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We propose a new technique to obtain super-resolution images with radio interferometry using sparse modeling. In standard radio interferometry, sampling of (u, v) is quite often incomplete and thus obtaining an image from observed visibilities becomes an underdetermined problem, and a technique of so-called "zero-padding" is often used to fill up unsampled grids in the (u, v) plane, resulting in image degradation by finite beam size as well as numerous side-lobes. In this paper we show that directly solving such an underdetermined problem based on sparse modeling (in this paper, Least Absolute Shrinkage and Selection Operator, known as LASSO) avoids the above problems introduced by zero-padding, leading to super-resolution images in which structure finer than the standard beam size (diffraction limit) can be reproduced. We present results of onedimensional and two-dimensional simulations of interferometric imaging, and discuss its implications for super-resolution imaging, particularly focusing on imaging of black hole shadows with millimeter VLBI (Very Long Baseline Interferometry). [ABSTRACT FROM AUTHOR]

The reconstruction of Faraday depth structure from incomplete spectral polarization radio measurements using the RM synthesis technique is an underconstrained problem requiring additional regularization. In this paper, we present cs-romer : a novel object-oriented compressed sensing framework to reconstruct Faraday depth signals from spectropolarization radio data. Unlike previous compressed sensing applications, this framework is designed to work directly with data that are irregularly sampled in wavelength-squared space and to incorporate multiple forms of compressed sensing regularization. We demonstrate the framework using simulated data for the VLA telescope under a variety of observing conditions, and we introduce a methodology for identifying the optimal basis function for reconstruction of these data, using an approach that can also be applied to data sets from other telescopes and over different frequency ranges. In this work, we show that the delta basis function provides optimal reconstruction for VLA L -band data and we use this basis with observations of the low-mass galaxy cluster Abell 1314 in order to reconstruct the Faraday depth of its constituent cluster galaxies. We use the cs-romer framework to de-rotate the Galactic Faraday depth contribution directly from the wavelength-squared data and to handle the spectral behaviour of different radio sources in a direction-dependent manner. The results of this analysis show that individual galaxies within Abell 1314 deviate from the behaviour expected for a Faraday-thin screen such as the intra-cluster medium and instead suggest that the Faraday rotation exhibited by these galaxies is dominated by their local environments. [ABSTRACT FROM AUTHOR]

Compressed sensing is a very powerful and popular tool for sparse recovery of high dimensional signals. Random sensing matrices are often employed in compressed sensing. In this paper we introduce a new method named aggressive betting using sure independence screening for sparse noiseless signal recovery. The proposal exploits the randomness structure of random sensing matrices to greatly boost computation speed. When using sub-Gaussian sensing matrices, which include the Gaussian and Bernoulli sensing matrices as special cases, our proposal has the exact recovery property with overwhelming probability. We also consider sparse recovery with noise and explicitly reveal the impact of noise-to-signal ratio on the probability of sure screening. [ABSTRACT FROM PUBLISHER]

Airborne electromagnetic (AEM) exploration produces large amounts of data due to its high sampling rate, so that the 3-D inversions take extremely big computation and time consumption. We present a fast 3-D inversion framework for large-scale AEM explorations using a pre-conditioned stochastic gradient descent combined with Gauss–Newton (PSG-GN) method. We adopt a compressed sensing (CS) in the 3-D forward modelling, in which a random undersampling is used to reduce the calculation, while the responses for all survey stations are obtained via a reconstruction technique. For our 3-D AEM inversions, a method of combining the stochastic gradient descent with Gauss–Newton (SG-GN) that requires only a small data set in each iteration instead of the conventional full-batch data (complete original data) inversion have been investigated. To further speed up the 3-D inversion, we develop a pre-conditioner considering the random sampling rate and gradient noise to achieve a fast convergence. We use two synthetic models to test the accuracy, convergence and efficiency of our algorithm. The results show that the conventional inversion with full-batch data and the PSG-GN method can both converge quickly, but our method can enhance the inversion efficiency up to 78 per cent. Finally, we invert a field data set acquired from a massive sulfide deposit in Ireland and obtain the results that agree well with the known geologies. [ABSTRACT FROM AUTHOR]

