Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods – based on a single noise level for the whole image – fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.     

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Cubic helimagnets in magnetic field and at pressure

Cubic helimagnets with B20 structure display several unusual properties such as anisotropy of the spin-wave spectrum al small momenta q, rotation of the helix vector k in magnetic field and quantum phase transition at pressure. We demonstrate that first two phenomena are a result of umklapp processes mixing excitations with momenta q, q+k and q−k. At very low magnetic field perpendicular to k the helical structure remains stable due to spin-wave gap Δ. Its square is sum of two parts. The first one is a result of the magnon interaction and the second negative part stems from magneto-elastic interaction. It is suggested that competition between these parts leads to the quantum phase transition observed in MnSi and FeGe. For MnSi from rough estimations at ambient pressure was shown that both parts are comparable with the experimentally observed gap. The magneto-elastic interaction is also responsible for 2k modulation of the lattice and contributes to the magnetic anisotropy. Experimental observation by X-ray and neutron scattering of this lattice modulation allows to determine the strength of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.     

An improved POCS super-resolution infrared image reconstruction algorithm based on visual mechanism

The traditional projection onto convex sets (POCS) super-resolution (SR) reconstruction algorithm can only get reconstructed images with poor contrast, low signal-to-noise ratio and blurring edges. In order to solve the above disadvantages, an improved POCS SR infrared image reconstruction algorithm based on visual mechanism is proposed, which introduces data consistency constraint with variable correction thresholds to highlight the target edges and filter out background noises; further, the algorithm introduces contrast constraint considering the resolving ability of human eyes into the traditional algorithm, enhancing the contrast of the image reconstructed adaptively. The experimental results show that the improved POCS algorithm can acquire high quality infrared images whose contrast, average gradient and peak signal to noise ratio are improved many times compared with traditional algorithm.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics

The statistical properties of background noise such as its standard deviation and mean value are frequently used to estimate the original noise level of the acquired data. This requires the knowledge of the statistical intensity distribution of the background signal, that is, the probability density of the occurrence of a certain signal intensity. The influence of many new MRI techniques and, in particular, of various parallel-imaging methods on the noise statistics has neither been rigorously investigated nor experimentally demonstrated yet. In this study, the statistical distribution of background noise was analyzed for MR acquisitions with a single-channel and a 32-channel coil, with sum-of-squares (SoS) and spatial-matched-filter (SMF) data combination, with and without parallel imaging using k-space and image-domain algorithms, with real-part and conventional magnitude reconstruction and with several reconstruction filters. Depending on the imaging technique, the background noise could be described by a Rayleigh distribution, a noncentral chi-distribution or the positive half of a Gaussian distribution. In particular, the noise characteristics of SoS-reconstructed multichannel acquisitions (with k-space-based parallel imaging or without parallel imaging) differ substantially from those with image-domain parallel imaging or SMF combination. These effects must be taken into account if mean values or standard deviations of background noise are employed for data analysis such as determination of local noise levels. Assuming a Rayleigh distribution as in conventional MR images or a noncentral chi-distribution for all multichannel acquisitions is invalid in general and may lead to erroneous estimates of the signal-to-noise ratio or the contrast-to-noise ratio.     

Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity

By employing a simplified nonlinear coupled mode theory, we discuss the influence of two-photon absorption (TPA) on the characteristics of bistable switching. It is revealed that the critical value of frequency detuning for bistability rises linearly with increasing TPA coefficient k (when k is less than 30), and eventually access to a saturated value. It is also found that TPA effect will be enhanced for a greater frequency detuning, especially when transmission reaches its peak value. As a result, the peak transmission will decrease monotonously with the increasing frequency detuning. Based on this simplified model, the TPA-induced temperature rise in microcavity is also estimated. The theoretical predictions show good agreement with the simultaneous results, as well as the proposed experimental phenomena.     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.     

