We introduce a mathematical framework that generalizes the three standard pillars of compressed sensing - namely, sparsity, incoherence and uniform random subsampling - to three new concepts: asymptotic sparsity and multilevel random sampling.Expand

This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymmptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing.Expand

We present Multi-Carrier Burst Contention, a cross-layer protocol based on a contention scheme that spans both time and frequency domains, employing short and unmodulated energy bursts and a randomized and recursive node-elimination mechanism in order to resolve collisions.Expand

We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications.Expand

We propose a theory and set of methods for infinite-dimensional compressed sensing, or as we shall also refer to it, compressed sensing over the continuum.Expand

An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the object to recover, but also on its structure.Expand

We propose a high performance solution based on an innovative node elimination algorithm that uses short and unmodulated bursts of energy during contention - no data is exchanged.Expand

We give the first proof of near-optimal recovery from discrete Fourier samples taken according to an appropriate variable density sampling scheme.Expand

Sparsity is the traditional mainstay of the majority of compressed sensing. However, recent evidence suggests that in many applications where the sampling mechanism is fixed one does not recover allâ€¦ Expand

We introduce the Activity Based Sector Synchronisation (ABSS) algorithm and show by trace-drivensimulations that ABSS is able to deliver a useful trade-off with a data transmission overhead between 0.3% and 2.4% of a gigabit link whilst incurring in the majority of cases a migration latency of less than 1.1 s.Expand