Non-negative Least Squares Research Articles

Расширение зоны покрытия при связи вне прямой видимости MIMO с использованием пассивных ретрансляторов

In MIMO communications, high buildings in cities and other obstructions can prevent the propagation of radio waves, resulting in blind spots and poor communications. This problem can be solved using passive repeaters, which, by distributing them in the communication environment, the blind spots can be accessed and the coverage area can be extended. The distribution of these repeaters in the MIMO communication should be optimized in order to maximally cover the target area. In this article, an approach based on non-negative least square (NNLS) algorithm is proposed for optimizing the distribution of the minimum number of repeaters in none-line-of sight (NLOS) MIMO communications. The proposed approach is implemented using passive repeaters consisting of two parabolic antennas connected through a flexible cable. The numerical analysis is performed to verify the validity of the proposed approach, and it is found that the proposed method helps to optimally distribute passive repeaters and extend coverage area with minimum number of repeaters.

Feasibility of intravoxel incoherent motion in the assessment of tumor microvasculature and blood-brain barrier integrity: a case-based evaluation of gliomas.

To evaluate the feasibility of intravoxel incoherent motion (IVIM) in assessing blood-brain barrier (BBB) integrity and microvasculature in tumoral tissue of glioma patients. Images from 8 high-grade and 4 low-grade glioma patients were acquired on a 3T MRI scanner. Acquisition protocol included pre- and post-contrast T1- and T2-weighted imaging, FLAIR, dynamic susceptibility contrast (DSC), and susceptibility-weighted imaging (SWI). In addition, IVIM was acquired with 15 b-values and fitted under the non-negative least square (NNLS) model to output the diffusion (D) and pseudo-diffusion (D*) coefficients, perfusion fraction (f), and f times D* (fD*) maps. IVIM perfusion-related maps were sensitive to (1) blood flow and perfusion alterations within the microvasculature of brain tumors, in agreement with intra-tumoral susceptibility signal (ITSS); (2) enhancing areas of BBB breakdown in agreement with DSC maps as well as areas of BBB abnormality that was not detected on DSC maps; (3) enhancing perfusion changes within edemas; (4) detecting early foci of increased perfusion within low-grade gliomas. The results suggest IVIM may be a promising approach to delineate tumor extension and progression in size, and to predict histological grade, which are clinically relevant information that characterize tumors and guide therapeutic decisions in patients with glioma.

Raman Imaging as a powerful tool to elucidate chemical processes in a matrix: Medicated chewing gums with nicotine

Extruded medicated chewing gum is a convenient but complex drug delivery system. Description of gum ingredient distribution and interactions in literature is sparse, but fundamental in product characterization and stability prediction. Although Raman spectroscopy has been used for such characterization of numerous dosage forms, its applicability to medicated chewing gum has not been studied until now. The objective was to investigate the applicability of confocal Raman imaging on chewing gum for identification and distribution of excipients and the model drug nicotine, including changes occurring during shelf life. A sample preparation protocol was composed to present an even surface of a gum cross section without altering the gum matrix texture. High-resolution Raman maps were obtained by Non Negative Least Squares (NNLS) analysis for a reference gum and gums stored for 6 months at mild (25 °C/60% RH) and accelerated (40 °C/75% RH) conditions. Additional Empty Modelling™ analysis confirmed the results of NNLS. The NNLS analysis located nicotine and the following excipients: gum base, calcium carbonate, sorbitol, xylitol, sodium carbonate, sodium bicarbonate and talc in distinct domains of the reference sample. Changes of the sample stored at accelerated conditions was discovered as sodium carbonate was not observed in this sample. Additionally, stereo light microscopy showed changes in product appearance and high-performance liquid chromatography confirmed formation of the oxidation product nicotine-1′-N-oxide in this sample. The gum formulation and its ingredients displayed characteristic Raman spectra, proving Raman imaging as a useful method for characterizing medicated chewing gums, including changes occurring during stability testing.

A minimum curvature algorithm for tomographic reconstruction of atmospheric chemicals based on optical remote sensing

Abstract. Optical remote sensing (ORS) combined with the computerized tomography (CT) technique is a powerful tool to retrieve a two-dimensional concentration map over an area under investigation. Whereas medical CT usually uses a beam number of hundreds of thousands, ORS-CT usually uses a beam number of dozens, thus severely limiting the spatial resolution and the quality of the reconstructed map. The smoothness a priori information is, therefore, crucial for ORS-CT. Algorithms that produce smooth reconstructions include smooth basis function minimization, grid translation and multiple grid (GT-MG), and low third derivative (LTD), among which the LTD algorithm is promising because of the fast speed. However, its theoretical basis must be clarified to better understand the characteristics of its smoothness constraints. Moreover, the computational efficiency and reconstruction quality need to be improved for practical applications. This paper first treated the LTD algorithm as a special case of the Tikhonov regularization that uses the approximation of the third-order derivative as the regularization term. Then, to seek more flexible smoothness constraints, we successfully incorporated the smoothness seminorm used in variational interpolation theory into the reconstruction problem. Thus, the smoothing effects can be well understood according to the close relationship between the variational approach and the spline functions. Furthermore, other algorithms can be formulated by using different seminorms. On the basis of this idea, we propose a new minimum curvature (MC) algorithm by using a seminorm approximating the sum of the squares of the curvature, which reduces the number of linear equations to half that in the LTD algorithm. The MC algorithm was compared with the non-negative least square (NNLS), GT-MG, and LTD algorithms by using multiple test maps. The MC algorithm, compared with the LTD algorithm, shows similar performance in terms of reconstruction quality but requires only approximately 65 % the computation time. It is also simpler to implement than the GT-MG algorithm because it directly uses high-resolution grids during the reconstruction process. Compared with the traditional NNLS algorithm, it shows better performance in the following three aspects: (1) the nearness of reconstructed maps is improved by more than 50 %, (2) the peak location accuracy is improved by 1–2 m, and (3) the exposure error is improved by 2 to 5 times. Testing results indicated the effectiveness of the new algorithm according to the variational approach. More specific algorithms could be similarly further formulated and evaluated. This study promotes the practical application of ORS-CT mapping of atmospheric chemicals.

