Fast Second Degree Total Variation Method for Image Compressive Sensing

This paper presents a computationally efficient algorithm for image compressive sensing reconstruction using a second degree total variation (HDTV2) regularization. Firstly, a preferably equivalent formulation of the HDTV2 functional is derived, which can be formulated as a weighted L ₁-L ₂ mixed norm of second degree image derivatives under the spectral decomposition framework. Secondly, using the equivalent formulation of HDTV2, we introduce an efficient forward-backward splitting (FBS) scheme to solve the HDTV2-based image reconstruction model. Furthermore, from the averaged non-expansive operator point of view, we make a detailed analysis on the convergence of the proposed FBS algorithm. Experiments on medical images demonstrate that the proposed method outperforms several fast algorithms of the TV and HDTV2 reconstruction models in terms of peak signal to noise ratio (PSNR), structural similarity index (SSIM) and convergence speed.     

An Augmented Lagrangian Based Compressed Sensing Reconstruction for Non-Cartesian Magnetic Resonance Imaging without Gridding and Regridding at Every Iteration

Background

Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability.

Methods

We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate.

Results

Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time.

Conclusions

The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity.     

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ₁-regularized parallel imaging methods.     

Biases of acoustic indices measuring biodiversity in urban areas

Urban green infrastructure, GI (e.g., parks, gardens, green roofs) are potentially important biodiversity habitats, however their full ecological capacity is poorly understood, in part due to the difficulties of monitoring urban wildlife populations. Ecoacoustic surveying is a useful way of monitoring habitats, where acoustic indices (AIs) are used to measure biodiversity by summarising the activity or diversity of biotic sounds. However, the biases introduced to AIs in acoustically complex urban habitats dominated by anthropogenic noise are not well understood. Here we measure the level of activity and diversity of the low (0–12 kHz, _l) and high (12–96 kHz, _h) frequency biotic, anthropogenic, and geophonic components of 2452 h of acoustic recordings from 15 sites across Greater London, UK from June to October 2013 based on acoustic and visual analysis of recordings. We used mixed-effects models to compare these measures to those from four commonly used AIs: Acoustic Complexity Index (ACI), Acoustic Diversity Index (ADI), Bioacoustic Index (BI), and Normalised Difference Soundscape Index (NDSI). We found that three AIs (ACI_l, BI_l, NDSI_l) were significantly positively correlated with our measures of biotic_l activity and diversity. However, all three were also correlated with anthropogenic_l activity, and BI_l and NDSI_l were correlated with anthropogenic_l diversity. All low frequency AIs were correlated with the presence of geophonic_l sound. Regarding the high frequency recordings, only one AI (ACI_h) was positively correlated with measured biotic_h activity, but was also positively correlated with anthropogenic_h activity, and no index was correlated with biotic_h diversity. The AIs tested here are therefore not suitable for monitoring biodiversity acoustically in anthropogenically dominated habitats without the prior removal of biasing sounds from recordings. However, with further methodological research to overcome some of the limitations identified here, ecoacoustics has enormous potential to facilitate urban biodiversity and ecosystem monitoring at the scales necessary to manage cities in the future.     

Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging

In dynamic Positron Emission Tomography (PET), an estimate of the radio activity concentration is obtained from a series of frames of sinogram data taken at ranging in duration from 10 seconds to minutes under some criteria. So far, all the well-known reconstruction algorithms require known data statistical properties. It limits the speed of data acquisition, besides, it is unable to afford the separated information about the structure and the variation of shape and rate of metabolism which play a major role in improving the visualization of contrast for some requirement of the diagnosing in application. This paper presents a novel low rank-based activity map reconstruction scheme from emission sinograms of dynamic PET, termed as SLCR representing Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging. In this method, the stationary background is formulated as a low rank component while variations between successive frames are abstracted to the sparse. The resulting nuclear norm and l ₁ norm related minimization problem can also be efficiently solved by many recently developed numerical methods. In this paper, the linearized alternating direction method is applied. The effectiveness of the proposed scheme is illustrated on three data sets.     

