Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit

We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of weighted sparsity. The proposed recovery strategy is based on a formal derivation of the greedy index selection rule. Numerical experiments show that the proposed weighted orthogonal matching pursuit algorithm is able to reach accuracy levels similar to those of weighted $\ell^1$ minimization programs while considerably improving the computational efficiency for small values of the sparsity level

Adaptive Measurement Network for CS Image Reconstruction

Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image recovery with high quality not only de- pends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measuremen- t rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one.Comment: 11pages,8figure

Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

Untypical ageing off-flavour and masking effects due to long-term nitrogen fertilization

The off-flavour UTA (untypical ageing) of wines produced from the vintages 1996-1999 within the scope of a long-term N fertilization experiment was compared to the o-aminoacetophenone (AAP) concentrations found in these wines. The wines were made of plants treated with 0, 60 and 150 kg N ha-1·N fertilization led to higher UTA intensities and AAP concentrations in aged wines; due to stronger fruity aromas with increasing N fertilization, young wines were able to mask AAP. Controls had a stronger masking effect in older wines, caused by antioxidants (phenols) and possibly higher alcohols. Moreover, at the same AAP level, wines from the vintages 1996 and 1998 exhibited lower UTA intensity than wines from 1997 and 1999. This is influenced by N supply, yield and time of harvest which can not be separated from each other.

Ambivalence of the influence of nitrogen supply on o-aminoacetophenone in 'Riesling' wine

AAP (o-aminoacetophenone) is the aroma substance responsible for the untypical ageing off-flavour (UTA). The impact of nitrogen supply on the formation of AAP was investigated between 1994 and 1999. The experiment was carried out in the Rheingau (Germany) with six fertigation treatments of annual quantities of N (0, 30, 60, 90, 150 kg·N·ha-1). Results indicated that the long-term varied N fertilization affected AAP concentration in wine as much as the year. Whereas a better N supply of the grapes due to effects of the year coincided with lower AAP values, the fertilization effect was reversal: higher N fertilization increased the concentrations of AAP. AAP did not correlate with its precursor IAA and only slightly with antioxidative capacity. Neither varying yield nor soluble solids could explain the high variance of AAP. An indicator for potential AAP formation could not be found, neither in must nor in wine.

Erratum

Untypical ageing off-ßavour and masking effects due to long-term nitrogen fertilizationVitis 46 (1), 33-38 (2007

On the linear independence of spikes and sines

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.Comment: 16 pages, 4 figures. Revision with new proof of major theorem

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page