Reconstruction of the distribution of ground motion due to an earthquake is one of the key technologies for the prediction of seismic damage to infrastructure. Particularly, the immediate reconstruction of the spatially continuous wavefield is valuable for decision-making of disaster response decisions in the initial phase. For a fast and accurate reconstruction, utilization of prior information is essential. In fluid mechanics, full-state recovery, which recovers the full state from sparse observation using a data-driven model reduced-order model, is actively used. In this study, the framework developed in the field of fluid mechanics is applied to seismic wavefield reconstruction. A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated from the data set of the wavefield using the singular value decomposition. The spatially continuous seismic wavefield is reconstructed from the sparse and discrete observation and the data-driven ROM. The observation sites used for reconstruction are effectively selected by the sensor optimization method for linear inverse problems based on a greedy algorithm. The proposed framework was applied to simulation data of theoretical waveform with the subsurface structure of the horizontally stratified three layers. The validity of the proposed method was confirmed by the reconstruction based on the noise-free observation. Since the ROM of the wavefield is used as prior information, the reconstruction error is reduced to an approximately lower error bound of the present framework, even though the number of sensors used for reconstruction is limited and randomly selected. In addition, the reconstruction error obtained by the proposed framework is much smaller than that obtained by the Gaussian process regression. For the numerical experiment with noise-contaminated observation, the reconstructed wavefield is degraded due to the observation noise, but the reconstruction error obtained by the present framework with all available observation sites is close to a lower error bound, even though the reconstructed wavefield using the Gaussian process regression is fully collapsed. Although the reconstruction error is larger than that obtained using all observation sites, the number of observation sites used for reconstruction can be reduced while minimizing the deterioration and scatter of the reconstructed data by combining it with the sensor optimization method. Hence, a better and more stable reconstruction of the wavefield than randomly selected observation sites can be realized, even if the reconstruction is carried out with a smaller number of observations with observation noise, by combining it with the sensor optimization method. [ABSTRACT FROM AUTHOR]

We present the Early Data Release of the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. The SAMI Galaxy Survey is an ongoing integral field spectroscopic survey of 3400 low-redshift (z < 0.12) galaxies, covering galaxies in the field and in groups within the Galaxy And Mass Assembly (GAMA) survey regions, and a sample of galaxies in clusters. In the Early Data Release, we publicly release the fully calibrated data cubes for a representative selection of 107 galaxies drawn from the GAMA regions, along with information about these galaxies from the GAMA catalogues. All data cubes for the Early Data Release galaxies can be downloaded individually or as a set from the SAMI Galaxy Survey website. In this paper we also assess the quality of the pipeline used to reduce the SAMI data, giving metrics that quantify its performance at all stages in processing the raw data into calibrated data cubes. The pipeline gives excellent results throughout, with typical sky subtraction residuals in the continuum of 0.9-1.2 per cent, a relative flux calibration uncertainty of 4.1 per cent (systematic) plus 4.3 per cent (statistical), and atmospheric dispersion removed with an accuracy of 0.09 arcsec, less than a fifth of a spaxel. [ABSTRACT FROM AUTHOR]

Motivation In silico saturation mutagenesis (ISM) is a popular approach in computational genomics for calculating feature attributions on biological sequences that proceeds by systematically perturbing each position in a sequence and recording the difference in model output. However, this method can be slow because systematically perturbing each position requires performing a number of forward passes proportional to the length of the sequence being examined. Results In this work, we propose a modification of ISM that leverages the principles of compressed sensing to require only a constant number of forward passes, regardless of sequence length, when applied to models that contain operations with a limited receptive field, such as convolutions. Our method, named Yuzu, can reduce the time that ISM spends in convolution operations by several orders of magnitude and, consequently, Yuzu can speed up ISM on several commonly used architectures in genomics by over an order of magnitude. Notably, we found that Yuzu provides speedups that increase with the complexity of the convolution operation and the length of the sequence being analyzed, suggesting that Yuzu provides large benefits in realistic settings. Availability and implementation We have made this tool available at https://github.com/kundajelab/yuzu. [ABSTRACT FROM AUTHOR]

Motivation The classification of high-throughput protein data based on mass spectrometry (MS) is of great practical significance in medical diagnosis. Generally, MS data are characterized by high dimension, which inevitably leads to prohibitive cost of computation. To solve this problem, one-bit compressed sensing (CS), which is an extreme case of quantized CS, has been employed on MS data to select important features with low dimension. Though enjoying remarkably reduction of computation complexity, the current one-bit CS method does not consider the unavoidable noise contained in MS dataset, and does not exploit the inherent structure of the underlying MS data. Results We propose two feature selection (FS) methods based on one-bit CS to deal with the noise and the underlying block-sparsity features, respectively. In the first method, the FS problem is modeled as a perturbed one-bit CS problem, where the perturbation represents the noise in MS data. By iterating between perturbation refinement and FS, this method selects the significant features from noisy data. The second method formulates the problem as a perturbed one-bit block CS problem and selects the features block by block. Such block extraction is due to the fact that the significant features in the first method usually cluster in groups. Experiments show that, the two proposed methods have better classification performance for real MS data when compared with the existing method, and the second one outperforms the first one. Availability and implementation The source code of our methods is available at: https://github.com/tianyan8023/OBCS. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