Herbicide Resistance in Datura innoxia: Kinetic Characterization of Acetolactate Synthase from Wild-Type and Sulfonylurea-Resistant Cell Variants

Acetolactate synthase (ALS, EC 4. 1.3. 18), the first enzyme in the biosynthesis of branched-chain amino acids, was isolated from wild-type and sulfonylurea-resistant Datura innoxia cell variants and characterized. Apparent K_m values of the ALS for pyruvate from three sulfonylurea-resistant variants (CSR2, CSR6, and CSR10) were manyfold greater than that of the wild type. The inhibition of wild-type and herbicide-resistant ALS activity by chlorsulfuron (CS), a sulfonylurea herbicide, and l-leucine (l-Leu), one of the feedback inhibitors of the enzyme, was examined. ALS from two CS-resistant variants exhibited severalfold greater resistance to CS than did the wild-type enzyme. Inhibition of ALS by l-Leu fitted a partially competitive pattern most closely. It is proposed that the herbicide resistance mutation accentuated the partial inhibition characteristics of ALS by l-Leu. ALS from one of the two CS-resistant variants (CSR6) had a K_i for l-Leu an order of magnitude greater than that of the wild-type enzyme. The alterations in kinetic properties observed in the ALS from sulfonylurea-resistant variants are discussed in relation to the possible evolutionary significance of the herbicide binding site of this enzyme, the physiological effects of such biochemical alterations, and their practical utility in genetic studies.     

Unsaturation in binuclear cyclopentadienyliron carbonyl thiocarbonyls: Four-electron donor bridging thiocarbonyl groups versus metal-metal multiple bonds

Theoretical studies on the binuclear cyclopentadienyliron carbonyl thiocarbonyl derivatives Cp₂Fe₂(CO)₂(μ-CS)(μ-CO) and Cp₂Fe₂(CO)₂(μ-CS)₂ indicate that the trans and cis isomers are nearly degenerate in energy, consistent with experiment. Structures with bridging CS groups are of lower energy than corresponding structures with bridging CO groups. The corresponding unbridged Cp₂Fe₂(CS)(CO)₃ and Cp₂Fe₂(CS)₂(CO)₂ isomers are predicted to lie 11 and 16 kcal/mol, respectively, above their global minima, indicating increasing activation energies for the cis/trans interconversion as bridging CO groups are replaced by bridging CS groups. The unsaturated species Cp₂Fe₂(μ-CS)(μ-CO)₂ and Cp₂Fe₂(μ-CS)₂(μ-CO) are predicted to have triply bridged triplet spin state structures with FeFe double bonds of lengths 2.26 Å, analogous to the experimentally known triplet (Me₅C₅)₂Fe₂(μ-CO)₃. However, low-lying singlet Cp₂Fe₂(CS)(CO)₂ and Cp₂Fe₂(CS)₂(CO) structures with four-electron donor bridging η²-μ-CS groups and formal Fe-Fe single bonds are also found. The lowest lying Cp₂Fe₂(CS)(CO) and Cp₂Fe₂(CS)₂ structures have two bridging groups and very short FeFe distances of ∼2.14 Å, suggesting formal triple bonds. Several higher energy four-electron donor η²-μ-CS bridged structures are also found for Cp₂Fe₂(CS)(CO) and Cp₂Fe₂(CS)₂. In addition, singlet and triplet structures are found for Cp₂Fe₂(CS)₂ in which the two CS ligands have coupled to form a bridging SCCS group with a carbon-carbon bond. Only a η²-μ-CS bridged singlet structure is predicted for Cp₂Fe₂(CS), rather than the normal bridged structure with a FeFe quadruple bond such as that predicted for the carbonyl analog Cp₂Fe₂(CO).     

EPR properties of a g=2 broad signal trapped in an S1 state in Ca-depleted Photosystem II

We investigated a new EPR signal that gives a broad line shape around g=2 in Ca²⁺-depleted Photosystem (PS) II. The signal was trapped by illumination at 243 K in parallel with the formation of Y_Z. The ratio of the intensities between the g=2 broad signal and the Y_Z signal was 1:3, assuming a Gaussian line shape for the former. The g=2 broad signal and the Y_Z signal decayed together in parallel with the appearance of the S₂ state multiline at 243 K. The g=2 broad signal was assigned to be an intermediate S₁X state in the transition from the S₁ to the S₂ state, where X represents an amino acid radical nearby manganese cluster, such as D1-His337. The signal is in thermal equilibrium with Y_Z. Possible reactions in the S state transitions in Ca²⁺-depleted PS II were discussed.     

