Abstract: A method separates foreground from background in a sequence of images, by first acquiring the sequence of images and a depth map of a scene by a camera. Groups of pixels are determined based on the depth map. Then, the sequence of images is decomposed into a sparse foreground component, and a low rank background component, according to apparent motion in the sequence of images, and the groups.

Abstract: A method and system determines flows by first acquiring a video of the flows with a camera, wherein the flows are pedestrians in a scene, wherein the video includes a set of frames. Motion vectors are extracted from each frame in the set, and a data matrix is constructed from the motion vectors in the set of frames. A low rank Koopman operator is determined from the data matrix and a spectrum of the low rank Koopman operator is analyzed to determine a set of Koopman modes. Then, the frames are segmented into independent flows according to a clustering of the Koopman modes.

Abstract: A method extracts a low-rank descriptor of a video acquired of a scene by first extracting a set of descriptors for each image in the video. The sets of descriptors for the video are aggregated to form a descriptor matrix. Iteratively, a low-rank descriptor matrix is determined from the descriptor matrix, as well as a selection matrix that associates each column in the descriptor matrix to a corresponding column in the low-rank descriptor matrix. The low-rank descriptor matrix is output upon convergence.

Abstract: A method processes a signal represented as a graph by first determining a graph spectral transform based on the graph. In a spectral domain, parameters of a graph filter are estimated using a training data set of unenhanced and corresponding enhanced signals. The graph filter is derived based on the graph spectral transform and the estimated graph filter parameters. Then, the signal is processed using the graph filter to produce an output signal. The processing can enhance signals such as images by denoising or interpolating missing samples.

Abstract: A method processes a signal by first constructing a graph from the signal, and then determining a graph matrix from the graph and the signal. A Krylov-based subspace is determined based on the graph matrix and the signal. A filter for the Krylov subspace is determined. The filter transforms the signal to produce a filtered signal, which is output.

Abstract: A method and system determines flows by first acquiring a video of the flows with a camera, wherein the flows are pedestrians in a scene, wherein the video includes a set of frames. Motion vectors are extracted from each frame in the set, and a data matrix is constructed from the motion vectors in the set of frames. A low rank Koopman operator is determined from the data matrix and a spectrum of the low rank Koopman operator is analyzed to determine a set of Koopman modes. Then, the frames are segmented into independent flows according to a clustering of the Koopman modes.

Abstract: A method and system for generating an image of a scene behind a wall, wherein the scene is represented as a grid, by first transmitting a radar pulse through the wall using a transmitter and receiving a set of echoes corresponding to the radar pulse being reflected by the scene in a receiver at a known location. Based on the location, an imaging operator that relates the set of echoes to the grid is determined. Using the imaging operator, a sparse delay kernel that matches a response of a current image to a similar response in the set of echoes is determined. Then, the current image is updated, based on the set of echoes, the imaging operator, and the sparse delay kernel. The transmitting, the receiving, the determining, the obtaining, and the updating steps are repeated for different locations until a termination condition is reached.

Abstract: A method reconstructs a signal by sampling the signal using a sampling procedure to obtain an input signal. A consistent set is determined from the input signal including the first elements such that applying the sampling procedure to the first elements results in the input signal. According to the type of the signal, a guiding set is determined including second elements disjoint from the first elements. A reconstruction set including third elements is generated so that the third elements minimize a sum of a first similarity measure of the third elements to the second elements and a second similarity measure of the third elements to the first elements. A transformed signal that minimizes a function on the reconstruction set is determined. A reconstructed signal is rendered so that a third similarity measure of the reconstructed signal to the transformed signal is smaller than a tolerance.

Abstract: A method segments an image acquired by a sensor of a scene by first obtaining motion vectors corresponding to the image and generating a motion vanishing point image, wherein each pixel in the motion vanishing point image represents a number of intersections of pairs of motion vectors at the pixel. In the motion vanishing point image, a representation point for each motion vector is generated and distances between the motion vectors are determined based on the representation points. Then, a motion graph is constructed wherein each node represents a motion vector, and each edge represents a weight based on the distance between the nodes. Graph spectral clustering is performed on the motion graph to produce segments of the image.

Abstract: A method separates foreground from background in a sequence of images, by first acquiring the sequence of images and a depth map of a scene by a camera. Groups of pixels are determined based on the depth map. Then, the sequence of images is decomposed into a sparse foreground component, and a low rank background component, according to apparent motion in the sequence of images, and the groups.

