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

Ecosystem services from woody vegetation in East African rangelands

Drylands cover nearly half of the Earth's land surface and are dominated by croplands and rangelands. Dryland ecosystems worldwide are affected by land degradation. Increased population pressure, climate change and unsustainable land use threaten essential ecosystem services and adversely impact people’s livelihoods and well-being. Dryland inhabitants in developing countries are highly dependent on ecosystem services from woody plants, and tree-based restoration measures are thus of utmost importance. However, effective restoration requires a better understanding of the complexity and variability of these ecosystems and the needs of the people living there, a perspective that is often lacking. Restoration interventions have mostly focused on agricultural land and farmers and less on rangelands and (agro)pastoralists. Rangelands are characterized by a naturally low tree cover, and the importance of trees in these areas has thus often been overlooked. This study aims to contribute more knowledge on the importance of woody plants to rangeland inhabitants, focusing on the contribution of different species in providing important ecosystem services, as well as how people manage woody vegetation and how this management, in turn, affects woody vegetation. Two different sites with different dominant livelihood strategies were selected for this study; Chepareria in West Pokot County, Kenya, dominated by agro-pastoralists, and Rupa in Moroto District, Uganda, dominated by pastoralists. Findings from this study show that people in these two sites possessed significant knowledge of woody plants and their benefits. People perceived several ecosystem services from woody plants, most of which were associated with native species. The most valued ecosystem services were food, firewood, fodder and improved local climate. Although most ecosystem services identified in both sites were similar, the associated species often differed. In Chepareria, the land was dominated by privately managed enclosures, while in Rupa, it was mainly open common access communal land. In both sites, people actively managed woody plants to preserve and protect them, although with more emphasis on assisted natural regeneration in Rupa. Despite this, local people perceived that the native tree cover had decreased in both sites, negatively affecting the availability of critical ecosystem services. In Chepareria, the decline was attributed to land use change and increased grazing pressure, while in Rupa, it was attributed to a shift in livelihood strategies from livestock keeping to charcoal production. Due to insufficient data, results on links between land-use, access to land, preferred species and ecosystem services, and woody species presence and abundance in the landscape were inconclusive. The many differences between the two studied sites clearly highlight that restoration requires tailored strategies with a bottom-up approach that considers the local people's knowledge, experience, needs, and aspirations

Targeting smooth muscle microRNAs for therapeutic benefit in vascular disease.

In view of the bioinformatic projection that a third of all protein coding genes and essentially all biological pathways are under control of microRNAs (miRNAs), it is not surprising that this class of small RNAs plays roles in vascular disease progression. MiRNAs have been shown to be involved in cholesterol turnover, thrombosis, glucose homeostasis and vascular function. Some miRNAs appear to be specific for certain cells, and the role that such cell-specific miRNAs play in vascular disease is only beginning to be appreciated. A notable example is the miR-143/145 cluster which is enriched in mature and highly differentiated smooth muscle cells (SMCs). Here we outline and discuss the recent literature on SMC-expressed miRNAs in major vascular diseases, including atherosclerosis, neointima formation, aortic aneurysm formation, and pulmonary arterial hypertension. Forced expression of miR-145 emerges as a promising strategy for reduction and stabilization of atherosclerotic plaques as well as for reducing neointimal hyperplasia. It is concluded that if obstacles in the form of delivery and untoward effects of antimirs and mimics can be overcome, the outlook for targeting of SMC-specific miRNAs for therapeutic benefit in vascular disease is bright

Predicting living and dead wood volumes in a mature managed Swedish forest with airborne laser scanning

