Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing

This paper focuses on the estimation of low-complexity signals when they are observed through $M$ uniformly quantized compressive observations. Among such signals, we consider 1-D sparse vectors, low-rank matrices, or compressible signals that are well approximated by one of these two models. In this context, we prove the estimation efficiency of a variant of Basis Pursuit Denoise, called Consistent Basis Pursuit (CoBP), enforcing consistency between the observations and the re-observed estimate, while promoting its low-complexity nature. We show that the reconstruction error of CoBP decays like $M^{-1/4}$ when all parameters but $M$ are fixed. Our proof is connected to recent bounds on the proximity of vectors or matrices when (i) those belong to a set of small intrinsic "dimension", as measured by the Gaussian mean width, and (ii) they share the same quantized (dithered) random projections. By solving CoBP with a proximal algorithm, we provide some extensive numerical observations that confirm the theoretical bound as $M$ is increased, displaying even faster error decay than predicted. The same phenomenon is observed in the special, yet important case of 1-bit CS.Comment: Keywords: Quantized compressed sensing, quantization, consistency, error decay, low-rank, sparsity. 10 pages, 3 figures. Note abbout this version: title change, typo corrections, clarification of the context, adding a comparison with BPD

Reversible watermarking scheme with image-independent embedding capacity

Permanent distortion is one of the main drawbacks of all the irreversible watermarking schemes. Attempts to recover the original signal after the signal passing the authentication process are being made starting just a few years ago. Some common problems, such as salt-and-pepper artefacts owing to intensity wraparound and low embedding capacity, can now be resolved. However, some significant problems remain unsolved. First, the embedding capacity is signal-dependent, i.e., capacity varies significantly depending on the nature of the host signal. The direct impact of this is compromised security for signals with low capacity. Some signals may be even non-embeddable. Secondly, while seriously tackled in irreversible watermarking schemes, the well-known problem of block-wise dependence, which opens a security gap for the vector quantisation attack and transplantation attack, are not addressed by researchers of the reversible schemes. This work proposes a reversible watermarking scheme with near-constant signal-independent embedding capacity and immunity to the vector quantisation attack and transplantation attack

Emissions from pre-Hispanic metallurgy in the South American atmosphere

Peer reviewedPublisher PD

Invariant Spectral Hashing of Image Saliency Graph

Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image. The gist of our approach relies on the geometric characterization of salient point distribution in the image. This is achieved by the definition of a saliency graph connecting these points jointly with an image intensity function on the graph nodes. An invariant hash is then obtained by considering the spectrum of this function in the eigenvector basis of the graph Laplacian, that is, its graph Fourier transform. Interestingly, this spectrum is invariant under any relabeling of the graph nodes. The graph reveals geometric information of the image, making the hash robust to image transformation, yet distinct for different visual content. The efficiency of the proposed method is assessed on a set of MRI 2-D slices and on a database of faces

Coring and sub-sampling of peatlands for palaeoenvironmental research

Every palaeoenvironmental, palaeoecological and palaeogeochemical study of a peatland begins with coring or section sampling and sub-sampling. This first step in a peat-based palaeoenvironmental study is the most crucial, as a high-quality investigation can be achieved only from a foundation of high-quality stratigraphic sampling and sub-sampling. Various techniques for coring, sampling and sub-sampling are described, aiming to: (a) provide the reader with an overview of existing approaches and techniques; (b) offer guidance on good practice for achieving high-quality results efficiently; and (c) standardise the methodology in order to achieve comparable sequences and samples for future multiproxy, multi-site and multi-core projects

Mineral Chemistry Of The Llaima Pumice, Southern Chile : Evidence For Magma Mixing

This paper details the mineralogy and the chemistry of the Llaima pumice deposit from in southern Chile. This andesitic to dacitic pumice was erupted from Llaima Volcano. This eruption took place in the early Holocene through at least two pulses that are well recorded in deposits around the Icalma-Galletué area. In 2001, the Llaima pumice was sampled from six outcrops. The mineralogy has been studied under polarizing microscope and electron microprobe (EPMA).The Llaima pumice contains phenocrystals of orthopyroxene, clinopyroxene, olivine and titano–magnetite. The olivine is characterized by two chemically distinguishable populations (i.e. Fo32 to Fo35 and Fo76 to Fo82). The respective chemical compositions of these two distinct olivines emphazise that the eruption was triggered by magma mixing