Purpose: Exploiting the x-ray measurements obtained in different energy bins, spectral computed tomography (CT) has the ability to recover the 3-D description of a patient in a material basis. This may be achieved solving two subproblems, namely the material decomposition and the tomographic reconstruction problems. In this work, we address the material decomposition of spectral x-ray projection images, which is a nonlinear ill-posed problem. Methods: Our main contribution is to introduce a material-dependent spatial regularization in the projection domain. The decomposition problem is solved iteratively using a Gauss-Newton algorithm that can benefit from fast linear solvers. A Matlab implementation is available online. The proposed regularized weighted least squares Gauss-Newton algorithm (RWLS-GN) is validated on numerical simulations of a thorax phantom made of up to five materials (soft tissue, bone, lung, adipose tissue, and gadolinium), which is scanned with a 120 kV source and imaged by a 4-bin photon counting detector. To evaluate the method performance of our algorithm, different scenarios are created by varying the number of incident photons, the concentration of the marker and the configuration of the phantom. The RWLS-GN method is compared to the reference maximum likelihood Nelder-Mead algorithm (ML-NM). The convergence of the proposed method and its dependence on the regularization parameter are also studied. Results: We show that material decomposition is feasible with the proposed method and that it converges in few iterations. Material decomposition with ML-NM was very sensitive to noise, leading to decomposed images highly affected by noise, and artifacts even for the best case scenario. The proposed method was less sensitive to noise and improved contrast-to-noise ratio of the gadolinium image. Results were superior to those provided by ML-NM in terms of image quality and decomposition was 70 times faster. For the assessed experiments, material decomposition was possible with the proposed method when the number of incident photons was equal or larger than 10 5 and when the marker concentration was equal or larger than 0.03 gÁcm À3 . Conclusions: The proposed method efficiently solves the nonlinear decomposition problem for spectral CT, which opens up new possibilities such as material-specific regularization in the projection domain and a parallelization framework, in which projections are solved in parallel.

Single pixel camera imaging is an emerging paradigm that allows high-quality images to be provided by a device only equipped with a single point detector. A single pixel camera is an experimental setup able to measure the inner product of the scene under view-the image-with any user-defined pattern. Post-processing a sequence of point measurements obtained with different patterns permits to recover spatial information, as it has been demonstrated by state-of-theart approaches belonging to the compressed sensing framework. In this paper, a new framework for the choice of the patterns is proposed together with a simple and efficient image recovery scheme. Our goal is to overcome the computationally demanding 1-minimization of compressed sensing. We propose to choose patterns among a wavelet basis in an adaptive fashion, which essentially relies onto the prediction of the significant wavelet coefficients' location. More precisely, we adopt a multiresolution strategy that exploits the set of measurements acquired at coarse scales to predict the set of measurements to be performed at a finer scale. Prediction is based on a fast cubic interpolation in the image domain. A general formalism is given so that any kind of wavelets can be used, which enables one to adjust the wavelet to the type of images related to the desired application. Both simulated and experimental results demonstrate the ability of our technique to reconstruct biomedical images with improved quality compared to CS-based recovery. Application to real-time fluorescence imaging of biological tissues could benefit from the proposed method.

Time-resolved multispectral imaging has many applications in different fields, which range from characterization of biological tissues to environmental monitoring. In particular, optical techniques, such as lidar and fluorescence lifetime imaging, require imaging at the subnanosecond scales over an extended area. In this paper, we demonstrate experimentally a time-resolved multispectral acquisition scheme based on single-pixel imaging. Single-pixel imaging is an emerging paradigm that provides low-cost high-quality images. Here, we use an adaptive strategy that allows acquisition and image reconstruction times to be reduced drastically or full basis scans. Adaptive time-resolved multispectral imaging scheme can have significant applications in biological imaging, at scales from macroscopic to microscopic.

Full-wavelet approach for fluorescence diffuse optical tomography with structured illuminatio

International audienceIn recent years, an increasing effort has been devoted to the optimization of acquisition and reconstruction schemes for fluorescence molecular tomography (FMT). In particular, wide-field structured illumination and compression of the measured images have enabled significant reduction of the data set and, consequently, a decrease in both acquisition and processing times. FMT based on this concept has been recently demonstrated on a cylindrical phantom with a rotating-view scheme that significantly increases the reconstruction quality. In this work, we generalize the rotating-view scheme to arbitrary geometries and experimentally demonstrate its applicability to murine models. To the best of our knowledge this is the first time that FMT based on a rotating-view scheme with structured illumination and image compression has been applied to animals

A method to perform fast 3-D optical reconstruction, based on structured light, in thick samples is demonstrated and experimentally validated. The experimental and reconstruction procedure, based on Finite Elements Method, used to reconstruct absorbing heterogeneities, with arbitrary arrangement in space, is discussed. In particular we demonstrated that a 2D sampling of the source Fourier plane is required to improve the imaging capability.

In this paper, we address the resolution of material decomposition, which is a nonlinear inverse problem encountered in spectral computed tomography (CT). The problem is usually solved in a variational framework but, due to the nonlinearity of the forward operator, the objective function may be nonconvex and standard approaches may fail. Regularized iterative schemes based on the Bregman distance have been suggested for improving global convergence properties. In this work, we analyze the convexity of the material decomposition problem and propose a regularized iterative scheme based on the Bregman distance to solve it. We evaluate our Bregman iterative algorithm and compare it with a regularized Gauss-Newton (GN) method using data simulated in a realistic thorax phantom. First, we prove the existence of a convex set where the usual data fidelity term is convex. Interestingly, this set includes zero, making it a good initial guess for iterative minimization schemes. Using numerical simulations, we show that the data fidelity term can be nonconvex for large values of the decomposed materials. Second, the proposed Bregman iterative scheme is evaluated in different situations. It is observed to be robust to the selection of the initial guess, leading to the global minimum in all tested examples while the GN method fails to converge when the initial guess is not well chosen. Moreover, it is found to avoid the selection of the regularization parameter for little extra computation. In conclusion, we have provided a suitable initialization strategy to solve the nonlinear material decomposition problem using convex optimization methods and evaluated a Bregman iterative scheme for this problem. The improvement in global convergence of Bregman iterative scheme combined with other interesting properties of the Bregman distance appears as a compelling strategy for nonlinear inverse problems.

The enhancement and control of non-linear phenomena at a nanometer scale has a wide range of applications in science and in industry. Among these phenomena, high-harmonic generation in solids is a recent focus of research to realize next generation petahertz optoelectronic devices or compact all solid state EUV sources. Here, we report on the realization of the first nanoscale high harmonic source. The strong field regime is reached by confining the electric field from a few nanojoules femtosecond laser in a single 3D semiconductor waveguide. We reveal a strong competition between enhancement of coherent harmonics and incoherent fluorescence favored by excitonic processes. However, far from the band edge, clear enhancement of the harmonic emission is reported with a robust sustainability offering a compact nanosource for applications. We illustrate the potential of our harmonic nano-device by performing a coherent diffractive imaging experiment. Ultra-compact UV/X-ray nanoprobes are foreseen to have other applications such as petahertz electronics, nano-tomography or nano-medicine.