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l₁-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.     

Electrochemical monitoring of chlorhexidine digluconate effect on polyelectrolyte immobilized bacteria and kinetic cell adhesion

The electrochemical impedance spectroscopy (EIS) technique has been used as a sensitive method to explore the effect of antibacterial molecules on immobilized bacteria and biofilm formation. In this work, we describe the electrochemical spectroscopy as a powerful method to monitor the effect of Chlorhexidine Digluconate (CHX-Dg) on polyelectrolyte immobilized Escherichia coli K12 MG1655 and the kinetics of cell adhesion on gold electrodes. The experimental impedance data were modelised with a Zview program to find the best equivalent electrical circuit and analyse its parameter's properties. Polyelectrolyte multilayer formation on the electrode surface and bacteria immobilization greatly increased the electron-transfer resistance (R_et) and reduced the constant phase element (CPE_dl). The effect of CHX-Dg was studied in a 0.5 × 10⁻⁴ mmol l⁻¹ to 0.5 mmol l⁻¹ range. The relation between the evolution of R_et and CHX-Dg concentration was found to be negatively correlated. When CHX-Dg was added, the electrochemical monitoring of the bacterial kinetic adhesion showed that the electrode's capacity (C_P) variation remained stable, demonstrating that the addition of CHX-Dg in the broth inhibited bacterial adhesion.     

Theoretical series elastic element length in Rana pipiens sartorius muscles

Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dl_s, from the relation, See PDF for Equation From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (P₀ - P)/T for dP/dt and (P₀ - P)/(P + a) times b for v, dP/dl_s = (P + a) /bT, where P < P₀, and a, b are constants for any lengths l ≤ l₀ (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, l₀, although the series elastic, l_s, and the contractile component, l_c, are changing, the total muscle length, l₀ remains fixed and therefore the time constant, T. Integrating, See PDF for Equation the stress-strain relation for the series elastic element, See PDF for Equation is obtained; l_sc0 - l_s + l_c0where l_co equals the contractile component length for a muscle exerting a tension of P₀. For a given P/P₀, l_s is uniquely determined and must be the same whether on the isotonic or isometric length-tension-time curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.     

Improvements to Hoang et al.'s method for measuring passive length–tension properties of human gastrocnemius muscle in vivo

While the passive mechanical properties of a musculo-articular complex can be determined using the relationship between the articular angle and the passive torque developed in resistance to motion, the properties of different structures of the musculo-articular complex cannot be easily assessed. Recently, an elegant method has been proposed to estimate the passive length–tension properties of gastrocnemius muscle–tendon unit (Hoang et al., 2005). In the present paper, two improvements of this method are proposed to decrease the number of parameters required to assess the passive length–tension relationship from 9 to 2. Furthermore, these two parameters have physical meaning as they represent a passive muscle–tendon stiffness index (α) and the muscle–tendon slack length (l₀). α and l₀ are relevant clinical parameters to study the chronic effects of aging, training protocols or neuromuscular pathologies on the passive mechanical properties of the muscle–tendon unit. Eight healthy subjects performed passive loading/unloading cycles at 5°/s with knee angle at 6 knee angles to assess the torque–angle relationships and to apply the modified method. Numerical optimization was used to minimize the squared error between the experimental and the modeled relationships. The experiment was performed twice to assess the reliability of α and l₀ across days. The results showed that the reliability of the two parameters was good (α: ICC=0.82, SEM=6.1 m^?1, CV=6.3% and l₀: ICC=0.83, SEM=0.29 cm, CV=0.9%). Using a sensitivity analysis, it was shown that the numerical solution was unique. Overall, the findings may provide increased interest in the method proposed by Hoang et al. (2005).     

