Related papers: A Weighted Generalized Coherence Approach for Sens…
In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the high-dimensional limit: while previous works on this model…
This paper proposes matrix-scaled consensus algorithm, which generalizes the scaled consensus algorithm in \cite{Roy2015scaled}. In (scalar) scaled consensus algorithms, the agents' states do not converge to a common value, but to different…
With the advent of multi-coil imaging and compressed sensing, a number of model based reconstruction algorithms have been created. They incorporate a multitude of different regularization functions based on physics, observed phenomenology,…
A novel unified approach to jointly optimize structural design parameters, actuator and sensor precision and controller parameters is presented in this paper. The joint optimization problem is posed as a covariance control problem, where…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence,…
In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete Fourier transform matrix. The…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
This paper proposes a generalization of the conjugate gradient (CG) method used to solve the equation $Ax=b$ for a symmetric positive definite matrix $A$ of large size $n$. The generalization consists of permitting the scalar control…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…
Mean-squared-error (MSE) is one of the most widely used performance metrics for the designs and analysis of multi-input-multiple-output (MIMO) communications. Weighted MSE minimization, a more general formulation of MSE minimization, plays…
Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy…