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.

Simple Method for High-Performance Digit Recognition Based on Sparse Coding

Abstract: In this brief paper, we propose a method of feature extraction for digit recognition that is inspired by vision research: a sparse-coding strategy and a local maximum operation. We show that our method, despite its simplicity, yields state-of-the-art classification results on a highly competitive digit-recognition benchmark. We first employ the unsupervised Sparsenet algorithm to learn a basis for representing patches of handwritten digit images. We then use this basis to extract local coefficients. In a second step, we apply a local maximum operation to implement local shift invariance. Finally, we train a support vector machine (SVM) on the resulting feature vectors and obtain state-of-the-art classification performance in the digit recognition task defined by the MNIST benchmark. We compare the different classification performances obtained with sparse coding, Gabor wavelets, and principal component analysis (PCA). We conclude that the learning of a sparse representation of local image patches combined with a local maximum operation for feature extraction can significantly improve recognition performance.

Efficient Blind Compressed Sensing Using Sparsifying Transforms with Convergence Guarantees and Application to Magnetic Resonance Imaging

Abstract: Natural signals and images are well known to be approximately sparse in transform domains such as wavelets and discrete cosine transform. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the sparsifying transform from highly undersampled measurements. The proposed block coordinate descent-type algorithms involve highly efficient optimal updates. Importantly, we prove that although the proposed blind compressed sensing formulations are highly nonconvex, our algorithms are globally convergent (i.e., they converge from any initialization) to the set of critical points of the objectives def...

Sparse Recovery From Combined Fusion Frame Measurements

Abstract: Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as compressed sensing (CS). Fusion frames are very rich new signal representation methods that use collections of subspaces instead of vectors to represent signals. This work combines these exciting fields to introduce a new sparsity model for fusion frames. Signals that are sparse under the new model can be compressively sampled and uniquely reconstructed in ways similar to sparse signals using standard CS. The combination provides a promising new set of mathematical tools and signal models useful in a variety of applications. With the new model, a sparse signal has energy in very few of the subspaces of the fusion frame, although it does not need to be sparse within each of the subspaces it occupies. This sparsity model is captured using a mixed l1/l2 norm for fusion frames. A signal sparse in a fusion frame can be sampled using very few random projections and exactly reconstructed using a convex optimization that minimizes this mixed l1/l2 norm. The provided sampling conditions generalize coherence and RIP conditions used in standard CS theory. It is demonstrated that they are sufficient to guarantee sparse recovery of any signal sparse in our model. More over, a probabilistic analysis is provided using a stochastic model on the sparse signal that shows that under very mild conditions the probability of recovery failure decays exponentially with in creasing dimension of the subspaces.

DOA Estimation for Sparse Array via Sparse Signal Reconstruction

Abstract: The problem of direction-of-arrival (DOA) estimation for sparse array is addressed. The perspective that DOA estimation in virtual array response model can be cast as the problem of sparse recovery is introduced. Two methods are proposed, based on different optimization problems, which are solvable using second-order cone (SOC) programming. Without the knowledge of the number of sources, the proposed methods yield superior performances, which are verified by numerical simulations.

Visual Tracking Using Strong Classifier and Structural Local Sparse Descriptors

Abstract: Sparse coding methods have achieved great success in visual tracking, and we present a strong classifier and structural local sparse descriptors for robust visual tracking. Since the summary features considering the sparse codes are sensitive to occlusion and other interfering factors, we extract local sparse descriptors from a fraction of all patches by performing a pooling operation. The collection of local sparse descriptors is combined into a boosting-based strong classifier for robust visual tracking using a discriminative appearance model. Furthermore, a structural reconstruction error based weight computation method is proposed to adjust the classification score of each candidate for more precise tracking results. To handle appearance changes during tracking, we present an occlusion-aware template update scheme. Comprehensive experimental comparisons with the state-of-the-art algorithms demonstrated the better performance of the proposed method.