Abstract: A method reconstructs a signal by sampling the signal using a sampling procedure to obtain an input signal. A consistent set is determined from the input signal including the first elements such that applying the sampling procedure to the first elements results in the input signal. According to the type of the signal, a guiding set is determined including second elements disjoint from the first elements. A reconstruction set including third elements is generated so that the third elements minimize a sum of a first similarity measure of the third elements to the second elements and a second similarity measure of the third elements to the first elements. A transformed signal that minimizes a function on the reconstruction set is determined. A reconstructed signal is rendered so that a third similarity measure of the reconstructed signal to the transformed signal is smaller than a tolerance.

Abstract: A method segments and tracks content in a video stream including sets of one or more images by first determining measured data from each set of one or more images. An adaptive step-size parameter and a low-dimensional subspace characterizing motion of the content the measured data are initialized. A sparse vector representing a sparse component that characterizes the motion of the content different from the motion of the content characterized by the low-dimensional subspace is determined. A change in the low-dimensional subspace for the measured data is determined using a proximal point iteration and the parameter, which is updated according to the change. A low-rank subspace matrix representing the low-dimensional subspace is updated according to the change and the parameter. Then, the low-rank matrix representing the low-dimensional subspace and the sparse vector are outputted.

Abstract: Targets are detected in a scene behind a wall by first transmitting a pulse through the wall. Then, a primary impulse response is detected by a sparse regularized least squares inversion applied to received signals corresponding to the reflected pulse. A delay operator that matches the primary impulse response to similar impulse responses in the received signals is also determined. A distortion of the pulse after the pulse passes through the wall but before the pulse is reflected by the target can also be determined. The distortion is used in an iterative process to refine the detection of the target and to suppress ghosting artifacts.

Abstract: A method reconstructs a scene behind a wall by transmitting a signal through the wall into the scene. Parameters of the wall are estimated from a reflected signal. A model of a permittivity of the wall is generated using the parameters, and then the scene is reconstructed as an image from the reflected signal using the model and sparse recovery.

Abstract: A method processes a video acquired of a scene by first aligning a group of video images using compressed domain motion information and then solving for a low rank component and a sparse component of the video. A homography map is computed from the motion information to determine image alignment parameters. The video images are then warped using the homography map to share a similar camera perspective. A Newton root step is followed to traverse separately Pareto curves of each low rank component and sparse component. The solving for the low rank component and the sparse component is repeated alternately until a termination condition is reached. Then, the low ranks component and the sparse component are outputted. The low rank component represents a background in the video, and the sparse component represents moving objects in the video.

Abstract: A system and method determines a noise free image of a scene located behind a wall. A transmit antenna emits a radar pulse from different locations in front of the wall, wherein the radar pulses propagate through the wall and are reflected by the scene as echoes. A set of stationary receive antennas acquire the echoes corresponding to each pulse transmitted from each different location. A radar imaging subsystem connected to the transmit antenna and the set of receive antennas determines a noisy image of the scene for each location of the transmit antenna. A total variation denoiser denoises each noisy image to produce a corresponding denoised image. A combiner combines incoherently the denoised images to produce the noise free image.

Abstract: A method processes a signal by first constructing a graph from the signal, and then determining a graph matrix from the graph and the signal. A Krylov-based subspace is determined based on the graph matrix and the signal. A filter for the Krylov subspace is determined. The filter transforms the signal to produce a filtered signal, which is output.

Abstract: A method extracts a low-rank descriptor of a video acquired of a scene by first extracting a set of descriptors for each image in the video. The sets of descriptors for the video are aggregated to form a descriptor matrix. Iteratively, a low-rank descriptor matrix is determined from the descriptor matrix, as well as a selection matrix that associates each column in the descriptor matrix to a corresponding column in the low-rank descriptor matrix. The low-rank descriptor matrix is output upon convergence.

Abstract: A method reconstructs a scene behind a wall by transmitting a signal through the wall into the scene. Parameters of the wall are estimated from a reflected signal. A model of a permittivity of the wall is generated using the parameters, and then the scene is reconstructed as an image from the reflected signal using the model and sparse recovery.

Abstract: A method processes a video acquired of a scene by first aligning a group of video images using compressed domain motion information and then solving for a low rank component and a sparse component of the video. A homography map is computed from the motion information to determine image alignment parameters. The video images are then warped using the homography map to share a similar camera perspective. A Newton root step is followed to traverse separately Pareto curves of each low rank component and sparse component. The solving for the low rank component and the sparse component is repeated alternately until a termination condition is reached. Then, the low ranks component and the sparse component are outputted. The low rank component represents a background in the video, and the sparse component represents moving objects in the video.