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Yi Ma

Publications and source records attributed to Yi Ma.

252 records · Page 14Linked to original sources
arXiv2014

Blind Image Deblurring by Spectral Properties of Convolution Operators

In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired blur kernel. We shall show that the blurry image itself encodes rich information about the blur kernel. Such information can be found through analyzing and comparing how the spectrum of an image as a convolution operator changes before and after blurring. Our analysis leads to an effective convex regularizer on the blur kernel which depends only on the given blurry image. We show that the minimizer of this regularizer guarantees to give good approximation to the blur kernel if the original image is sharp enough. By combining this powerful regularizer with conventional image deblurring techniques, we show how we could significantly improve the deblurring results through simulations and experiments on real images. In addition, our analysis and experiments help explaining a widely accepted doctrine; that is, the edges are good features for deblurring.

cs.CV↗
arXiv2014

Collaborative Representation based Classification for Face Recognition

By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1- norm sparsity constraint on coding coefficients plays a key role in the success of SRC, while its use of all training samples to collaboratively represent the query sample is rather ignored. In this paper we discuss how SRC works, and show that the collaborative representation mechanism used in SRC is much more crucial to its success of face classification. The SRC is a special case of collaborative representation based classification (CRC), which has various instantiations by applying different norms to the coding residual and coding coefficient. More specifically, the l1 or l2 norm characterization of coding residual is related to the robustness of CRC to outlier facial pixels, while the l1 or l2 norm characterization of coding coefficient is related to the degree of discrimination of facial features. Extensive experiments were conducted to verify the face recognition accuracy and efficiency of CRC with different instantiations.

cs.CV↗
arXiv2014

Sparse Illumination Learning and Transfer for Single-Sample Face Recognition with Image Corruption and Misalignment

Single-sample face recognition is one of the most challenging problems in face recognition. We propose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required gallery images to one sample per class. To compensate for the missing illumination information traditionally provided by multiple gallery images, a sparse illumination learning and transfer (SILT) technique is introduced. The illumination in SILT is learned by fitting illumination examples of auxiliary face images from one or more additional subjects with a sparsely-used illumination dictionary. By enforcing a sparse representation of the query image in the illumination dictionary, the SILT can effectively recover and transfer the illumination and pose information from the alignment stage to the recognition stage. Our extensive experiments have demonstrated that the new algorithms significantly outperform the state of the art in the single-sample regime and with less restrictions. In particular, the single-sample face alignment accuracy is comparable to that of the well-known Deformable SRC algorithm using multiple gallery images per class. Furthermore, the face recognition accuracy exceeds those of the SRC and Extended SRC algorithms using hand labeled alignment initialization.

cs.CV↗
arXiv2013

The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.html

math.OC↗
arXiv2012

Fast L1-Minimization Algorithms For Robust Face Recognition

L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

cs.CV↗
arXiv2012

Robust Recovery of Subspace Structures by Low-Rank Representation

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.

cs.IT↗
arXiv2012

Principal Component Pursuit with Reduced Linear Measurements

In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple images or rectifying regular texture, where the goal is to recover a low-rank matrix with a large fraction of corrupted entries in the presence of nonlinear domain transformation. We consider a natural convex heuristic to this problem which is a variant to the recently proposed Principal Component Pursuit. We prove that under suitable conditions, this convex program guarantees to recover the correct low-rank and sparse components despite reduced measurements. Our analysis covers both random and deterministic measurement models.

cs.IT↗
arXiv2012

Compressive Principal Component Pursuit

We consider the problem of recovering a 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 structured high-dimensional signals such as videos and hyperspectral images, as well as in the analysis of transformation invariant low-rank 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 of the component signals by a polylogarithmic factor. Our analysis introduces several ideas that may be of independent interest for the more general problem of compressed sensing and decomposing superpositions of multiple structured signals.

cs.IT↗
arXiv2012

Generalized Principal Component Analysis (GPCA)

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high- dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.

cs.CV↗
arXiv2011

Sparsity and Robustness in Face Recognition

This report concerns the use of techniques for sparse signal representation and sparse error correction for automatic face recognition. Much of the recent interest in these techniques comes from the paper "Robust Face Recognition via Sparse Representation" by Wright et al. (2009), which showed how, under certain technical conditions, one could cast the face recognition problem as one of seeking a sparse representation of a given input face image in terms of a "dictionary" of training images and images of individual pixels. In this report, we have attempted to clarify some frequently encountered questions about this work and particularly, on the validity of using sparse representation techniques for face recognition.

