Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

Intra-Class Variation Reduction Using Training Expression Images for Sparse Representation Based Facial Expression Recognition

Abstract: Automatic facial expression recognition (FER) is becoming increasingly important in the area of affective computing systems because of its various emerging applications such as human-machine interface and human emotion analysis. Recently, sparse representation based FER has become popular and has shown an impressive performance. However, sparse representation could often produce less meaningful sparse solution for FER due to intra-class variation such as variation in identity or illumination. This paper proposes a new sparse representation based FER method, aiming to reduce the intra-class variation while emphasizing the facial expression in a query face image. To that end, we present a new method for generating an intra-class variation image of each expression by using training expression images. The appearance of each intra-class variation image could be close to the appearance of the query face image in identity and illumination. Therefore, the differences between the query face image and its intra-class variation images are used as the expression features for sparse representation. Experimental results show that the proposed FER method has high discriminating capability in terms of improving FER performance. Further, the intra-class variation images of non-neutral expressions are complementary with that of neutral expression, for improving FER performance.

Sparse Regularization with $l^q$ Penalty Term

Abstract: We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the standard range condition, we derive the usual convergence rate $O(\sqrt{\delta})$ of the regularized solutions in dependence of the noise level $\delta$. Particular emphasis lies on the case, where the true solution is known to have a sparse representation in a given basis. In this case, if the differential of the operator satisfies a certain injectivity condition, we can show that the actual convergence rate improves up to $O(\delta)$.

A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise

Abstract: This paper proposes a general weighted l2-l0 norms energy minimization model to remove mixed noise such as Gaussian-Gaussian mixture, impulse noise, and Gaussian-impulse noise from the images. The approach is built upon maximum likelihood estimation framework and sparse representations over a trained dictionary. Rather than optimizing the likelihood functional derived from a mixture distribution, we present a new weighting data fidelity function, which has the same minimizer as the original likelihood functional but is much easier to optimize. The weighting function in the model can be determined by the algorithm itself, and it plays a role of noise detection in terms of the different estimated noise parameters. By incorporating the sparse regularization of small image patches, the proposed method can efficiently remove a variety of mixed or single noise while preserving the image textures well. In addition, a modified K-SVD algorithm is designed to address the weighted rank-one approximation. The experimental results demonstrate its better performance compared with some existing methods.

Compressive coded aperture imaging

Abstract: Nonlinear image reconstruction based upon sparse representations of images has recently received widespread attention with the emerging framework of compressed sensing (CS). This theory indicates that, when feasible, judicious selection of the type of distortion induced by measurement systems may dramatically improve our ability to perform image reconstruction. However, applying compressed sensing theory to practical imaging systems poses a key challenge: physical constraints typically make it infeasible to actually measure many of the random projections described in the literature, and therefore, innovative and sophisticated imaging systems must be carefully designed to effectively exploit CS theory. In video settings, the performance of an imaging system is characterized by both pixel resolution and field of view. In this work, we propose compressive imaging techniques for improving the performance of video imaging systems in the presence of constraints on the focal plane array size. In particular, we describe a novel yet practical approach that combines coded aperture imaging to enhance pixel resolution with superimposing subframes of a scene onto a single focal plane array to increase field of view. Specifically, the proposed method superimposes coded observations and uses wavelet-based sparsity recovery algorithms to reconstruct the original subframes. We demonstrate the effectiveness of this approach by reconstructing with high resolution the constituent images of a video sequence.