Performance evaluation of typical approximation algorithms for nonconvex l(p)-minimization in diffuse optical tomography

The sparse estimation methods that utilize the l(p)-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These l(p)-norm-based regularizations make the optimization function nonconvex, and algorithms that implement l(p)-norm minimization utilize approximations to the original l(p)-norm function. In this work, three such typical methods for implementing the l(p)-norm were considered, namely, iteratively reweighted l(1)-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of l(p)-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. (C) 2014 Optical Society of America

Optimum Parameter Selection in Sparse Reconstruction of Frequency-Domain Optical-Coherence Tomography Signals

For a multilayered specimen, the back-scattered signal in frequency-domain optical-coherence tomography (FDOCT) is expressible as a sum of cosines, each corresponding to a change of refractive index in the specimen. Each of the cosines represent a peak in the reconstructed tomogram. We consider a truncated cosine series representation of the signal, with the constraint that the coefficients in the basis expansion be sparse. An l(2) (sum of squared errors) data error is considered with an l(1) (summation of absolute values) constraint on the coefficients. The optimization problem is solved using Weiszfeld's iteratively reweighted least squares (IRLS) algorithm. On real FDOCT data, improved results are obtained over the standard reconstruction technique with lower levels of background measurement noise and artifacts due to a strong l(1) penalty. The previous sparse tomogram reconstruction techniques in the literature proposed collecting sparse samples, necessitating a change in the data capturing process conventionally used in FDOCT. The IRLS-based method proposed in this paper does not suffer from this drawback.

Robust Savitzky-Golay Filters

Local polynomial approximation of data is an approach towards signal denoising. Savitzky-Golay (SG) filters are finite-impulse-response kernels, which convolve with the data to result in polynomial approximation for a chosen set of filter parameters. In the case of noise following Gaussian statistics, minimization of mean-squared error (MSE) between noisy signal and its polynomial approximation is optimum in the maximum-likelihood (ML) sense but the MSE criterion is not optimal for non-Gaussian noise conditions. In this paper, we robustify the SG filter for applications involving noise following a heavy-tailed distribution. The optimal filtering criterion is achieved by l(1) norm minimization of error through iteratively reweighted least-squares (IRLS) technique. It is interesting to note that at any stage of the iteration, we solve a weighted SG filter by minimizing l(2) norm but the process converges to l(1) minimized output. The results show consistent improvement over the standard SG filter performance.

M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Is preeclampsia associated with restless legs syndrome?

OBJECTIVE Restless legs syndrome (RLS) is a common neurologic disorder. Secondary RLS includes pregnancy and iron deficiency. Prevalence of RLS in pregnancy ranges from 11% to 27%. We aimed to assess the frequency and characteristics of RLS in pregnancy in a Peruvian population and to evaluate the possible pregnancy or delivery complications due to RLS. METHODS We assessed 218 consecutive expectant mothers at the inpatient clinic of the Hospital San Bartolome in Lima, Peru. Assessment was performed by using the standard diagnostic criteria for RLS and by using a clinical and diagnostic interview. Questionnaires for RLS severity, idiopathic RLS (IRLS), and excessive daytime sleepiness (EDS) according to the Epworth sleepiness scale (ESS) were used. Blood examination was performed for hemoglobin and hematocrit. For comparison, RLS patients were matched for age and body mass index (BMI) with pregnant women without RLS. RESULTS Out of 218 patients, 40 (18.4%) fulfilled diagnostic criteria for RLS. In RLS patients, prophylactic iron supplementation therapy during pregnancy was less frequently taken (P=.02). Pregnant women with RLS had a higher ESS score than pregnant controls (10.6 +/- 3.1 vs 7.6. +/- 3.6; P<.001). Preeclampsia was more frequent in RLS (7/40 vs 1/39; P=.03). CONCLUSIONS In our study, RLS was frequent in pregnant Peruvian women, especially in those without prophylactic iron supplementation. RLS patients described more EDS. Preeclampsia was more common in RLS. Our study is the first study to indicate a possible association between RLS and preeclampsia.

Actigraphic assessment of periodic leg movements in patients with restless legs syndrome.

The diagnosis of restless legs syndrome (RLS) relies upon diagnostic criteria which are based on history only, and dopaminergic treatment is not normally the first choice of treatment for all patients. It would be worthwhile to identify patients non-responsive to dopaminergic treatment beforehand, because they may suffer from a restless legs-like syndrome and may require alternative treatment. We included retrospectively 24 adult patients fulfilling the four essential criteria for restless legs and 12 age-matched healthy controls. They were investigated by ambulatory actigraphy from both legs over three nights, and patients started treatment with dopamine agonists after this diagnostic work-up. We examined 12 responders to dopaminergic treatment and 12 non-responders and studied the association between response to dopaminergic treatment and the periodic limb movement index (PLMI) as assessed with actigraphy. Demographic characteristics, excessive daytime sleepiness and fatigue at baseline were similar in all three groups. Baseline RLS severity was similar between responders and non-responders [International Restless Legs Severity Scale (IRLS): 25 ± 9 and 24 ± 8]. Group comparisons of PLMI before treatment initiation showed significant differences between the three groups. Post-hoc pairwise comparisons revealed that healthy controls had significantly lower PLMI (4.9 ± 4.5) than responders (29.3 ± 22.7) and non-responders (13.3 ± 11.2). Similarly, the PLMI in responders was lower than in non-responders. PLMI day-to-day variability did not differ between responders and non-responders and there was no correlation between treatment effect, as assessed by the decrease of the IRLS and baseline PLMI. Our retrospective study indicates that actigraphy to assess periodic limb movements may contribute to a better diagnosis of dopamine-responsive restless legs syndrome.

Effects of short- and long-term variations in RLS severity on perceived health status - the COR-study.

