This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results show that accurate outlier identification is achievable using very few linear summaries of the original data matrix—as few as the squared rank of the low-rank component plus the number of outliers, times constant and logarithmic factors. We demonstrate the performance of our approach experimentally in two stylized applications, one motivated by robust collaborative filtering tasks, and the other by saliency map estimation tasks arising in computer vision and automated surveillance, and also investigate extensions to settings where the data are noisy, or possibly incomplete.
A component of our numerical evaluation here entails assessing the performance of our approach in a stylized image processing task of saliency map estimation. We note that several recent works have utilized techniques from the sparse representation literature in salient region identification, and in compressive imaging scenarios. A seminal effort in this direction was @cite_29 , which proposed a model for feature identification via the human visual cortex based on parsimonious (sparse) representations. More recently, @cite_61 applied techniques from @cite_29 @cite_27 and low-rank-plus-sparse matrix decomposition @cite_6 @cite_4 in a procedure to identify salient regions of an image from (uncompressed) measurements. Similar sparse representation techniques for salient feature identification were also examined in @cite_42 . An adaptive compressive imaging procedure driven by a saliency map'' obtained via low-resolution discrete cosine transform (DCT) measurements was demonstrated in @cite_16 . Here, unlike in @cite_42 @cite_63 , we consider salient feature identification based on compressive samples, and while our approach is similar in spirit to the problem examined in @cite_16 , here we provide theoretical guarantees for the performance of our approach. Finally, we note several recent works @cite_41 @cite_24 that propose methods for identifying salient elements in a data set using compressive samples.
@cite_61 @cite_4 @cite_41 @cite_29 @cite_42 @cite_6 @cite_24 @cite_27 @cite_63 @cite_16
2610921592 2074208271 2156686129 2126131432
In this paper, we present a novel salient object detection method, efficiently combining Laplacian sparse subspace clustering (LSSC) and unified low-rank representation (ULRR). Unlike traditional low-rank matrix recovery (LRMR) based saliency detection methods which mainly extract saliency from pixels or super-pixels, our method advocates the saliency detection on the super-pixel clusters generated by LSSC. By doing so, our method succeeds in extracting large-size salient objects from cluttered backgrounds, against the detection of small-size salient objects from simple backgrounds obtained by most existing work. The entire algorithm is carried out in two stages: region clustering and cluster saliency detection. In the first stage, the input image is segmented into many super-pixels, and on top of it, they are further grouped into different clusters by using LSSC. Each cluster contains multiple super-pixels having similar features (e.g., colors and intensities), and may correspond to a part of a salient object in the foreground or a local region in the background. In the second stage, we formulate the saliency detection of each super-pixel cluster as a unified low-rankness and sparsity pursuit problem using a ULRR model, which integrates a Laplacian regularization term with respect to the sparse error matrix into the traditional low-rank representation (LRR) model. The whole model is based on a sensible cluster-consistency assumption that the spatially adjacent super-pixels within the same cluster should have similar saliency values, similar representation coefficients as well as similar reconstruction errors. In addition, we construct a primitive dictionary for the ULRR model in terms of the local-global color contrast of each super-pixel. On top of it, a global saliency measure covering the representation coefficients and a local saliency measure considering the sparse reconstruction errors are jointly employed to define the final saliency measure. Comprehensive experiments over diverse publicly available benchmark data sets demonstrate the validity of the proposed method. We present a framework for robustly estimating registration between a 3D volume image and a 2D projection image and evaluate its precision and robustness in spine interventions for vertebral localization in the presence of anatomical deformation. The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch. The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization. Experiments involved a cadaver specimen and two CT datasets (supine and prone) and 36 C-arm fluoroscopy images acquired with the specimen in four positions (supine, prone, supine with lordosis, prone with kyphosis), three regions (thoracic, abdominal, and lumbar), and three levels of geometric magnification (1.7, 2.0, 2.4). Registration accuracy was evaluated in terms of projection distance error (PDE) between the estimated and true target points in the projection image, including 14 400 random trials (200 trials on the 72 registration scenarios) with initialization error up to ±200 mm and ±10°. The resulting median PDE was better than 0.1 mm in all cases, depending somewhat on the resolution of input CT and fluoroscopy images. The cadaver experiments illustrated the tradeoff between robustness and computation time, yielding a success rate of 99.993 in vertebral labeling (with 'success' defined as PDE <5 mm) using 1,718 664 ± 96 582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690). Parameters yielding a faster search (e.g., fewer multi-starts) reduced robustness under conditions of large deformation and poor initialization (99.535 success for the same data registered in 13.1 s), but given good initialization (e.g., ±5 mm, assuming a robust initial run) the same registration could be solved with 99.993 success in 6.3 s. The ability to register CT to fluoroscopy in a manner robust to patient deformation could be valuable in applications such as radiation therapy, interventional radiology, and an assistant to target localization (e.g., vertebral labeling) in image-guided spine surgery. This paper addresses the problem of detecting salient areas within natural images. We shall mainly study the problem under unsupervised setting, i.e., saliency detection without learning from labeled images. A solution of multitask sparsity pursuit is proposed to integrate multiple types of features for detecting saliency collaboratively. Given an image described by multiple features, its saliency map is inferred by seeking the consistently sparse elements from the joint decompositions of multiple-feature matrices into pairs of low-rank and sparse matrices. The inference process is formulated as a constrained nuclear norm and as an l2,1 -norm minimization problem, which is convex and can be solved efficiently with an augmented Lagrange multiplier method. Compared with previous methods, which usually make use of multiple features by combining the saliency maps obtained from individual features, the proposed method seamlessly integrates multiple features to produce jointly the saliency map with a single inference step and thus produces more accurate and reliable results. In addition to the unsupervised setting, the proposed method can be also generalized to incorporate the top-down priors obtained from supervised environment. Extensive experiments well validate its superiority over other state-of-the-art methods. The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications, including object and target recognition, we are ultimately interested in making a decision about an image rather than computing a reconstruction. We propose here a framework for compressive classification that operates directly on the compressive measurements without first reconstructing the image. We dub the resulting dimensionally reduced matched filter the smashed filter. The first part of the theory maps traditional maximum likelihood hypothesis testing into the compressive domain; we find that the number of measurements required for a given classification performance level does not depend on the sparsity or compressibility of the images but only on the noise level. The second part of the theory applies the generalized maximum likelihood method to deal with unknown transformations such as the translation, scale, or viewing angle of a target object. We exploit the fact the set of transformed images forms a low-dimensional, nonlinear manifold in the high-dimensional image space. We find that the number of measurements required for a given classification performance level grows linearly in the dimensionality of the manifold but only logarithmically in the number of pixels samples and image classes. Using both simulations and measurements from a new single-pixel compressive camera, we demonstrate the effectiveness of the smashed filter for target classification using very few measurements.