Related papers: Two are better than one: Fundamental parameters of…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used,…

Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than…

Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…

So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…

Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To…

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…

Video anomaly detection is an essential but challenging task. The prevalent methods mainly investigate the reconstruction difference between normal and abnormal patterns but ignore the semantics consistency between appearance and motion…

We consider the recovery of sparse signals that share a common support from multiple measurement vectors. The performance of several algorithms developed for this task depends on parameters like dimension of the sparse signal, dimension of…

Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied.…

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…

Recently it has been established that asymptotic incoherence can be used to facilitate subsampling, in order to optimize reconstruction quality, in a variety of continuous compressed sensing problems, and the coherence structure of certain…

As compared to using randomly generated sensing matrices, optimizing the sensing matrix w.r.t. a carefully designed criterion is known to lead to better quality signal recovery given a set of compressive measurements. In this paper, we…

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…

Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but…

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…