
Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering
In Compressive Sensing theory and its applications, quantization of sign...
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Restricted Structural Random Matrix for Compressive Sensing
Compressive sensing (CS) is wellknown for its unique functionalities of...
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Sparse Depth Sensing for ResourceConstrained Robots
We consider the case in which a robot has to navigate in an unknown envi...
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(l1,l2)RIP and Projected BackProjection Reconstruction for PhaseOnly Measurements
This letter analyzes the performances of a simple reconstruction method,...
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Mixed onebit compressive sensing with applications to overexposure correction for CT reconstruction
When a measurement falls outside the quantization or measurable range, i...
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Fast Binary Compressive Sensing via ℓ_0 Gradient Descent
We present a fast Compressive Sensing algorithm for the reconstruction o...
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EnergyEfficient Sensor Censoring for Compressive Distributed Sparse Signal Recovery
To strike a balance between energy efficiency and data quality control, ...
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One Bit to Rule Them All : Binarizing the Reconstruction in 1bit Compressive Sensing
This work focuses on the reconstruction of sparse signals from their 1bit measurements. The context is the one of 1bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution shows that, in addition to the measurement process, we can additionally reconstruct the signal with a binarization of the sensing matrix. This binary representation of both the measurements and sensing matrix can dramatically simplify the hardware architecture on embedded systems, enabling cheaper and more power efficient alternatives. Within this framework, given a sensing matrix respecting the restricted isometry property (RIP), we prove that for any sparse signal the quantized projected backprojection (QPBP) algorithm achieves a reconstruction error decaying like O(m1/2)when the number of measurements m increases. Simulations highlight the practicality of the developed scheme for different sensing scenarios, including random partial Fourier sensing.
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