Compressive Sensing and Structured Random Matrices
نویسنده
چکیده
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-minimization.
منابع مشابه
Compressive Sensing, Structured Random Matrices and Recovery of Functions in High Dimensions
Compressive sensing predicts that sparse vectors can be recovered efficiently from highly undersampled measurements. While it is well-understood by now that Gaussian random matrices provide optimal measurement matrices in this context, such “highly” random matrices suffer from certain drawbacks: applications require more structure arising from physical or other constraints, and recovery algorit...
متن کاملStructured sublinear compressive sensing via belief propagation
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured...
متن کاملThe Restricted Isometry Property for Random Block Diagonal Matrices
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparsevectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Itis by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIPunder certain conditions on the number of measurements. Their use can be limi...
متن کاملDeterministic Sensing Matrices in Compressive Sensing: A Survey
Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensi...
متن کاملRecovery guarantees for multifrequency chirp waveforms in compressed radar sensing
Radar imaging systems transmit modulated wideband waveform to achieve high range resolution resulting in high sampling rates at the receiver proportional to the bandwidth of the transmit waveform. Analog processing techniques can be used on receive to reduce the number of measurements to N , the number of potential delay bins. If the scene interrogated by the radar is assumed to be sparse consi...
متن کامل