In a cohort study among 2751 members (71.5% females) of the German and Swiss RLS patient organizations changes in restless legs syndrome (RLS) severity over time was assessed and the impact on quality of life, sleep quality and depressive symptoms was analysed. A standard set of scales (RLS severity scale IRLS, SF-36, Pittsburgh Sleep Quality Index and the Centre for Epidemiologic Studies Depression Scale) in mailed questionnaires was repeatedly used to assess RLS severity and health status over time and a 7-day diary once to assess short-term variations. A clinically relevant change of the RLS severity was defined by a change of at least 5 points on the IRLS scale. During 36 months follow-up minimal improvement of RLS severity between assessments was observed. Men consistently reported higher severity scores. RLS severity increased with age reaching a plateau in the age group 45-54 years. During 3 years 60.2% of the participants had no relevant (±5 points) change in RLS severity. RLS worsening was significantly related to an increase in depressive symptoms and a decrease in sleep quality and quality of life. The short-term variation showed distinctive circadian patterns with rhythm magnitudes strongly related to RLS severity. The majority of participants had a stable course of severe RLS over three years. An increase in RLS severity was accompanied by a small to moderate negative, a decrease by a small positive influence on quality of life, depressive symptoms and sleep quality.

DTI and VBM reveal white matter changes without associated gray matter changes in patients with idiopathic restless legs syndrome

BACKGROUND AND PURPOSE We evaluated cerebral white and gray matter changes in patients with iRLS in order to shed light on the pathophysiology of this disease. METHODS Twelve patients with iRLS were compared to 12 age- and sex-matched controls using whole-head diffusion tensor imaging (DTI) and voxel-based morphometry (VBM) techniques. Evaluation of the DTI scans included the voxelwise analysis of the fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD). RESULTS Diffusion tensor imaging revealed areas of altered FA in subcortical white matter bilaterally, mainly in temporal regions as well as in the right internal capsule, the pons, and the right cerebellum. These changes overlapped with changes in RD. Voxel-based morphometry did not reveal any gray matter alterations. CONCLUSIONS We showed altered diffusion properties in several white matter regions in patients with iRLS. White matter changes could mainly be attributed to changes in RD, a parameter thought to reflect altered myelination. Areas with altered white matter microstructure included areas in the internal capsule which include the corticospinal tract to the lower limbs, thereby supporting studies that suggest changes in sensorimotor pathways associated with RLS.

Carbon dioxide concentrations for the Last Millennium, Antarctica

The most direct method of investigating past variations of the atmospheric CO2 concentration before 1958, when continuous direct atmospheric CO2 measurements started, is the analysis of air extracted from suitable ice cores. Here we present a new detailed CO2 record from the Dronning Maud Land (DML) ice core, drilled in the framework of the European Project for Ice Coring in Antarctica (EPICA) and some new measurements on a previously drilled ice core from the South Pole. The DML CO2 record shows an increase from about 278 to 282 parts per million by volume (ppmv) between ad 1000 and ad 1200 and a fairly continuous decrease to a mean value of about 277 ppmv around ad 1700. While the new South Pole measurements agree well with DML at the minimum at ad 1700 they are on average about 2 ppmv lower during the period ad 1000-1500. Published measurements from the coastal high-accumulation site Law Dome are considered as very reliable because of the reproducibility of the measurements, high temporal resolution and an accurate time scale. Other Antarctic ice cores could not, or only partly, reproduce the pre-industrial measurements from Law Dome. A comparison of the trends of DML and Law Dome shows a general agreement. However we should be able to rule out co-variations caused by the same artefact. Two possible effects are discussed, first production of CO2 by chemical reactions and second diffusion of dissolved air through the ice matrix into the bubbles. While the first effect cannot be totally excluded, comparison of the Law Dome and DML record shows that dissolved air diffusing to bubbles cannot be responsible for the pre-industrial variation. Therefore, the new record is not a proof of the Law Dome results but the first very strong support from an ice core of the Antarctic plateau.

EPICA Dome C carbon dioxide concentrations from 650 to 391 kyr BP

A record of atmospheric carbon dioxide (CO2) concentrations measured on the EPICA (European Project for Ice Coring in Antarctica) Dome Concordia ice core extends the Vostok CO2 record back to 650,000 years before the present (yr B.P.). Before 430,000 yr B.P., partial pressure of atmospheric CO2 lies within the range of 260 and 180 parts per million by volume. This range is almost 30% smaller than that of the last four glacial cycles; however, the apparent sensitivity between deuterium and CO2 remains stable throughout the six glacial cycles, suggesting that the relationship between CO2 and Antarctic climate remained rather constant over this interval.

Age determination and radiometric dates of cores from Okarito Pakihi in Australia

In agreement with the Milankovitch orbital forcing hypothesis (Imbrie et al., 1993) it is often assumed that glacial-interglacial climate transitions occurred synchronously in the Northern and Southern hemispheres of the Earth. It is difficult to test this assumption, because of the paucity of long, continuous climate records from the Southern Hemisphere that have not been dated by tuning them to the presumed Northern Hemisphere signals (Lynch-Stieglitz, 2004). Here we present an independently dated terrestrial pollen record from a peat bog on South Island, New Zealand, to investigate global and local factors in Southern Hemisphere climate changes during the last two glacial-interglacial cycles. Our record largely corroborates the Milankovitch model of orbital forcing but also exhibits some differences: in particular, an earlier onset and longer duration of the Last Glacial Maximum. Our results suggest that Southern Hemisphere insolation may have been responsible for these differences in timing. Our findings question the validity of applying orbital tuning to Southern Hemisphere records and suggest an alternative mechanism to the bipolar seesaw for generating interhemispheric asynchrony in climate change.