We propose a new wavelet-based compressive sensing method to image coseismic radiation sources with teleseismic array data. Compared to the sliding-window-based technique, our method avoids choosing the window length by taking advantages of the adaptive resolution feature of the wavelet transform. Thus artefacts caused by inappropriate window length and waveform truncation can be removed. As waveforms usually become less aligned at late arrivals due to the increasing distance of actual radiation sources with respect to the hypocentre, we introduce a time-correction scheme to realign waveforms with the reference point obtained from beamforming at every time step. Synthetic tests indicate that the new method can better resolve the seismic radiation sources with more reliable locations and source times. To demonstrate its feasibility, we apply the method to the M w9.0 Tohoku earthquake. We find similar spatial rupture and seismic radiation patterns, such as repeating rupture in the region close to the hypocentre and along-dip frequency-dependent radiation, as indicated by previous models from finite-fault inversion and back projection. In addition, our results show structure-controlled rupture characteristics, with the seismic radiation in the first 80 s mainly confined in the off-Miyagi high-wave-speed region. The rupture speed shows clear along-dip variations, with updip rupture slower than that of downdip, which corresponds well with the depth-varying characteristics along the megathrust. [ABSTRACT FROM AUTHOR]

Recent advances in various fields such as telecommunications, biomedicine and economics, among others, have created enormous amount of data that are often characterized by their huge size and high dimensionality. It has become evident, from research in the past couple of decades, that sparsity is a flexible and powerful notion when dealing with these data, both from empirical and theoretical viewpoints. In this survey, we review some of the most popular techniques to exploit sparsity, for analyzing high-dimensional vectors, matrices and higher-order tensors. [ABSTRACT FROM AUTHOR]

Motivation Adverse drug reactions (ADRs) are one of the main causes of death and a major financial burden on the world’s economy. Due to the limitations of the animal model, computational prediction of serious and rare ADRs is invaluable. However, current state-of-the-art computational methods do not yield significantly better predictions of rare ADRs than random guessing. Results We present a novel method, based on the theory of ‘compressed sensing’ (CS), which can accurately predict serious side-effects of candidate and market drugs. Not only is our method able to infer new chemical-ADR associations using existing noisy, biased and incomplete databases, but our data also demonstrate that the accuracy of CS in predicting a serious ADR for a candidate drug increases with increasing knowledge of other ADRs associated with the drug. In practice, this means that as the candidate drug moves up the different stages of clinical trials, the prediction accuracy of our method will increase accordingly. Availability and implementation The program is available at https://github.com/poleksic/side-effects. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

Dense arrays allow sampling of seismic wavefield without significant aliasing, and surface wave tomography has benefitted from exploiting wavefield coherence among neighbouring stations. However, explicit or implicit assumptions about wavefield, irregular station spacing and noise still limit the applicability and resolution of current surface wave methods. Here, we propose to apply the theory of compressive sensing (CS) to seek a sparse representation of the surface wavefield using a plane-wave basis. Then we reconstruct the continuous surface wavefield on a dense regular grid before applying any tomographic methods. Synthetic tests demonstrate that wavefield CS improves robustness and resolution of Helmholtz tomography and wavefield gradiometry, especially when traditional approaches have difficulties due to sub-Nyquist sampling or complexities in wavefield. [ABSTRACT FROM AUTHOR]

We propose a newapproach to the linear Radon transform(LRT) based on compressive sensing (CS) theory. This method can be used to extract signals of interest embedded in teleseismic measurements recorded by regional seismic arrays. We pose the problem of enhancing the resolution of the LRT as an inverse problem formulated in the frequency domain and solved according to a CS framework. We show how irregularity in the measurements along with sparsity constraints can be used to reach very compact and meaningful representations in the Radon domain, offering a benefit for both signal isolation and spatial interpolation during data reconstruction. We demonstrate the effectiveness of our approach and its benefits on both synthetic and USArray seismograms. This CS-based version of the LRT presents a valuable tool relevant for both global and exploration seismic processing, and which can be used as a basis for signal enhancement techniques exploiting irregularly sampled data. [ABSTRACT FROM AUTHOR]

Background: One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained systems of linear equations. These methods can be applied to the problem of determining the best model relating genotype to phenotype, and generally deliver better performance than simply regressing the phenotype against each genetic variant, one at a time. We introduce a Compressed Sensing method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. Our method uses L1-penalized regression applied to nonlinear functions of the sensing matrix. Results: The computational and data resource requirements for our method are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using simulated human genomes and the small amount of currently available real data. A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application. Conclusion: Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h2~0.5), can be extracted from data sets comprised of n?~100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ~10 k loci, roughly a million individuals would be sufficient for application of the method. [ABSTRACT FROM AUTHOR]

