Elisabeth Lahalle

Continuous ARMA spectral estimation from irregularly sampled observations

In a previous paper we introduced the pseudo correlation vector concept which extends the classical correlation vector to the non uniform sampling context (A. Rivoira et al., IEEE Int. Conf. on Acoustic Speech and Sigpro., vol.11, p.1725-1728, 2002). The dependence relations between the pseudo correlation vector and the parameters of a CAR signal were established. An analytical inversion procedure was carried out for CAR models of order 2. As many applications require CARMA models, or CAR models but of higher orders, the purpose of the present paper is to deal with spectral estimation of such modelled signals. The performance of the numerical method proposed here is evaluated and compared with those of the slotting method, commonly used for laser Doppler anemometry data.

Compressed sensing based 3d tomographic reconstruction for rotational angiography

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.

Compressed sensing dynamic reconstruction in rotational angiography

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.

Lattice Algorithm for Adaptive Stable Identification and Robust Reconstruction of Nonstationary AR Processes With Missing Observations

This paper deals with the problem of adaptive reconstruction and identification of nonstationary AR processes with randomly missing observations. Existent methods use a direct realization of the filter. Therefore, the estimated parameters may not correspond to a stable all-pole filter. In addition, when the probability of missing a sample is high, existent methods may converge slowly or even fail to converge. We propose, at our knowledge, the first algorithm based on the lattice structure for online processing of signals with missing samples. It is an extension of the RLSL algorithm to the case of missing observations, using a Kalman filter for the prediction of missing samples. The estimated parameters guarantee the stability of the corresponding all-pole filter. In addition it is robust to high probabilities of missing a sample. It offers a fast parameter tracking even for high probabilities of missing a sample. It is compared to the Kalman pseudolinear RLS algorithm, an already proposed algorithm using a direct realization of the filter. The proposed algorithm shows better performance in reconstruction of audio signals.

New Fast Algorithm for Simultaneous Identification and Optimal Reconstruction of Non Stationary AR Processes with Missing Observations

This paper deals with the problem of adaptive reconstruction and identification of AR processes with randomly missing observations. A new real time algorithm is proposed. It uses combined pseudo-linear RLS algorithm and Kalman filter. It offers an unbiased estimation of the AR parameters and an optimal reconstruction error in the least mean square sense. In addition, thanks to the pseudo-linear RLS identification, this algorithm can be used for the identification of non stationary AR signals. Moreover, simplifications of the algorithm reduces the calculation time, thus this algorithm can be used in real time applications

Compressed‐sensing‐based content‐driven hierarchical reconstruction: Theory and application to C‐arm cone‐beam tomography

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.

Vibration signals compression with Time-Frequency Adaptive Quantization

A novel quantization method, well suited to the case of vibration signal compression is introduced in this paper. This method, applied in the domain of the Discrete Cosine Transform, is called Time-Frequency Adaptive Quantization (TFAQ) and it efficiently allocates the coding bits based on the time-frequency properties of the vibration signals. The method is compared to other transform-based compression techniques. Experiments are carried on a rich database of vibration signals, issued by the plane engines, in various stages of the flight. The results prove the superiority of TFAQ versus the other tested methods, for the experimental data set we dispose on.

New Nonuniform Transmission and ADPCM Coding System for Improving Both Signal-to-Noise Ratio and Bit Rate

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.

Compressed sensing subtracted rotational angiography with multiple sparse penalty

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.

Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm

The following paper addresses a problem of inference in financial engineering, namely, online time-varying volatility estimation. The proposed method is based on an adaptive predictor for the stock price, built from an implicit integration formula. An estimate for the current volatility value which minimizes the mean square prediction error is calculated recursively using an LMS algorithm. The method is then validated on several synthetic examples as well as on real data. Throughout the illustration, the proposed method is compared with both UKF and offline volatility estimation.