaptive reconstruction of dynamic image sequences from linear (typically undersampled) measurements. In particular, the spatiotemporal patches of the underlying dynamic image sequence are assumed to be sparse in a DIctioNary with lOw-ranK AToms (DINO-KAT), and the dictionary model and images are simultaneously and sequentially estimated from streaming measurements. The proposed online algorithm involves efficient memory usage and simple and efficient updates of the low-rank atoms, sparse coefficients, and images. Our numerical experiments show the usefulness of the proposed scheme in inverse problem settings such as video reconstruction or inpainting from limited and noisy pixels.

This paper introduces a novel approach to robust surface reconstruction from photometric stereo normal vector maps that is particularly well-suited for reconstructing surfaces from noisy gradients. Specifically, we propose an adaptive dictionary learning based approach that attempts to simultaneously integrate the gradient fields while sparsely representing the spatial patches of the reconstructed surface in an adaptive dictionary domain. We show that our formulation learns the underlying structure of the surface, effectively acting as an adaptive regularizer that enforces a smoothness constraint on the reconstructed surface. Our method is general and may be coupled with many existing approaches in the literature to improve the integrity of the reconstructed surfaces. We demonstrate the performance of our method on synthetic data as well as real photometric stereo data and evaluate its robustness to noise.

Photometric stereo is a method for estimating the normal vectors of an object from images of the object under varying lighting conditions. Motivated by several recent works that extend photometric stereo to more general objects and lighting conditions, we study a new robust approach to photometric stereo that utilizes dictionary learning. Specifically, we propose and analyze two approaches to adaptive dictionary regularization for the photometric stereo problem. First, we propose an image preprocessing step that utilizes an adaptive dictionary learning model to remove noise and other non-idealities from the image dataset before estimating the normal vectors. We also propose an alternative model where we directly apply the adaptive dictionary regularization to the normal vectors themselves during estimation. We study the practical performance of both methods through extensive simulations, which demonstrate the state-of-the-art performance of both methods in the presence of noise.

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery fromundersampledmeasurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamicmagnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method.

We consider the problem of estimating the singular vectors of low-rank signal matrices buried in noise in the setting where the singular vectors are assumed to be Kronecker products of unknown vectors. We propose four algorithms for estimating such singular vectors, analyze their performance and show that they asymptotically fail to estimate to latent singular vector below the same critical SNR. We corroborate our theoretical findings with numerical simulations and illustrate the improved performance on a STAP beamforming application.

method is proposed for identifying five crowd behaviors (bottlenecks, fountainheads, lanes, arches, and blocking) in visual scenes. In the algorithm, a scene is overlaid by a grid of particles initializing a dynamical system defined by the optical flow. Time integration of the dynamical system provides particle trajectories that represent the motion in the scene; these trajectories are used to locate regions of interest in the scene. Linear approximation of the dynamical system provides behavior classification through the Jacobian matrix; the eigenvalues determine the dynamic stability of points in the flow and each type of stability corresponds to one of the five crowd behaviors. The eigenvalues are only considered in the regions of interest, consistent with the linear approximation and the implicated behaviors. The algorithm is repeated over sequential clips of a video in order to record changes in eigenvalues, which may imply changes in behavior. The method was tested on over 60 crowd and traffic videos.

A novel method for crowd flow modeling and anomaly detection is proposed for both coherent and incoherent scenes. The novelty is revealed in three aspects. First, it is a unique utilization of particle trajectories for modeling crowded scenes, in which we propose new and efficient representative trajectories for modeling arbitrarily complicated crowd flows. Second, chaotic dynamics are introduced into the crowd context to characterize complicated crowd motions by regulating a set of chaotic invariant features, which are reliably computed and used for detecting anomalies. Third, a probabilistic framework for anomaly detection and localization is formulated. The overall work-flow begins with particle advection based on optical flow. Then particle trajectories are clustered to obtain representative trajectories for a crowd flow. Next, the chaotic dynamics of all representative trajectories are extracted and quantified using chaotic invariants known as maximal Lyapunov exponent and correlation dimension. Probabilistic model is learned from these chaotic feature set, and finally, a maximum likelihood estimation criterion is adopted to identify a query video of a scene as normal or abnormal. Furthermore, an effective anomaly localization algorithm is designed to locate the position and size of an anomaly. Experiments are conducted on known crowd data set, and results show that our method achieves higher accuracy in anomaly detection and can effectively localize anomalies.