So yesterday, you saw the ability to approximate a data matrix through some sort of quantization of said matrix. But these data came from a sensor that quantized an analog data in the first place. Compressive sensing offers a new way to explore that trade-off that come with quantization.. In related news, Petros Boufounos tells us that

*"The page with resources on quantization has been updated to include the slides from the [ICASSP] tutorial. [ on Modern Quantization Strategies for Compressive Sensing and Acquisition Systems]*" . Today we have a paper making the bridge between 1-bit compressive sensing and your average run-of-the-mill quantization strategy. This is timely in light of all the discussions currently going on about the internet of things and related wireless communication protocols like SigFox. To come back to the original argument above, one wonders when data matrix will exploit the quantization found either here or in matrix sampling. Without further due, here is the paper:
Quantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing by Laurent Jacques, Kévin Degraux, Christophe De Vleeschouwer

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 consistency of the reconstructed signal with respect to the quantization model. The performance of this algorithm, simply called quantized IHT (QIHT), is evaluated in comparison with other approaches (e.g., IHT, basis pursuit denoise) for several quantization scenarios.

The implementation for the QIHT demo can be found here.

The quantization page is part of the Highly Technical Reference Pages

The quantization page is part of the Highly Technical Reference Pages

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