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.

Robust Visual Tracking Via Consistent Low-Rank Sparse Learning

Abstract: Object tracking is the process of determining the states of a target in consecutive video frames based on properties of motion and appearance consistency. In this paper, we propose a consistent low-rank sparse tracker (CLRST) that builds upon the particle filter framework for tracking. By exploiting temporal consistency, the proposed CLRST algorithm adaptively prunes and selects candidate particles. By using linear sparse combinations of dictionary templates, the proposed method learns the sparse representations of image regions corresponding to candidate particles jointly by exploiting the underlying low-rank constraints. In addition, the proposed CLRST algorithm is computationally attractive since temporal consistency property helps prune particles and the low-rank minimization problem for learning joint sparse representations can be efficiently solved by a sequence of closed form update operations. We evaluate the proposed CLRST algorithm against $$14$$ 14 state-of-the-art tracking methods on a set of $$25$$ 25 challenging image sequences. Experimental results show that the CLRST algorithm performs favorably against state-of-the-art tracking methods in terms of accuracy and execution time.

UWB Through-Wall Imaging Based on Compressive Sensing

Abstract: To achieve high-resolution 2-D images, through-wall imaging (TWI) radar with ultra-wideband and long antenna arrays faces considerable technical challenges such as a prolonged data collection time, a huge amount of data, and a high hardware complexity. This paper presents a novel data acquisition scheme and an imaging algorithm for TWI radar based on compressive sensing (CS), which states that a signal having a sparse representation can be reconstructed from a small number of nonadaptive randomized projections by solving a tractable convex program. Instead of measuring all spatial-frequency data, a few samples, by employing an overcomplete dictionary, are sufficient to obtain reliable target space images even at high noise levels. Preliminary simulated and experimental results show that the proposed algorithm outperforms the conventional delay-and-sum beamforming method even though many fewer CS measurements are used.

Is Levenberg-Marquardt the most efficient optimization algorithm for implementing bundle adjustment?

Abstract: In order to obtain optimal 3D structure and viewing parameter estimates, bundle adjustment is often used as the last step of feature-based structure and motion estimation algorithms. Bundle adjustment involves the formulation of a large scale, yet sparse minimization problem, which is traditionally solved using a sparse variant of the Levenberg-Marquardt optimization algorithm that avoids storing and operating on zero entries. This paper argues that considerable computational benefits can be gained by substituting the sparse Levenberg-Marquardt algorithm in the implementation of bundle adjustment with a sparse variant of Powell's dog leg non-linear least squares technique. Detailed comparative experimental results provide strong evidence supporting this claim

Blind source separation by sparse decomposition

Abstract: The blind source separation problem is to extract the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. This situation is common, eg in acoustics, radio, and medical signal processing. We exploit the property of the sources to have a sparse representation in a corresponding signal dictionary. Such a dictionary may consist of wavelets, wavelet packets, etc., or be obtained by learning from a given family of signals. Starting from the maximum a posteriori framework, which is applicable to the case of more sources than mixtures, we derive a few other categories of objective functions, which provide faster and more robust computations, when there are an equal number of sources and mixtures. Our experiments with artificial signals and with musical sounds demonstrate significantly better separation than other known techniques.

Sparse canonical correlation analysis

Abstract: We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the correlation between the two views. The method is compared to alternative sparse solutions as well as demonstrated on paired corpuses for mate-retrieval. We are able to observe, in the mate-retrieval, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.