Development of a method for reconstruction of crowded NMR spectra from undersampled time-domain data

NMR is a unique methodology for obtaining information about the conformational dynamics of proteins in heterogeneous biomolecular systems. In various NMR methods, such as transferred cross-saturation, relaxation dispersion, and paramagnetic relaxation enhancement experiments, fast determination of the signal intensity ratios in the NMR spectra with high accuracy is required for analyses of targets with low yields and stabilities. However, conventional methods for the reconstruction of spectra from undersampled time-domain data, such as linear prediction, spectroscopy with integration of frequency and time domain, and analysis of Fourier, and compressed sensing were not effective for the accurate determination of the signal intensity ratios of the crowded two-dimensional spectra of proteins. Here, we developed an NMR spectra reconstruction method, “conservation of experimental data in analysis of Fourier” (Co-ANAFOR), to reconstruct the crowded spectra from the undersampled time-domain data. The number of sampling points required for the transferred cross-saturation experiments between membrane proteins, photosystem I and cytochrome b ₆ f, and their ligand, plastocyanin, with Co-ANAFOR was half of that needed for linear prediction, and the peak height reduction ratios of the spectra reconstructed from truncated time-domain data by Co-ANAFOR were more accurate than those reconstructed from non-uniformly sampled data by compressed sensing.     

A Stochastic Model for Detecting Overlapping and Hierarchical Community Structure

Community detection is a fundamental problem in the analysis of complex networks. Recently, many researchers have concentrated on the detection of overlapping communities, where a vertex may belong to more than one community. However, most current methods require the number (or the size) of the communities as a priori information, which is usually unavailable in real-world networks. Thus, a practical algorithm should not only find the overlapping community structure, but also automatically determine the number of communities. Furthermore, it is preferable if this method is able to reveal the hierarchical structure of networks as well. In this work, we firstly propose a generative model that employs a nonnegative matrix factorization (NMF) formulization with a l_2,1 norm regularization term, balanced by a resolution parameter. The NMF has the nature that provides overlapping community structure by assigning soft membership variables to each vertex; the l_2,1 regularization term is a technique of group sparsity which can automatically determine the number of communities by penalizing too many nonempty communities; and hence the resolution parameter enables us to explore the hierarchical structure of networks. Thereafter, we derive the multiplicative update rule to learn the model parameters, and offer the proof of its correctness. Finally, we test our approach on a variety of synthetic and real-world networks, and compare it with some state-of-the-art algorithms. The results validate the superior performance of our new method.     

Resolution and noise performance of sparse view X-ray CT reconstruction via Lp-norm regularization

ObjectivesAdaptive steepest descent projection onto convex sets (ASD-POCS) algorithms with Lp-norm (0 < p ≤ 1) regularization have shown great promise in sparse-view X-ray CT reconstruction. However, the difference in p value selection can lead to varying algorithm performance of noise and resolution. Therefore, it is imperative to develop a reliable method to evaluate the resolution and noise properties of the ASD-POCS algorithms under different Lp-norm priors.MethodsA comparative performance evaluation of ASD-POCS algorithms under different Lp-norm (0 < p ≤ 2) priors were performed in terms of modulation transfer function (MTF), noise power spectrum (NPS) and noise equivalent quanta (NEQ). Simulation data sets from the EGSnrc/BEAMnrc Monte Carlo system and an actual mouse data set were used for algorithms comparison.ResultsA considerable MTF improvement can be achieved with the decrement of p. L1 regularization based algorithm obtains the best noise performance, and shows superiority in NEQ evaluation. The advantage of L1-norm prior is also confirmed by the reconstructions from the actual mouse data set through contrast to noise ratio (CNR) comparison.ConclusionAlthough the ASD-POCS algorithms using small Lp-norm (p ≤ 0.5) priors yield a higher MTF than do the high Lp-norms, the best noise-resolution performance is achieved when p is between 0.8 and 1. The results are expected to be a reference to the choice of p in Lp-norm (0 < p ≤ 2) regularization.     

