Quantized Compressive Sensing
نویسندگان
چکیده
We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or characterized via bounds. We adapt two benchmark CS reconstruction algorithms to accommodate quantization errors, and empirically demonstrate that these methods significantly reduce the reconstruction distortion when compared to standard CS techniques.
منابع مشابه
Quantized Compressive Sensing Measurement Based on Improved Subspace Pursuit Algorithm
Recent research results in compressive sensing have shown that sparse signals can be recovered from a small number of random measurements. Whether quantized compressive measurements can provide an efficient representation of sparse signals in information-theoretic needs discuss. In this paper, the distortion rate functions are used as a tool to research the quantizing compressive sensing measur...
متن کاملQuantized Compressive Sensing with RIP Matrices: The Benefit of Dithering
In Compressive Sensing theory and its applications, quantization of signal measurements, as integrated into any realistic sensing model, impacts the quality of signal reconstruction. In fact, there even exist incompatible combinations of quantization functions (e.g., the 1-bit sign function) and sensing matrices (e.g., Bernoulli) that cannot lead to an arbitrarily low reconstruction error when ...
متن کاملQuantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing
In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from 1-bit to high resolution assumption. This is achieved by generalizing the iterative hard thresholding (IHT) algorithm and its binary variant (BIHT) introduced in previous works to enforce the consistenc...
متن کاملDistribution of Compressive Measurements Generated by Structurally Random Matrices
— Structurally random matrices (SRMs) have been proposed as a practical alternative to fully random matrices (FRMs) for generating compressive sensing measurements. If the compressive measurements are transmitted over a communication channel, they need to be efficiently quantized and coded and hence knowledge of the measurements' statistics reequired. In this paper we study the statistical dist...
متن کاملAngle-preserving Quantized Phase Embeddings
We demonstrate that the phase of randomized complex-valued projections of real-valued signals preserves information about the angle, i.e., the correlation, between those signals. This information can be exploited to design quantized angle-preserving embeddings, which represent such correlations using a finite bit-rate. The proposed embeddings generalize known results on binary embeddings and 1-...
متن کامل