cs.CV↗
arXiv2010

TILT: Transform Invariant Low-rank Textures

In this paper, we show how to efficiently and effectively extract a class of "low-rank textures" in a 3D scene from 2D images despite significant corruptions and warping. The low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as all kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects. Our approach to finding these low-rank textures leverages the recent breakthroughs in convex optimization that enable robust recovery of a high-dimensional low-rank matrix despite gross sparse errors. In the case of planar regions with significant affine or projective deformation, our method can accurately recover both the intrinsic low-rank texture and the precise domain transformation, and hence the 3D geometry and appearance of the planar regions. Extensive experimental results demonstrate that this new technique works effectively for many regular and near-regular patterns or objects that are approximately low-rank, such as symmetrical patterns, building facades, printed texts, and human faces.

cs.CV↗
arXiv2010

Underlay Cognitive Radio with Full or Partial Channel Quality Information

Underlay cognitive radios (UCRs) allow a secondary user to enter a primary user's spectrum through intelligent utilization of multiuser channel quality information (CQI) and sharing of codebook. The aim of this work is to study two-user Gaussian UCR systems by assuming the full or partial knowledge of multiuser CQI. Key contribution of this work is motivated by the fact that the full knowledge of multiuser CQI is not always available. We first establish a location-aided UCR model where the secondary user is assumed to have partial CQI about the secondary-transmitter to primary-receiver link as well as full CQI about the other links. Then, new UCR approaches are proposed and carefully analyzed in terms of the secondary user's achievable rate, denoted by $C_2$, the capacity penalty to primary user, denoted by $ΔC_1$, and capacity outage probability. Numerical examples are provided to visually compare the performance of UCRs with full knowledge of multiuser CQI and the proposed approaches with partial knowledge of multiuser CQI.

cs.IT↗
arXiv2010

Segmentation of Natural Images by Texture and Boundary Compression

We present a novel algorithm for segmentation of natural images that harnesses the principle of minimum description length (MDL). Our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a Gaussian distribution and the region boundary can be effectively coded by an adaptive chain code. The optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image, and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes as multi-scale texture features. The optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image. We test our algorithm on the publicly available Berkeley Segmentation Dataset. It achieves state-of-the-art segmentation results compared to other existing methods.

cs.CV↗
arXiv2010

Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit

We consider the problem of recovering a low-rank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been shown that this problem can be solved efficiently and effectively by a convex program named Principal Component Pursuit (PCP), provided that the fraction of corrupted entries and the rank of the matrix are both sufficiently small. In this paper, we extend that result to show that the same convex program, with a slightly improved weighting parameter, exactly recovers the low-rank matrix even if "almost all" of its entries are arbitrarily corrupted, provided the signs of the errors are random. We corroborate our result with simulations on randomly generated matrices and errors.

cs.IT↗
arXiv2010

Stable Principal Component Pursuit

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To our knowledge, this is the first result that shows the classical Principal Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to gross sparse errors; or the first that shows the newly proposed PCP can be made stable to small entry-wise perturbations.

cs.IT↗
arXiv2009

Robust Principal Component Analysis?

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the L1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.

cs.IT↗
arXiv2008

Dense Error Correction via L1-Minimization

This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded. Motivated by an observation from face recognition in computer vision, this paper proves that for highly correlated (and possibly overcomplete) dictionaries $A$, any non-negative, sufficiently sparse signal $\x$ can be recovered by solving an $\ell^1$-minimization problem: $\min \|\x\|_1 + \|\e\|_1 \quad {subject to} \quad \y = A\x + \e.$ More precisely, if the fraction $ρ$ of errors is bounded away from one and the support of $\x$ grows sublinearly in the dimension $m$ of the observation, then as $m$ goes to infinity, the above $\ell^1$-minimization succeeds for all signals $\x$ and almost all sign-and-support patterns of $\e$. This result suggests that accurate recovery of sparse signals is possible and computationally feasible even with nearly 100% of the observations corrupted. The proof relies on a careful characterization of the faces of a convex polytope spanned together by the standard crosspolytope and a set of iid Gaussian vectors with nonzero mean and small variance, which we call the ``cross-and-bouquet'' model. Simulations and experimental results corroborate the findings, and suggest extensions to the result.

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