A3: Accurate, Adaptable, and Accessible Error Metrics for Predictive Models: abbyyR: Access to Abbyy Optical Character Recognition (OCR) API: abc: Tools for. We thus consider the low-rank constraint in our metric learning model and learn a low dimensional representation of the data in a discriminative way, where low- rank matrix models can therefore scale to handle substantially many more features. low rank and sparse modeling for visual analysis Disentangling Task Transfer Learning" by Amir R. Zamir, Alexander Sax, William Shen, Leonidas J. Bibliographic content of Low-Rank and Sparse Modeling for Visual Analysis. low rank and sparse modeling for visual analysis Download low rank and sparse modeling for visual analysis or read online here in PDF or EPUB. Please click button to get low rank and sparse modeling for visual analysis book now. All books are in clear copy here, and all .
- Low-rank and sparse modeling for visual analysis
- Low-Rank and Sparse Modeling for Visual Analysis
- Year: 2014
Low-rank and sparse modeling for visual analysis
Low-rank modeling reduces the dimension of the data, whereas sparse modeling reduces the description of the data by selecting a few features from a large dictionary. These two paradigms can be combined, e. The goal of this workshop is to discuss some of the very recent and exciting developments of such modeling and highlight fundamental mathematical theories related to these explorations.
Furthermore, the workshop will discuss interesting areas of applications for these developments. Greenway C - Level 2 Discrete images, consisting of slowly-varying pixel values except across edges, have sparse or compressible representations with respect to the discrete gradient.
Despite being a primary motivation for compressed sensing, stability results for total-variation minimization do not follow directly from the standard "l1" theory of compressed sensing.
In this talk, we present near-optimal reconstruction guarantees for total-variation minimization and discuss several related open problems. Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient methods for solving such problems, working within a high-dimensional framework that allows the data dimension d to grow with and possibly exceed the sample size n.
This high-dimensional structure precludes the usual global assumptionsnamely, strong convexity and smoothness conditionsthat underlie much of classical optimization analysis.
We define appropriately restricted versions of these conditions, and show that they are satisfied with high probability for various statistical models.
Low-Rank and Sparse Modeling for Visual Analysis
This result is substantially sharper than previous convergence results, which yielded sublinear convergence, or linear convergence only up to the noise level. This work investigates the limits of a convex optimization procedure for the deconvolution of structured signals. The geometry of the convex program leads to a precise, yet intuitive, characterization of successful deconvolution. Coupling this geometric picture with a random model reveals sharp thresholds for success, and failure, of the deconvolution procedure.
These generic results are applicable to a wide variety of problems. This work considers deconvolving two sparse vectors, analyzes a spread-spectrum coding scheme for impulsive noise, and shows when it is possible to deconvolve a low-rank matrix corrupted with a special type of noise. As an additional benefit, this analysis recovers, and extends, known weak and strong thresholds for the basis pursuit problem. Recent developments in compressive and adaptive sensing have demonstrated the tremendous improvements in sensing resource efficiency that can be achieved by exploiting sparsity in high-dimensional inference tasks.
In this talk we describe how compressive sensing techniques can be extended to exploit saliency.
We discuss our recent work quantifying the effectiveness of a compressive sensing strategy that accurately identifies salient features from compressive measurements, and we demonstrate the performance of this technique in a two-stage active compressive imaging approach to automated surveillance.
Greenway C - Level 2 4: In this talk I describe a novel theoretical characterization of the performance of non-local means NLM for noise removal. NLM has proven effective in a variety of empirical studies, but little is understood fundamentally about how it performs relative to classical methods based on wavelets or how various parameters e.
The trade-off between global and local search for matching patches is examined, and the bias reduction associated with the local polynomial regression version of NLM is analyzed. The theoretical results are validated via simulations for 2D images corrupted by additive white Gaussian noise. We formulate a convex minimization to robustly recover a subspace from a contaminated data set, partially sampled around it, and propose a fast iterative algorithm to achieve the corresponding minimum.
We establish exact recovery by this minimizer, quantify the effect of noise and regularization, explain how to take advantage of a known intrinsic dimension and establish linear convergence of the iterative algorithm. We compare our method with many other algorithms for Robust PCA on synthetic and real data sets and demonstrate state-of-the-art speed and accuracy.
We consider the problem of recovering target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of videos and hyperspectral images, as well as in the analysis of transformation invariant low-rank matrix recovery.
We analyze the performance of the natural convex heuristic for solving this problem, under the assumption that measurements are chosen uniformly at random. We prove that this heuristic exactly recovers low-rank and sparse terms, provided the number of observations exceeds the number of intrinsic degrees of freedom by a polylogarithmic factor.
Our analysis introduces several ideas that may be of independent interest for the more general problem of compressed sensing of superpositions of structured signals. Slides of Talk 5: I will talk about the problems of denoising images corrupted by impulsive noise and blind inpainting i. Our basic approach is to model the set of patches of pixels in an image as a union of low-dimensional subspaces, corrupted by sparse but perhaps large magnitude noise.
For this purpose, we develop a robust and iterative method for single subspace modeling and extend it to an iterative algorithm for modeling multiple subspaces.
I will also cover the convergence for the algorithm and demonstrate state of the art performance of our method for both imaging problems.