A new reconstruction method in the Fourier domain for 3D positron emission tomography

This article describes a new exact 3D reconstruction algorithm dedicated to cylindrical positron emission tomographs that does not require an estimation of missing projection data nor complex 3D interpolation procedures. This algorithm uses the 2D Fast Fourier Transform of non-transaxial projections to place suitable voxel values in the 3D FFT of the radioactive distribution. This leads to a direct fully 3D reconstruction algorithm with a limited amount of computation that requires only 1D interpolation procedures and benefits from redundant projection data to improve the signal to noise ratio in the radioactive distribution. To cite this article: D. Mariano-Goulart, J.-F. Crouzet, C. R. Physique 6 (2005).     

TOWARDS DEEP AND SIMPLE UNDERSTANDING OF THE TRANSCENDENTAL EIGENPROBLEM OF STRUCTURAL VIBRATIONS

When using exact methods for undamped free vibration problems the generalized linear eigenvalue problem (K−ω²M) D=0 of approximate methods, e.g., finite elements, is replaced by the transcendental eigenvalue problem K (ω) D=0. Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K (ω) is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations. The natural frequencies of this transcendental eigenvalue problem are generally found by the Wittrick-Williams algorithm which gives the number of natural frequencies below ω_t, a trial value of ω, as ∑J_m+s{K (ω_t)} wheres {} denotes the readily computed sign count property of K (ω) and the summation is over the clamped-clamped natural frequencies of all elements of the structure. Understanding the alternative solution forms of the transcendental eigenvalue problem is important both to accelerate convergence to natural frequencies, e.g., by plotting ∣K (ω)∣, and to improve the mode calculations, which lack the complete reliability of natural frequencies obtained by using the Wittrick-Williams algorithm. The three solution forms are: ∣K (ω)∣=0; D=0 with ∣K (ω)∣→∞; and ∣K (ω)∣≠0 with D≠0. The literature covers the first two forms thoroughly but the third form has been almost totally ignored. Therefore, it is now examined thoroughly, principally by analytical studies of simple bar structures and also by confirmatory numerical results for a rigidly jointed plane frame. Although structures are unlikely to have exactly the properties giving this form, it needs to be understood, particularly because ill-conditioning can occur for structures approximating those for which it occurs.     

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

Symmetrized Hamiltonian versus ‘Foreman’ Hamiltonian for semiconductor valence band: an insight

A quantitative comparison of different k·p calculations of valence-band states in quantum-confined semiconductor heterostructures is presented. The importance of using the appropriate Hamiltonian form is studied quantitatively following a numerical method which enables discrimination between existing Hamiltonians. The correct form of the Hamiltonian appears to be the Foreman Hamiltonian, which gives physically reasonable results contrary to the symmetrized Hamiltonian.     

Intermolecular photoinduced electron-transfer processes between C60 and aniline derivatives in benzonitrile

The quenching behavior of the triplets of C₆₀ by various aniline derivatives (1a-d and 2a-e) was investigated by means of laser flash photolysis in benzonitrile at 293 K. Electron transfer process was proposed to be the main mechanism because of the direct detection of radical ions of aniline derivatives and C₆₀ in time-resolved transient absorption spectra. The quenching rate constants (k_q) of by different substrates determined at 740 nm approach or reach the diffusion-controlled limit. DFT method was employed to calculate the unknown oxidation potentials of substrates in solution. With these E_ox values, free energy changes (ΔG) were obtained through Rehm-Weller equation. Dependence of observed quenching rate constants on the free energy changes further indicates the photoinduced reactions between ³C₆₀^* and substrates proceed through an electron transfer mechanism. Obtained k_q values for the aniline derivatives are impacted obviously by ground-state configurations and the kinds substituents quantified by Hammett σ constant. Good correlation between log k_q and σ values conforms to the empirical Hammett equation. A more negative ρ value (−3.356) was gained for anilines (2a-e) than that of N,N-dimethylanilines (1a-d) (−1.382), which suggests a more susceptible reactivity for the former substrates. Charge density distribution of reaction center “N” originated from quantum calculation supports this suggestion. In addition, a relationship between quenching rate constants and solvent viscosity was gained from C₆₀/dimethyl-p-toluidine system in altered mixtures of acetonitrile and toluene.     

