Breaking the Coherence Barrier: A New Theory for Compressed Sensing

This paper presents a framework for compressed sensing that bridges a gap between existing theory and the current use of compressed sensing in many real-world applications. In doing so, it also introduces a new sampling method that yields substantially improved recovery over existing techniques. In many applications of compressed sensing, including medical imaging, the standard principles of incoherence and sparsity are lacking. Whilst compressed sensing is often used successfully in such applications, it is done largely without mathematical explanation. The framework introduced in this paper provides such a justification. It does so by replacing these standard principles with three more general concepts: asymptotic sparsity, asymptotic incoherence and multilevel random subsampling. Moreover, not only does this work provide such a theoretical justification, it explains several key phenomena witnessed in practice. In particular, and unlike the standard theory, this work demonstrates the dependence of optimal sampling strategies on both the incoherence structure of the sampling operator and on the structure of the signal to be recovered. Another key consequence of this framework is the introduction of a new structured sampling method that exploits these phenomena to achieve significant improvements over current state-of-the-art techniques

Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach

A key challenge of massive MTC (mMTC), is the joint detection of device activity and decoding of data. The sparse characteristics of mMTC makes compressed sensing (CS) approaches a promising solution to the device detection problem. However, utilizing CS-based approaches for device detection along with channel estimation, and using the acquired estimates for coherent data transmission is suboptimal, especially when the goal is to convey only a few bits of data. First, we focus on the coherent transmission and demonstrate that it is possible to obtain more accurate channel state information by combining conventional estimators with CS-based techniques. Moreover, we illustrate that even simple power control techniques can enhance the device detection performance in mMTC setups. Second, we devise a new non-coherent transmission scheme for mMTC and specifically for grant-free random access. We design an algorithm that jointly detects device activity along with embedded information bits. The approach leverages elements from the approximate message passing (AMP) algorithm, and exploits the structured sparsity introduced by the non-coherent transmission scheme. Our analysis reveals that the proposed approach has superior performance compared to application of the original AMP approach.Comment: Submitted to IEEE Transactions on Communication

Low-complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analysed: firstly, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.Comment: IEEE Transactions on Signal Processing, accepted for publication. Article in pres