A scanning mobility particle sizer (SMPS) is a high resolution nanoparticle sizing system that is widely used as the standard method to measure airborne particle size distributions (PSD) in the size range 1 nm-1 mu m. This paper addresses the problem to assess the uncertainty associated with PSD when a differential mobility analyzer (DMA) operates under scanning mode. The sources of uncertainty are described and then modeled either through experiments or knowledge extracted from the literature. Special care is brought to model the physics and to account for competing theories. Indeed, it appears that the modeling errors resulting from approximations of the physics can largely affect the final estimate of this indirect measurement, especially for quantities that are not measured during day-to-day experiments. The Monte Carlo method is used to compute the uncertainty associated with PSD. The method is tested against real data sets that are monosize polystyrene latex spheres (PSL) with nominal diameters of 100 nm, 200 nm and 450 nm. The median diameters and associated standard uncertainty of the aerosol particles are estimated as 101.22 nm +/- 0.18 nm, 204.39 nm +/- 1.71 nm and 443.87 nm +/- 1.52 nm with the new approach. Other statistical parameters, such as the mean diameter, the mode and the geometric mean and associated standard uncertainty, are also computed. These results are then compared with the results obtained by SMPS embedded software.

PURPOSE:This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing.METHODS:The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD.RESULTS:The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks.CONCLUSIONS:A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are defined over union of subspaces of differing dimensionality and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular RJ-MCMC method. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a "simple"-but still variable-dimensional-parametric distribution. The distance between the two distributions is measured using the Kullback-Leibler divergence, and a Stochastic EM-type algorithm, driven by the RJ-MCMC sampler, is proposed to estimate the parameters. The proposed algorithm is illustrated on the fundamental signal processing example of joint detection and estimation of sinusoids in white Gaussian noise.

Over the past decade there has been an explosion in the amount of genomic data available to biomedical researchers due to advances in biotechnology. For example, using gene microarrays, it is now possible to probe a person’s gene expression profile over the more than 30,000 genes of the human genome. Signals extracted from gene microarray experiments can be linked to genetic factors underlying disease, development. and aging in a population. This has greatly accelerated the pace of gene discovery. However, the massive scale and experimental variability of genomic data makes extraction of biologically significant genetic information very challenging. One of the most important problems is to select a list of genes which are both biologically and statistically significant based on the outcomes of gene microarray experiments. We will describe a novel multiple criterion method that we have developed for this gene selection problem that allows tight control of both minimum observable differential change (biological significance) and familywise error rate (statistical significance) and also provides a set of simultaneous confidence intervals for the differences.

Interventional imaging with cone-beam C-arm CT often lacks sufficient sampling. Compressed sensing based reconstruction algorithms have shown promising results to improve image quality in this context using sparsity constraints. Compressed sensing theory by itself assumes random measurements and l1 penalties. In practice, benefits are seen with uniform subsampling patterns. Here, we investigate substituting l1 total variation with a nonlinear diffusion constraint and show on a clinical data set that image quality is also improved. This result adds flexibility to the design of CS-based algorithms as C-arm CT images may not be so well approximated by piecewise constant functions.

This paper addresses the sensitivity of the algorithm proposed by Andrieu and Doucet (IEEE Trans. Signal Process., 47(10), 1999), for the joint Bayesian model selection and estimation of sinusoids in white Gaussian noise, to the values of a certain hyperparameter claimed to be weakly influential in the original paper. A deeper study of this issue reveals indeed that the value of this hyperparameter (the scale parameter of the expected signal-to-noise ratio) has a significant influence on 1) the mixing rate of the Markov chain and 2) the posterior distribution of the number of components. As a possible workaround for this problem, we investigate an Empirical Bayes approach to select an appropriate value for this hyperparameter in a data-driven way. Marginal likelihood maximization is performed by means of an importance sampling based Monte Carlo EM (MCEM) algorithm. Numerical experiments illustrate that the sampler equipped with this MCEM procedure provides satisfactory performances in moderate to high SNR situations.

