This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion of ill-con
ditioned linear problems, in particular for computed tomography with the dictionary learning method. A comparison with other state-of-art methods shows a significant reduction of the number of iterations, which makes this algorithm appealing for practical use.
We present the PyHST2 code which is in service at ESRF for phase-contrast and absorption tomography. This code has been engineered to sustain the high data flow typical of the third generation synchrotron facilities (10 terabytes per experiment) by a
dopting a distributed and pipelined architecture. The code implements, beside a default filtered backprojection reconstruction, iterative reconstruction techniques with a-priori knowledge. These latter are used to improve the reconstruction quality or in order to reduce the required data volume and reach a given quality goal. The implemented a-priori knowledge techniques are based on the total variation penalisation and a new recently found convex functional which is based on overlapping patches. We give details of the different methods and their implementations while the code is distributed under free license. We provide methods for estimating, in the absence of ground-truth data, the optimal parameters values for a-priori techniques.
We solve the image denoising problem with a dictionary learning technique by writing a convex functional of a new form. This functional contains beside the usual sparsity inducing term and fidelity term, a new term which induces similarity between ov
erlapping patches in the overlap regions. The functional depends on two free regularization parameters: a coefficient multiplying the sparsity-inducing $L_{1}$ norm of the patch basis functions coefficients, and a coefficient multiplying the $L_{2}$ norm of the differences between patches in the overlapping regions. The solution is found by applying the iterative proximal gradient descent method with FISTA acceleration. In the case of tomography reconstruction we calculate the gradient by applying projection of the solution and its error backprojection at each iterative step. We study the quality of the solution, as a function of the regularization parameters and noise, on synthetic datas for which the solution is a-priori known. We apply the method on experimental data in the case of Differential Phase Tomography. For this case we use an original approach which consists in using vectorial patches, each patch having two components: one per each gradient component. The resulting algorithm, implemented in the ESRF tomography reconstruction code PyHST, results to be robust, efficient, and well adapted to strongly reduce the required dose and the number of projections in medical tomography.
We apply Coupled Cluster Method to a strongly correlated lattice and develop the Spectral Coupled Cluster equations by finding an approximation to the resolvent operator, that gives the spectral response for an certain class of probe operators. We ap
ply the method to a $MnO_2$ plane model with a parameters choice which corresponds to previous experimental works and which gives a non-nominal symmetry ground state. We show that this state can be observed using our Spectral Coupled Cluster Method by probing the Coupled Cluster solution obtained from the nominal reference state. In this case one observes a negative energy resonance which corresponds to the true ground state.
The dependence with energy of the resonant soft x-ray Bragg diffraction intensity in DyB$_2$C$_2$ for the $(00{1/2})$ reflection at the Dy M$_{4,5}$ edges have been calculated by using an atomic multiplet hamiltonian including the effect of crystal f
ield and introducing an intra-atomic quadrupolar interaction between the 3d core and 4f valence shell. These calculations are compared with the experimental results (Mulders et al., J. Phys.: Condens. Matter 18 (2006) 11195) in the antiferroquadrupolar and antiferromagnetic phases of DyB$_2$C$_2$. We reproduce all the features appearing $(00{1/2})$ reflection energy profile in the antiferroquadrupolar ordered phase, and we reproduce the behaviour of the resonant x-ray scattering intensity at different energies in the vicinity of the Dy M$_5$ edge when the temperature is lowered within the antiferromagnetic phase.
We present here an installation guide, a hand-on mini-tutorial through examples, and the theoretical foundations of the Hilbert++ code.
