Wideband spectrum sensing is one of the most challenging aspects of Cognitive Radio Networks (CRNs). It should be performed as fast and as accurate as possible. Traditional wideband spectrum sensing techniques require excessively high sampling rate analog-to-digital converters (ADCs). Compressed sensing was considered to enable wideband spectrum sensing at a much lower sampling rate below the N...

In compressed sensing we seek to gain information about vector x ∈ R from d << N nonadaptive linear measurements. Candes, Donoho, Tao et. al. ( see e.g. [2, 4, 8]) proposed to seek good approximation to x via `1 minimisation. In this paper we show that in the case of Gaussian measurements it recovers the signal well from inacurate measurements, thus improving result from [4]. We also show that ...

We here model peripheral vision in a compressed sensing framework as a strategy of optimally guessing what stimulus corresponds to a sparsely encoded peripheral representation, and find that typical letter-crowding effects naturally arise from this strategy. The model is simple as it consists of only two convergence stages. We apply the model to the problem of crowding effects in reading. First...

We provide elementary proofs that Bernoulli and Gaussian random matrices satisfy the so-called approximate spherical section property. The best possible of this type was established by Kashin and by Garnaev and Gluskin. In the case of Gaussian matrices, our bound is weaker than theirs (by a factor of √ log n) but uses only elementary arguments. This analysis provides elementary proofs of the ma...

Compressed sensing (CS) using sparse measurement matrices and iterative messagepassing reconstruction algorithms have been recently investigated as a low-complexity alternative to traditional CS methods. In this paper, we investigate the adaptive version of well-known Sudocodes scheme, where the sparse measurement matrix is progressively created based on the outcomes of previous measurements. I...

Compressed Sensing Based Image Restoration Algorithm with Prior Information: Software and Hardware Implementations for Image-Guided Therapy

This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a fixed number of sparse measurements. Often, it may fail as the number of sparse measurements may be not enough, possibly due to an underestimate of the sign...

Bacteria are the unseen majority on our planet, with millions of species and comprising most of the living protoplasm. While current methods enable in-depth study of a small number of communities, a simple tool for breadth studies of bacterial population composition in a large number of samples is lacking. We propose a novel approach for reconstruction of the composition of an unknown mixture o...

We discuss the universality of the l1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that l1 recovery under a random matrix with orthogonal symmetry has a universal threshold. This indicates that the threshold of l1 recovery under a non-orthogonal random matrix differs from the universal one. Taking this...