We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

/pdf/robust-face-recognition-via-sparse-representation-4bfqv6y74o.pdf

Robust Face Recognition via Sparse Representation

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained l1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms l1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted l1-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations—not by reweighting the l1 norm of the coefficient sequence as is common, but by reweighting the l1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as Compressive Sensing.

/pdf/enhancing-sparsity-by-reweighted-l-1-minimization-znwoz4koxr.pdf

Enhancing Sparsity by Reweighted ℓ 1 Minimization

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ^2). Is it possible to estimate β reliably based on the noisy data y?

https://projecteuclid.org/download/pdfview_1/euclid.aos/1201012958

The Dantzig selector: Statistical estimation when p is much larger than n

A large number of vision applications rely on matching keypoints across images. The last decade featured an arms-race towards faster and more robust keypoints and association algorithms: Scale Invariant Feature Transform (SIFT)[17], Speed-up Robust Feature (SURF)[4], and more recently Binary Robust Invariant Scalable Keypoints (BRISK)[I6] to name a few. These days, the deployment of vision algorithms on smart phones and embedded devices with low memory and computation complexity has even upped the ante: the goal is to make descriptors faster to compute, more compact while remaining robust to scale, rotation and noise. To best address the current requirements, we propose a novel keypoint descriptor inspired by the human visual system and more precisely the retina, coined Fast Retina Keypoint (FREAK). A cascade of binary strings is computed by efficiently comparing image intensities over a retinal sampling pattern. Our experiments show that FREAKs are in general faster to compute with lower memory load and also more robust than SIFT, SURF or BRISK. They are thus competitive alternatives to existing keypoints in particular for embedded applications.

/pdf/freak-fast-retina-keypoint-53hq67wxuq.pdf

FREAK: Fast Retina Keypoint

Machine generated contents note: 1. Introduction to compressed sensing Mark A. Davenport, Marco F. Duarte, Yonina C. Eldar and Gitta Kutyniok; 2. Second generation sparse modeling: structured and collaborative signal analysis Alexey Castrodad, Ignacio Ramirez, Guillermo Sapiro, Pablo Sprechmann and Guoshen Yu; 3. Xampling: compressed sensing of analog signals Moshe Mishali and Yonina C. Eldar; 4. Sampling at the rate of innovation: theory and applications Jose Antonia Uriguen, Yonina C. Eldar, Pier Luigi Dragotta and Zvika Ben-Haim; 5. Introduction to the non-asymptotic analysis of random matrices Roman Vershynin; 6. Adaptive sensing for sparse recovery Jarvis Haupt and Robert Nowak; 7. Fundamental thresholds in compressed sensing: a high-dimensional geometry approach Weiyu Xu and Babak Hassibi; 8. Greedy algorithms for compressed sensing Thomas Blumensath, Michael E. Davies and Gabriel Rilling; 9. Graphical models concepts in compressed sensing Andrea Montanari; 10. Finding needles in compressed haystacks Robert Calderbank, Sina Jafarpour and Jeremy Kent; 11. Data separation by sparse representations Gitta Kutyniok; 12. Face recognition by sparse representation Arvind Ganesh, Andrew Wagner, Zihan Zhou, Allen Y. Yang, Yi Ma and John Wright.

Compressed sensing : theory and applications

http://webee.technion.ac.il/Sites/People/YoninaEldar/Info/Compressed%20Sensing%20with%20Coherent%20and%20Redundant%20Dictionaries.pdf

Compressed sensing with coherent and redundant dictionaries

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possible via an L1-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries. This condition imposes no incoherence restriction on the dictionary and our results may be the first of this kind. We discuss practical examples and the implications of our results on those applications, and complement our study by demonstrating the potential of L1-analysis for such problems.

Compressed Sensing with Coherent and Redundant Dictionaries

This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x in R^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g. quantization errors). 
We show that if one encodes the information as Ax where A is a suitable m by n coding matrix (m >= n), there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occur upon transmission (or equivalently as if one has an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well.

Highly robust error correction by convex programming

This article discusses a recently proposed error correction method involving convex optimization [1]. From an encoded and corrupted real-valued message, a receiver would like to determine the original message. A few entries of the encoded message are corrupted arbitrarily (which we call gross errors) and all the entries of the encoded message are corrupted slightly. We show that it is possible to recover the message with nearly the same accuracy as in the setting where no gross errors occur. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Paige Randall

Papers

Compressed sensing with coherent and redundant dictionaries

Compressed Sensing with Coherent and Redundant Dictionaries

Highly robust error correction by convex programming

Error correction and convex programming