The effect of additional Si and SiGe layers on the confinement potential of GeMn diluted ferromagnetic semiconductor

In this work we analyze the spin-polarized charge density distribution in the GeMn diluted ferromagnetic semiconductors (DFS). The calculations are performed within a self-consistent k·p method, in which the exchange correlation effects in the local density approximation, as well as the strain effects due to the lattice mismatch, are taken into account. Our findings show that the extra confinement potential provided by the barriers and the variation of the Mn content in the DFS are responsible for a separation between the different spin charge densities, giving rise to higher mobility spin-polarized currents or high ferromagnetism transition temperatures systems.     

q-Dependence of the giant bond-stretching phonon anomaly in the stripe compound La1.48Nd0.4Sr0.12CuO4 measured by IXS

Inelastic X-ray scattering (IXS) was used to study the Cu-O bond-stretching vibrations in the static stripe phase compound La_1.48Nd_0.4Sr_0.12CuO₄. It was found that the intrinsic width in Q-space of the previously reported huge anomalous phonon softening and broadening is approximately 0.08 r.l.u. HWHM. A detailed comparison was also made to inelastic neutron scattering (INS) studies, which indicate a two-peak lineshape (with superimposed broad and narrow peaks) in the vicinity of the anomaly. The high resolution IXS data show that the narrow peak is mostly an artifact of the poor transverse Q-resolution of INS. Otherwise, the agreement between the INS and IXS was excellent.     

Explicit form of an implicit method for inverse force identification

Most existing time domain force identification methods are based on the state space method, which has the disadvantage of large discretization error with a low sampling frequency or a long sampling duration. This work transforms the conventional implicit Newmark-β algorithm into an explicit form for the solution of the Ax=b equations, which is an equivalent transformation, and it exhibits the same characteristics of Newmark-β algorithm as an implicit method. The accuracy of this method for the dynamic force identification is illustrated with two shear-frame buildings and a planar truss structure. Numerical results are compared with reference analytical responses. The new method gives more accurate identified force time histories compared with those from the conventional state space method for multiple sinusoidal and white noise excitations with 10% measurement noise in the responses.     

Synthesis of 2,3-dimorpholino-6-aminoquinoxaline derivatives and application to a new intramolecular fluorescent probe

Two fluorescent monomers having a quinoxaline skeleton, N-(2,3-dimorpholinoquinoxalin-6-yl)acrylamide (QxA) and N-(1-(2,3-dimorpholinoquinoxalin-6-ylamino)prop-2-yl)methacrylamide (QxAlaMA), were synthesized. Thermo-responsive copolymers of N-isopropylacrylamide (NIPAM) and a small amount of a fluorescent monomer were synthesized and their fluorescence properties investigated. The fluorescent monomers showed intense solvatochromism in their fluorescence. The wavelength at the maximum fluorescence intensity of the QxAlaMA-labeled PNIPAM dramatically blue-shifted and the fluorescence intensity of the QxA-labeled PNIPAM significantly increased around the transition temperature. It was found that these fluorescent dyes can sense and report the thermo-responsive behavior of the PNIPAM in water. Both QxAlaMA and QxA were demonstrated to be applicable to new intramolecular fluorescent probes.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

Surface-modification of TiO2 with new metalloporphyrins and their photocatalytic activity in the degradation of 4-notrophenol

A new mono-functionalized porphyrin derivative, 5-mono-[4-(2-(4-hydroxy)-phenoxy)ethoxy]-10,15,20-triphenylporphyrin (3) and its Cu(II) (3a), Zn(II) (3b) and Ni(II) (3c) metalloporphyrins were synthesized and characterized by using various spectroscopic techniques. The corresponding 3a, 3b, 3c-TiO₂ photocatalysts were then prepared and characterized by means of FT-IR and diffused reflectance spectra, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The photocatalytic activities of 3a, 3b, 3c-TiO₂ were investigated by testing the photodegradation of 4-nitrophenol (4-NP) in aqueous solution under the halogen lamp irradiation. The results indicated that all the 3a, 3b, 3c enhanced the photocatalytic efficiency of bare TiO₂ in photodegrading the 4-NP, and 3a-TiO₂ exhibited the highest photocatalytic activity. The result is considered a combined action of potential match of 3a with TiO₂ CB and effective impregnated of 3a onto the surface of TiO₂.