The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it difficult to find explicit matrices that support recovery of signals from sketches of the optimal (smallest possible) dimension. A number of attempts have been made ...

These notes give a mathematical introduction to compressive sensing focusing on recovery using `1-minimization and structured random matrices. An emphasis is put on techniques for proving probabilistic estimates for condition numbers of structured random matrices. Estimates of this type are key to providing conditions that ensure exact or approximate recovery of sparse vectors using `1-minimiza...

In this article, an equilibrated gradient recovery error estimator is introduced and analyzed. Regional and global error bounds are established under the equilibrium condition. Furthermore, the error estimator based on the ZZ patch recovery technique is analyzed theoretically. Stability and consistent properties are proved under mild assumptions. All results are valid for arbitrary grids.

This paper provides a hierarchical control strategy for cooperative braking system of an electric vehicle with separated driven axles. Two layers are defined: the top layer is used to optimize the braking stability based on two sliding mode control strategies, namely, the interaxle control mode and signal-axle control strategies; the interaxle control strategy generates the ideal braking force ...

OBJECTIVES This investigation was designed to monitor altitude acclimatisation in an elite cohort of distance runners and follow the subsequent recovery from infectious mononucleosis which developed in one of these athletes. METHODS Twenty six national standard distance runners performed treadmill tests 24 days before they travelled to an altitude camp (1500 to 2000 m). One of these athletes ...

Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as l1-minimization find the sparsest solution to certain systems of equations. Random matrices have become a popular choice for the measurement matrix. Indeed, near-optimal uniform recovery results have been shown for such matrices. In this note we f...

Idiopathic unilateral diaphragmatic paralysis is a rare condition that typically causes minimal symptoms, especially during exercise. Several reports indicated progressive improvement or even complete recovery to normal function of diaphragmatic paralysis that complicated various thoracic and extrathoracic conditions. In this case we describe a 57-year-old male with spontaneous recovery of idio...

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 possib...

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a m-dimensional k-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result also improves the existing guarantees for Orthogonal Matching Pursuit (OMP) algori...