相关论文: Stronger L2/L2 Compressed Sensing; Without Iterati…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into…
Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind…
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…
Large language models deliver strong generative performance but at the cost of massive parameter counts, memory use, and decoding latency. Prior work has shown that pruning and structured sparsity can preserve accuracy under substantial…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Whereas classical compressed sensing algorithms do…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
In compressed sensing sparse solutions are usually obtained by solving an $\ell^1$-minimization problem. Furthermore, the sparsity of the signal does need not be directly given. In fact, it is sufficient to have a signal that is sparse…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
We show that for complex nonlinear systems, model reduction and compressive sensing strategies can be combined to great advantage for classifying, projecting, and reconstructing the relevant low-dimensional dynamics. $\ell_2$-based…