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From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
TLDR
This paper considers the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum, and proposes a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. Expand
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
TLDR
The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem. Expand
Linear precoding via conic optimization for fixed MIMO receivers
TLDR
The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem and can significantly outperform existing linear precoders. Expand
Structured Compressed Sensing: From Theory to Applications
TLDR
The prime focus is bridging theory and practice, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware in compressive sensing. Expand
Robust Recovery of Signals From a Structured Union of Subspaces
TLDR
This paper develops a general framework for robust and efficient recovery of nonlinear but structured signal models, in which x lies in a union of subspaces, and presents an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. Expand
Compressed Sensing with Coherent and Redundant Dictionaries
TLDR
A condition on the measurement/sensing matrix is introduced, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries. Expand
Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals
TLDR
This paper describes how to choose the parameters of the multi-coset sampling so that a unique multiband signal matches the given samples, and develops a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Expand
Phase Retrieval via Matrix Completion
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging, and many other applications. Our approach,Expand
Zero-Forcing Precoding and Generalized Inverses
TLDR
This work begins with the standard design under the assumption of a total power constraint and proves that precoders based on the pseudo-inverse are optimal among the generalized inverses in this setting, and examines individual per-antenna power constraints. Expand
Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow
TLDR
This paper presents a new algorithm, termed Truncated amplitude flow (TAF), to recover an unknown vector from a system of quadratic equations, and proves that as soon as the number of equations is on the order of theNumber of unknowns, TAF recovers the solution exactly. Expand
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