Estimating Sparse Signals Using Integrated Wideband Dictionaries

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance

Generalized Sparse Covariance-based Estimation

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem

Sparse Semi-Parametric Chirp Estimator

In this work, we present a method for estimating the parameters detailing an unknown number of linear chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted Lasso approach, and then use an iterative relaxation-based refining step to allow for high resolution estimates. The resulting estimates are found to be statistically efficient, achieving the Cramér-Rao lower bound. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches

Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this work, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cram´er-Rao lower bound

High resolution sparse estimation of exponentially decaying two-dimensional signals

In this work, we consider the problem of high-resolution estimation of the parameters detailing a two-dimensional (2-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Interpreting the estimation problem as a block (or group) sparse representation problem allows the decoupling of the 2-D data structure into a sum of outer-products of 1-D damped sinusoidal signals with unknown damping and frequency. The resulting non-zero blocks will represent each of the 1-D damped sinusoids, which may then be used as non-parametric estimates of the corresponding 1-D signals; this implies that the sought 2-D modes may be estimated using a sequence of 1-D optimization problems. The resulting sparse representation problem is solved using an iterative ADMM-based algorithm, after which the damping and frequency parameter can be estimated by a sequence of simple 1-D optimization problems

Computationally Efficient Estimation of Multi-Dimensional Spectral Lines

In this work, we propose a computationally efficient algorithm for estimating multi-dimensional spectral lines. The method treats the data tensor's dimensions separately, yielding the corresponding frequency estimates for each dimension. Then, in a second step, the estimates are ordered over dimensions, thus forming the resulting multidimensional parameter estimates. For high dimensional data, the proposed method offers statistically efficient estimates for moderate to high signal to noise ratios, at a computational cost substantially lower than typical non-parametric Fourier-transform based periodogram solutions, as well as to state-of-the-art parametric estimators

Regulation of smooth muscle dystrophin and synaptopodin 2 expression by actin polymerization and vascular injury

Producción CientíficaObjective: Actin dynamics in vascular smooth muscle is known to regulate contractile differentiation and may play a role in the pathogenesis of vascular disease. However, the list of genes regulated by actin polymerization in smooth muscle remains incomprehensive. Thus, the objective of this study was to identify actin-regulated genes in smooth muscle and to demonstrate the role of these genes in the regulation of vascular smooth muscle phenotype. Approach and Results: Mouse aortic smooth muscle cells were treated with an actin-stabilizing agent, jasplakinolide, and analyzed by microarrays. Several transcripts were upregulated including both known and previously unknown actin-regulated genes. Dystrophin and synaptopodin 2 were selected for further analysis in models of phenotypic modulation and vascular disease. These genes were highly expressed in differentiated versus synthetic smooth muscle and their expression was promoted by the transcription factors myocardin and myocardin-related transcription factor A. Furthermore, the expression of both synaptopodin 2 and dystrophin was significantly reduced in balloon-injured human arteries. Finally, using a dystrophin mutant mdx mouse and synaptopodin 2 knockdown, we demonstrate that these genes are involved in the regulation of smooth muscle differentiation and function. Conclusions: This study demonstrates novel genes that are promoted by actin polymerization, that regulate smooth muscle function, and that are deregulated in models of vascular disease. Thus, targeting actin polymerization or the genes controlled in this manner can lead to novel therapeutic options against vascular pathologies that involve phenotypic modulation of smooth muscle cells.Instituto de Salud Carlos III - Fondo Europeo de Desarrollo Regional (grant RD12/0042/0006)Ministerio de Economía, Industria y Competitividad (grants BFU2010-15898 and BFU2013-45867-R

Parameter Estimation - in sparsity we trust

This thesis is based on nine papers, all concerned with parameter estimation. The thesis aims at solving problems related to real-world applications such as spectroscopy, DNA sequencing, and audio processing, using sparse modeling heuristics. For the problems considered in this thesis, one is not only concerned with finding the parameters in the signal model, but also to determine the number of signal components present in the measurements. In recent years, developments in sparse modeling have allowed for methods that jointly estimate the parameters in the model and the model order. Based on these achievements, the approach often taken in this thesis is as follows. First, a parametric model of the considered signal is derived, containing different parameters that capture the important characteristics of the signal. When the signal model has been determined, an optimization problem is formed aimed at finding the parameters in the model as well as the model order. An important aspect when formulating the optimization problem is to include the characteristics and properties inherent in the signal model. For instance, if we know that the true set of parameters are smooth, this should also be a requirement reflected in the optimization problem. In the ideal case, the optimization problem is convex, in which case powerful solvers exist that may be used for finding the solution. In many cases, however, the original optimization problem is rather complex and definitely not convex. In this case, a common approach is to use a convex relaxation that approximates the original problem. In papers A, B, C, E, F, and H, this approach is utilized, however in different variations and for different applications. Paper A deals with estimation of periodic signals in symbolic sequences used in DNA sequences, paper B looks at the estimation of multi-dimensional sinusoids for NMR data, paper C considers the estimation of an unknown number of chirps for audio signals, papers E and F study pitch estimation, where the first paper considers online estimation and where the second paper proposes an off-grid method. Paper D proposes a generalization of a popular estimation method, whereas paper G introduces a new approach to frequency estimation. Paper I investigates how to sample a partially know signal to minimize the number of samples needed given a lower bound on the desired estimation performance. In all papers, the proposed methods are examined using simulated and/or measured data and compared to competing state-of-the-art methods

Resultatkontroll Skogbruk/Miljø - Noen av de pågående forandringene i norske skoger

Resultatkontrollen for 2002 viser at arealet som forynges naturlig og ved planting holder seg relativt stabilt sammenliknet med årene før. For 2002 er arealet avvirket ved snauhogst 64%. Dette er på samme nivå som de foregående årene