We introduce a new approach for image filtering in a Bayesian framework. In this case the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is based on the generalized Gaussian Markov random fields (GGMRF), a class of Markov random fields which are used as prior information into the Bayesian rule, which principal objective is to eliminate those effects caused by the excessive smoothness on the reconstruction process of images which are rich in contours or edges. Accordingly to the hypothesis made for the present work, it is assumed a limited knowledge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of Maximum a posteriori (MAP) robust estimators, since the real systems are always exposed to continuous perturbations of unknown nature. Some promising results of three new MAP entropy estimators (MAPEE) for image filtering are presented, together with some concluding remarks.

Scanning Mobility Particle Sizer (SMPS) is a high resolution nanoparticle sizing system that has long been hailed as the researcher's choice for airborne nanoparticle size characterization for nano applications including nanotechnology research and development. SMPS is widely used as the standard method to measure airborne particle size distributions below 1 μm. It is composed of two devices: a Differential Mobility Analyzer (DMA) selects particle sizes thanks to their electrical mobility and a Condensation Particle Counter (CPC) enlarges particles to make them detectable by common optical counters. System raw data represent the number of particles counted over several classes of mobility diameters. Then, common inversion procedures lead to the estimation of the aerosol size distribution. In this paper, we develop a methodology to compute the uncertainties associated with the estimation of the size distribution when several experiences have been carried out. The requirement to repeat the measure ensures a realistic variability on the simulated data to be generated. The work we present consists in considering both the uncertainties coming from the experimental dispersion and the uncertainties induced by the lack of knowledge on physical phenomena. Experimental dispersion is quantified with the experimental data while the lack of knowledge is modelled via the existing physical theories and the judgements of experts in the field of aerosol science. Thus, running Monte-Carlo simulations give an estimation of the size distribution and its corresponding confidence region.

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators.

This paper describes a processing method to estimate parameters of chirp signals for Laser Doppler Anemometry (LDA). The Doppler frequency as well as additional useful parameters are considered here. These parameters are the burst width and the frequency rate. Several estimators based on the spectrogram are proposed. Cramer-Rao bounds are given and performance of the estimators compared to the state of the art using Monte-Carlo simulations for synthesized LDA signals. The characteristics of these signals are provided by a flight test campaign. The proposed estimation procedure takes into account the requirements for a real-time application.

This work tackles three-dimensional reconstruction of tomographic acquisitions in C-arm-based rotational angiography. The relatively slow rotation speed of C-arm systems involves motion artifacts that limit the use of three-dimensional imaging in interventional procedures. The main contribution of this paper is a reconstruction algorithm that deals with the temporal variations due to intra-arterial injections. Based on a compressed-sensing approach, we propose a multiple phase reconstruction with spatio-temporal constraints. The algorithm was evaluated by qualitative and quantitative assessment of image quality on both numerical phantom experiments and clinical data from vascular C-arm systems. In this latter case, motion artifacts reduction was obtained in spite of the cone-beam geometry, the short-scan acquisition, and the truncated and subsampled data.

Digital Subtraction Rotational Angiography (DSRA) is a clinical protocol that allows three-dimensional (3D) visualization of vasculature during minimally invasive procedures. C-arm systems that are used to generate 3D reconstructions in interventional radiology have limited sampling rate and thus, contrast resolution. To address this particular subsampling problem, we propose a novel iterative reconstruction algorithm based on compressed sensing. To this purpose, we exploit both spatial and temporal sparsity of DSRA. For computational efficiency, we use a proximal implementation that accommodates multiple ℓ1-penalties. Experiments on both simulated and clinical data confirm the relevance of our strategy for reducing subsampling streak artifacts.

We introduce an approach for image filtering in a Bayesian framework. In this case, the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is complemented using Markov random fields, for instance the Semi-Huber Markov random field (SHMRF), which is used as prior information into the Bayesian rule, and the principal objective of it is to eliminate those effects caused by the excessive smoothness on the reconstruction process of signals which are rich in discontinuities. Accordingly to the hypothesis made for the present work, it is assumed a limited knowledge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of new Maximum a posteriori (MAP) robust estimators, and considering that real systems are always exposed to continuous perturbations of unknown nature. Some promising results have been obtained from two new MAP entropy estimators (MAPEE) for the case of robust image filtering, where such results have been compared with respect to the classical median image filter.