Background: One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained systems of linear equations. These methods can be applied to the problem of determining the best model relating genotype to phenotype, and generally deliver better performance than simply regressing the phenotype against each genetic variant, one at a time. We introduce a Compressed Sensing method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. Our method uses L1-penalized regression applied to nonlinear functions of the sensing matrix. Results: The computational and data resource requirements for our method are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using simulated human genomes and the small amount of currently available real data. A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application. Conclusion: Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h2 ∼ 0.5), can be extracted from data sets comprised of n* ∼ 100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ∼ 10 k loci, roughly a million individuals would be sufficient for application of the method. [ABSTRACT FROM AUTHOR]

Background: The aim of a genome-wide association study (GWAS) is to isolate DNA markers for variants affecting phenotypes of interest. This is constrained by the fact that the number of markers often far exceeds the number of samples. Compressed sensing (CS) is a body of theory regarding signal recovery when the number of predictor variables (i.e., genotyped markers) exceeds the sample size. Its applicability to GWAS has not been investigated. Results: Using CS theory, we show that all markers with nonzero coefficients can be identified (selected) using an efficient algorithm, provided that they are sufficiently few in number (sparse) relative to sample size. For heritability equal to one (h2 = 1), there is a sharp phase transition from poor performance to complete selection as the sample size is increased. For heritability below one, complete selection still occurs, but the transition is smoothed. We find for h2 ∼ 0.5 that a sample size of approximately thirty times the number of markers with nonzero coefficients is sufficient for full selection. This boundary is only weakly dependent on the number of genotyped markers. Conclusion: Practical measures of signal recovery are robust to linkage disequilibrium between a true causal variant and markers residing in the same genomic region. Given a limited sample size, it is possible to discover a phase transition by increasing the penalization; in this case a subset of the support may be recovered. Applying this approach to the GWAS analysis of height, we show that 70-100% of the selected markers are strongly correlated with height-associated markers identified by the GIANT Consortium. [ABSTRACT FROM AUTHOR]

Motivation: Estimation of bacterial community composition from a high-throughput sequenced sample is an important task in metagenomics applications. As the sample sequence data typically harbors reads of variable lengths and different levels of biological and technical noise, accurate statistical analysis of such data is challenging. Currently popular estimation methods are typically time-consuming in a desktop computing environment.Results: Using sparsity enforcing methods from the general sparse signal processing field (such as compressed sensing), we derive a solution to the community composition estimation problem by a simultaneous assignment of all sample reads to a pre-processed reference database. A general statistical model based on kernel density estimation techniques is introduced for the assignment task, and the model solution is obtained using convex optimization tools. Further, we design a greedy algorithm solution for a fast solution. Our approach offers a reasonably fast community composition estimation method, which is shown to be more robust to input data variation than a recently introduced related method.Availability and implementation: A platform-independent Matlab implementation of the method is freely available at http://www.ee.kth.se/ctsoftware; source code that does not require access to Matlab is currently being tested and will be made available later through the above Web site.Contact: sach@kth.se [ABSTRACT FROM AUTHOR]

Motivation: Many metagenomic studies compare hundreds to thousands of environmental and health-related samples by extracting and sequencing their 16S rRNA amplicons and measuring their similarity using beta-diversity metrics. However, one of the first steps—to classify the operational taxonomic units within the sample—can be a computationally time-consuming task because most methods rely on computing the taxonomic assignment of each individual read out of tens to hundreds of thousands of reads.Results: We introduce Quikr: a QUadratic, K-mer–based, Iterative, Reconstruction method, which computes a vector of taxonomic assignments and their proportions in the sample using an optimization technique motivated from the mathematical theory of compressive sensing. On both simulated and actual biological data, we demonstrate that Quikr typically has less error and is typically orders of magnitude faster than the most commonly used taxonomic assignment technique (the Ribosomal Database Project’s Naïve Bayesian Classifier). Furthermore, the technique is shown to be unaffected by the presence of chimeras, thereby allowing for the circumvention of the time-intensive step of chimera filtering.Availability: The Quikr computational package (in MATLAB, Octave, Python and C) for the Linux and Mac platforms is available at http://sourceforge.net/projects/quikr/.Contact: koslicki.1@mbi.osu.eduSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

In this article, we demonstrate the application of a new compressed sensing three-dimensional reconstruction algorithm for electron tomography that increases the accuracy of morphological characterization of nanostructured materials such as nanocrystalline iron oxide particles. A powerful feature of the algorithm is an anisotropic total variation norm for the L1 minimization during algebraic reconstruction that effectively reduces the elongation artifacts caused by limited angle sampling during electron tomography. The algorithm provides faithful morphologies that have not been feasible with existing techniques. [ABSTRACT FROM PUBLISHER]