Quantum tomography of electrical currents.

In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography.

PURPOSE: Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images. METHODS: This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed. RESULTS: The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions. CONCLUSIONS: The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF.

We propose a method for the reconstruction of signals and images observed partially through a linear operator with a large support (e.g., a Fourier transform on a sparse set). This inverse problem is ill-posed and we resolve it by incorporating the prior information that the reconstructed objects are composed of smooth regions separated by sharp transitions. This feature is modeled by a piecewise Gaussian (PG) Markov random field (MRF), known also as the weak-string in one dimension and the weak-membrane in two dimensions. The reconstruction is defined as the maximum a posteriori estimate. The prerequisite for the use of such a prior is the success of the optimization stage. The posterior energy corresponding to a PG MRF is generally multimodal and its minimization is particularly problematic. In this context, general forms of simulated annealing rapidly become intractable when the observation operator extends over a large support. In this paper, global optimization is dealt with by extending the graduated nonconvexity (GNC) algorithm to ill-posed linear inverse problems. GNC has been pioneered by Blake and Zisserman in the field of image segmentation. The resulting algorithm is mathematically suboptimal but it is seen to be very efficient in practice. We show that the original GNC does not correctly apply to ill-posed problems. Our extension is based on a proper theoretical analysis, which provides further insight into the GNC. The performance of the proposed algorithm is corroborated by a synthetic example in the area of diffraction tomography.

Bayesian approach with the maximum entropy principle in image reconstruction from microwave scattered field data.

Microwave imaging is of great interest in medical applications owing to its high sensitivity with respect to dielectric properties. It allows detection of very small inhomogeneities. The image reconstruction employing the microwave inverse scattering consists of reconstructing the image of an object from the scattered field measured behind the object. This reconstruction runs up against the nonuniqueness of the solution of the inverse scattering problem. The authors propose to solve the ill-posed inverse problem by a statistical regularization method based on the Bayesian maximum a posteriori estimation where the principle of maximum entropy is used for assigning the a priori laws. The results obtained demonstrate the power and potential of this method in image reconstruction.

Maximum entropy image reconstruction in X-ray and diffraction tomography.

The authors propose a Bayesian approach with maximum-entropy (ME) priors to reconstruct an object from either the Fourier domain data (the Fourier transform of diffracted field measurements) in the case of diffraction tomography, or directly from the original projection data in the case of X-ray tomography. The objective function obtained is composed of a quadratic term resulting from chi(2) statistics and an entropy term that is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results in X-ray and diffraction tomography are given to compare this method to the classical ones.

Maximum entropy Fourier synthesis with application to diffraction tomography.

In diffraction tomography, the generalized Radon theorem relates the Fourier transform (FT) of the diffracted field to the two-dimensional FT of the diffracting object. The relationship stands on algebraic contours, which are semicircles in the case of Born or Rytov first-order linear approximations. But the corresponding data are not sufficient to determine uniquely the solution. We propose a maximum entropy method to reconstruct the object from either the Fourier domain data or directly from the original diffracted field measurements. To do this, we give a new definition for the entropy of an object considered as a function of R(2) to C. To take into account the presence of noise, a chi-squared statistic is added to the entropy measure. The objective function thus obtained is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results are given which compare this new method with the classical ones.

Noninvasive recording of the his-purkinje system electrical activity by a digital system design.

The atrioventricular conduction pathways which are composed of the atrioventricular node and the His-Purkinje system (HPS) form a specialized conduction system in the heart that participates in the control of the ventricular conduction. His bundle recordings require cardiac catheterization in the diagnosis of abnormalities within the HPS. These recordings have limitations that include discomfort, a slight morbidity risk, and limited recording area within the heart. This report outlines a noninvasive technique that utilizes high gain, wide band filtering and coherent signals averaging to extract the electrical activity of the HPS at the body surface. We have designed a portable instrument which enables: (i) a high gain, very low noise, optically isolated differential amplifier, (ii) an online digital QRS detector based on the principle of contour limiting which detects the desired QRS complexes and generates a very accurate trigger for the coherent signal averaging; (iii) a digital memory averager. This instrument can be used as an automatic clinical tool or as a data acquisition and preprocessing system for high frequency ECG and many other low level electrophysiological signals.