We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited only after some other factors are activated. Precedence-ordering arise in applications where variables are activated in a specific order, which is unknown. The proposed method is based on a linear model that accounts for each factor's inherent delays and relative order. We present an algorithm to fit the model in an unsupervised manner using techniques from convex and nonconvex optimization that enforce sparsity of the factor scores and consistent precedence-order of the factor loadings. We illustrate the order-preserving factor analysis (OPFA) method for the problem of extracting precedence-ordered factors from a longitudinal (time course) study of gene expression data.

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new halfquadratic function is proposed. The Bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (halfquadratic) to be minimized. A comparison between the new introduced scheme and other three existent schemes, for the cases of noise filtering and image deblurring, is presented. Results showed a satisfactory performance and the effectiveness of the proposed estimator.1 Keywords— Image filtering, image deblurring, Markov Random Fields (MRF), Half-quadratic functions.

Reversible jump MCMC (RJ-MCMC) sampling techniques, which allow to jointly tackle model selection and parameter estimation problems in a coherent Bayesian framework, have become increasingly popular in the signal processing literature since the seminal paper of Andrieu and Doucet (IEEE Trans. Signal Process., 47(10), 1999). Crucial to the implementation of any RJ-MCMC sampler is the computation of the so-called Metropolis-Hastings-Green (MHG) ratio, which determines the acceptance probability for the proposed moves. It turns out that the expression of the MHG ratio that was given in the paper of Andrieu and Doucet for "Birth-or-Death" moves---the simplest kind of trans-dimensional move, used in virtually all applications of RJ-MCMC to signal decomposition problems---was erroneous. Unfortunately, this mistake has been reproduced in many subsequent papers dealing with RJ-MCMC sampling in the signal processing literature. This note discusses the computation of the MHG ratio, with a focus on the case where the proposal kernel can be decomposed as a mixture of simpler kernels, for which the MHG ratio is easy to compute. We provide sufficient conditions under which the MHG ratio of the mixture can be deduced from the MHG ratios of the elementary kernels of which it is composed. As an application, we consider the case of Birth-or-Death moves, and provide a corrected expression for the erroneous ratio in the paper of Andrieu and Doucet.

In this paper, we address three-dimensional tomographic reconstruction of rotational angiography acquisitions. In clinical routine, angular subsampling commonly occurs, due to the technical limitations of C-arm systems or possible improper injection. Standard methods such as filtered backprojection yield a reconstruction that is deteriorated by sampling artifacts, which potentially hampers medical interpretation. Recent developments of compressed sensing have demonstrated that it is possible to significantly improve reconstruction of subsampled datasets by generating sparse approximations through l1-penalized minimization. Based on these results, we present an extension of the iterative filtered backprojection that includes a sparsity constraint called soft background subtraction. This approach is shown to provide sampling artifact reduction when reconstructing sparse objects, and more interestingly, when reconstructing sparse objects over a non-sparse background. The relevance of our approach is evaluated in cone-beam geometry on real clinical data.

The scalar shrinkage-thresholding operator (SSTO) is a key ingredient of many modern statistical signal processing algorithms including: sparse inverse problem solutions, wavelet denoising, and JPEG2000 image compression. In these applications, it is customary to select the threshold of the operator by solving a scalar sparsity penalized quadratic optimization. In this work, we present a natural multidimensional extension of the scalar shrinkage thresholding operator. Similarly to the scalar case, the threshold is determined by the minimization of a convex quadratic form plus an euclidean penalty, however, here the optimization is performed over a domain of dimension N ges 1. The solution to this convex optimization problem is called the multidimensional shrinkage threshold operator (MSTO). The MSTO reduces to the standard SSTO in the special case of N = 1. In the general case of N > 1 the optimal MSTO threshold can be found by a simple convex line search. We present three illustrative applications of the MSTO in the context of non-linear regression: l2-penalized linear regression, Group LASSO linear regression and Group LASSO logistic regression.

Here we address the problem of adaptive digital-transmission systems. New systems based on a nonuniform transmission (NUT) principle are proposed, utilizing a recently proposed algorithm for adaptive identification and reconstruction of AR processes subject to missing data. We propose a new adaptive sampling (nonuniform transmission) method combined with the adaptive reconstruction algorithm. A new NUT-ADPCM coding-decoding system is designed. The proposed system is demonstrated for audio-signal compression and compared to the ADPCM G. 726 standard. The new system yields improvements in both signal-to-noise ratio and average bit rate.