Detecting dead wood with airborne laser scanning (ALS) would have many benefits. It would make it easier to find areas with high mortality rates, help make better decisions on which areas to preserve, and increase the accuracy of volume- and value-estimations. In this study, we tried to assess the accuracy of volume predictions of living wood, standing dead wood, and lying dead wood, as well as pinpoint the most descriptive ALS variables. The focus was on homogenous mature managed forests on good site indexes. A plane equipped with LiDAR was flown over a 7500 ha forest area in Dalarna, Sweden. Laser variables were made to describe the point cloud from the LiDAR. 102 field plots were generated in mature managed stands and all trees (including bigger lying wood) were measured for diameter and height. The volume of living wood, standing dead wood, and lying wood was found for each field plot. The field plots were then run in a simulation with 500 iterations. For each iteration, 81 random field plots were used as calibration plots and the remaining 21 field plots were used as prediction plots. For each iteration, multiple variable linear regression and a “k nearest neighbour”-algorithm (kNN) with one, two, and three neighbours were calibrated on the calibration plots and then used to predict the volumes on the prediction plots. The mean difference between predicted and real volume were found for each method (regression and kNN with one, two, and three neighbours) and tree class (living, standing dead, and lying dead). When predicting living volume, regression got a good fit with an adjusted R2 value of 0,73. Standing dead volume got a medium fit with an adjusted R2 value of 0,46. Lying dead volume got a very low fit with an adjusted R2 value of just 0,12. Overall, the kNN algorithm did better with one neighbour, compared to two or three. Regression achieved very low systematic errors across the board, while the kNN algorithm got higher systematic errors but slightly lower standard errors of the mean compared to regression. The most descriptive laser variables for living volume were related to branches in the upper and middle parts of the stems. The most descriptive laser variables for describing standing dead wood volume were related to tree heights and branches in the middle and lower parts of the stem. Lying dead wood had too low a correlation with the laser variables to find a clear pattern. When predicting wood volumes with kNN, a higher k did not improve the results.Å finne døde trær i skog med flybåren laserskanning (ALS) hadde hatt mange fordeler. Det hadde gjort det lettere å oppdage områder med høy mortalitet, hjulpet til med å ta bedre beslutninger om vern, og det kunne forbedret volum- og verdi-estimeringer i skog. I denne studien har vi sett på nøyaktigheten av volumprediksjoner av levende volum, stående dødt volum, og liggende dødt volum, i tillegg til å se på hvilke laservariabler som var mest beskrivende. Studien er gjort i eldre homogene skjøtte bestand på gode boniteter. Et fly utstyrt med en LiDAR-sensor ble fløyet over et 7500 ha stort skogsområde i Dalarna i Sverige. Det ble laget laservariabler som beskrev punktskyen fra LiDAR-sensoren. Så ble det generert 102 prøveflater i samme område. Alle trær på prøveflatene ble målt for høyde og diameter i brysthøyde (inkludert større liggende stammer/stokker). Levende volum, stående dødt volum, og liggende dødt volum ble beregnet for hver prøveflate. Prøveflatene ble kjørt i en simulering med 500 iterasjoner. For hver iterasjon ble 81 tilfeldige prøveflater brukt som kalibreringsflater, mens de resterende 21 prøveflatene ble brukt som predikeringsflater. For hver iterasjon ble kalibreringsflatene brukt til å finne den beste modellen for multippel lineær regresjon, i tillegg til å brukes som kalibreringsflater for en «k nearest neighbour»-algoritme (kNN) med en, to, og tre «naboer». Regresjonsmodellen og kNN-algoritmene ble så brukt til å predikere volumet på prediksjonsflatene. Gjennomsnittlig differanse mellom predikert volum og virkelig volum ble funnet for hver metode (regresjon og kNN med en, to, og tre «naboer») og hver tre-klasse (levende, stående dødt, og liggende dødt). Regresjon fungerte godt til å predikere levende volum, med en gjennomsnittlig justert R2 - verdi på 0,73. Stående dødt volum fikk en gjennomsnittlig justert R2 -verdi på 0,46 mens liggende dødt volum fikk veldig lave 0,12. kNN-algoritmen gjorde det generelt bedre med en «nabo», i forhold til to og tre. Regresjon ga veldig lave systematiske feil, klart lavere enn kNN. Standardfeilen til gjennomsnittet var derimot alltid noe lavere med kNN i forhold til regresjon. De mest beskrivende laservariablene for levende volum var relatert til mengden greiner fra toppen til midten av stammene. De mest beskrivende laservariablene for stående dødt volum var relatert til tre-høyder og mengden greiner fra midten av stammene og ned. Liggende død ved hadde for lav korrelasjon til å finne en klar sammenheng med laservariablene. Predikeringer med kNN ble ikke bedre med flere «naboer».M-S

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

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