Propagation of Biochirality: Crossovers and Nonclassical Crystallization Kinetics of Aspartic Acid in Water

All experimental procedures discussed could be treated as a screening tool for probing the existence of molecular association among the chiral molecules and the solvent system. The molecular association phases of a racemic conglomerate solution (CS) and a racemic compound solution (RCS), and the templating effect of aspartic acid solid surface were observed to minimize the chance of redissolving racemic conglomerate and racemic compound aspartic acid in water and reforming an RCS in crossovers experiments. Only 1 %wt% of l‐aspartic acid was adequate enough to induce a transformation from a racemic compound aspartic acid to a racemic conglomerate aspartic acid. This would make the propagation of biochirality more feasible and sound. However, tetrapeptide, (l‐aspartic acid)₄, failed to induce enantioseparation as templates purely by crystallization. Nonclassical crystallization theory was needed to take into account the existence of a CS. Fundamental parameters of the crystallization kinetics such as the induction time, interfacial energy, Gibbs energetic barrier, nucleation rate, and critical size of stable nuclei of: (i) racemic compound aspartic acid, (ii) racemic compound aspartic acid seeded with 1 %wt% l‐aspartic acid, (iii) racemic conglomerate aspartic acid, and (iv) l‐aspartic acid were evaluated and compared with different initial supersaturation ratios. Morphological studies of crystals grown from the crystallization kinetics were also carried out.Chirality 25:768–779, 2013. © 2013 Wiley Periodicals, Inc.     

Adaptive compressive learning for prediction of protein-protein interactions from primary sequence

Protein-protein interactions (PPIs) play an important role in biological processes. Although much effort has been devoted to the identification of novel PPIs by integrating experimental biological knowledge, there are still many difficulties because of lacking enough protein structural and functional information. It is highly desired to develop methods based only on amino acid sequences for predicting PPIs. However, sequence-based predictors are often struggling with the high-dimensionality causing over-fitting and high computational complexity problems, as well as the redundancy of sequential feature vectors. In this paper, a novel computational approach based on compressed sensing theory is proposed to predict yeast Saccharomyces cerevisiae PPIs from primary sequence and has achieved promising results. The key advantage of the proposed compressed sensing algorithm is that it can compress the original high-dimensional protein sequential feature vector into a much lower but more condensed space taking the sparsity property of the original signal into account. What makes compressed sensing much more attractive in protein sequence analysis is its compressed signal can be reconstructed from far fewer measurements than what is usually considered necessary in traditional Nyquist sampling theory. Experimental results demonstrate that proposed compressed sensing method is powerful for analyzing noisy biological data and reducing redundancy in feature vectors. The proposed method represents a new strategy of dealing with high-dimensional protein discrete model and has great potentiality to be extended to deal with many other complicated biological systems.     

On the elusive, non-emissive yet reactive, upper excited states of [(4,4′-bpy)Re(CO)3(dppz)]PF6 (dppz = dipyridil[3,2-a:2′3′-c]phenazine)

Gradual solvation of [(4,4′-bpy)Re^I(CO)₃(dppz)]⁺ (dppz = dipyridil[3,2-a:2′3′-c]phenazine) by water molecules causes a quenching of the emission in accordance with Perrin’s model of spheres. The calculated radius of the sphere, r = 2.6 ± 0.2 ?, is therefore very close to the distance from the Re center to the oxygen atom of the CO ligands, i.e., l = 2.73 ?. In addition, excited state reactions with TEA produce [(4,4′-bpy⁻)Re^I(CO)₃(dppz)] and [(4,4′-bpy)Re^I(CO)₃(dppz⁻)]. This experimental observation is inconsistent with the formation of the products in the lowest lying and emissive dppz-centered ³ππ* excited state. Jablonski schemes based on the participation of excited states other than the lowest ³ππ* excited state are proposed.     

Optimum substrate feed rate in fed-batch culture with the DO-stat method

In a fed-batch culture employing the DO-stat method, a rapid increase of dissolved oxygen concentration due to a lack of substrate (the DO signal) is used as an indicator for substrate feeding. The amount of substrate to be fed in response to the appearance of the DO signal is a very important factor for obtaining an optimal fed-batch culture. To select the optimum amount of substrate to be fed at the DO signal, a calculative procedure based on the growth yield, and the relationship between the specific growth rate and substrate concentration is proposed. This procedure is demonstrated in fed-batch cultures of Protaminobacter ruber (a methanol-utilizing bacterium) and Candida brassicae (an ethanol-utilizing yeast). The optimum feed rates calculated with the procedure, 2.5 ml (methanol/l/signal) for P. ruber and 5 ml (ethanol/l/signal) for C. brassicae, both gave good agreement with the cultivation results.