This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and improve results in real-world applications. The contribution of the paper is fourfold: First, it explains how the sampling strategy depends not only on the signa...

The common approaches to sample a signal generally follow the well-known Nyquist-Shannon’s theorem: the sampling rate must be at least twice the maximum frequency presented in the signal. A new emerging field, compressed sampling (CS), has made a paradigmatic step to sample a signal with much less measurements than those required by the Nyquist-Shannon’s theorem when the unknown signal is spars...

We investigate new sampling strategies for projection tomography, enabling one to employ fewer measurements than expected from classical sampling theory without significant loss of information. Inspired by compressed sensing, our approach is based on the understanding that many real objects are compressible in some known representation, implying that the number of degrees of freedom defining an...

Our goal is to demonstrate the usefulness and efficiency of a compressed sensing approach when applied to the problem of spike sorting. This approach involves four steps towards transforming the raw spikes into a sparse basis with the fewest number of measurements require to achieve accurate clustering. We first train a dictionary which converts a spike into a sparse signal. We then sample the ...

As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random sampling in data acquisition, which is difficult to implement in hardware. In this paper, we propose a deterministic and simple sampling scheme, that is, sam...

We consider compressed sampling over finite fields and investigate the number of compressed measurements needed for successful L0 recovery. Our results are obtained while the sparseness of the sensing matrices as well as the size of the finite fields are varied. One of interesting conclusions includes that unless the signal is “ultra” sparse, the sensing matrices do not have to be dense. Keywor...