AccuCor2: isotope natural abundance correction for dual-isotope tracer experiments

Stable isotope labeling techniques have been widely applied in the field of metabolomics and proteomics. Before the measured mass spectral data can be used for quantitative analysis, it must be accurately corrected for isotope natural abundance and tracer isotopic impurity. Despite the increasing popularity of dual-isotope tracing strategy such as 13C-15N or 13C-2H, there are no accurate tools for correcting isotope natural abundance for such experiments in a resolution-dependent manner. Here, we present AccuCor2 as an R-based tool to perform the correction for 13C-15N or 13C-2H labeling experiments. Our method uses a newly designed algorithm to construct the correction matrices that link labeling pattern and measured mass fractions, then use non-negative least-squares to solve the labeling patterns. Our results show that the dual-isotope experiments often require a mass resolution that is high enough to resolve 13C and 15N or 13C and 2H. Otherwise, the labeling pattern is not solvable. However, this mass resolution may not be sufficiently high to resolve other non-tracer elements such as oxygen or sulfur from the tracer elements. Therefore, we design AccuCor2 to perform the correction based on the actual mass resolution of the measurements. Using both simulated and experimental data, we show that AccuCor2 performs accurate and resolution-dependent correction for dual-isotope tracer data.The authors developed AccuCor2 as the first resolution-dependent method for accurate isotope natural abundance correction of experimental data generated from dual-isotope tracers. They show that such correction requires a minimum resolution to resolve tracer isotopologues. AccuCor2 showed improved accuracy more than previously developed tools, which assume infinite resolution of the instrument.

Frugal Coordinate Descent for Large-Scale NNLS

The Nonnegative Least Squares (NNLS) formulation arises in many important regression problems. We present a novel coordinate descent method which differs from previous approaches in that we do not explicitly maintain complete gradient information. Empirical evidence shows that our approach outperforms a state-of-the-art NNLS solver in computation time for calculating radiation dosage for cancer treatment problems.

Revisiting the T2 spectrum imaging inverse problem: Bayesian regularized non-negative least squares

Multi-echo T2 magnetic resonance images contain information about the distribution of T2 relaxation times of compartmentalized water, from which we can estimate relevant brain tissue properties such as the myelin water fraction (MWF). Regularized non-negative least squares (NNLS) is the tool of choice for estimating non-parametric T2 spectra. However, the estimation is ill-conditioned, sensitive to noise, and highly affected by the employed regularization weight. The purpose of this study is threefold: first, we want to underline that the apparently innocuous use of two alternative parameterizations for solving the inverse problem, which we called the standard and alternative regularization forms, leads to different solutions; second, to assess the performance of both parameterizations; and third, to propose a new Bayesian regularized NNLS method (BayesReg). The performance of BayesReg was compared with that of two conventional approaches (L-curve and Chi-square (X2) fitting) using both regularization forms. We generated a large dataset of synthetic data, acquired in vivo human brain data in healthy participants for conducting a scan-rescan analysis, and correlated the myelin content derived from histology with the MWF estimated from ex vivo data. Results from synthetic data indicate that BayesReg provides accurate MWF estimates, comparable to those from L-curve and X2, and with better overall stability across a wider signal-to-noise range. Notably, we obtained superior results by using the alternative regularization form. The correlations reported in this study are higher than those reported in previous studies employing the same ex vivo and histological data. In human brain data, the estimated maps from L-curve and BayesReg were more reproducible. However, the T2 spectra produced by BayesReg were less affected by over-smoothing than those from L-curve. These findings suggest that BayesReg is a good alternative for estimating T2 distributions and MWF maps.

A data-driven T2 relaxation analysis approach for myelin water imaging: Spectrum analysis for multiple exponentials via experimental condition oriented simulation (SAME-ECOS).

The decomposition of multi-exponential decay data into a T2 spectrum poses substantial challenges for conventional fitting algorithms, including non-negative least squares (NNLS). Based on a combination of the resolution limit constraint and machine learning neural network algorithm, a data-driven and highly tailorable analysis method named spectrum analysis for multiple exponentials via experimental condition oriented simulation (SAME-ECOS) was proposed. The theory of SAME-ECOS was derived. Then, a paradigm was presented to demonstrate the SAME-ECOS workflow, consisting of a series of calculation, simulation, and model training operations. The performance of the trained SAME-ECOS model was evaluated using simulations and six in vivo brain datasets. The code is available at https://github.com/hanwencat/SAME-ECOS. Using NNLS as the baseline, SAME-ECOS achieved over 15% higher overall cosine similarity scores in producing the T2 spectrum, and more than 10% lower mean absolute error in calculating the myelin water fraction (MWF), as well as demonstrated better robustness to noise in the simulation tests. Applying to in vivo data, MWF from SAME-ECOS and NNLS was highly correlated among all study participants. However, a distinct separation of the myelin water peak and the intra/extra-cellular water peak was only observed in the mean T2 spectra determined using SAME-ECOS. In terms of data processing speed, SAME-ECOS is approximately 30 times faster than NNLS, achieving a whole-brain analysis in 3 min. Compared with NNLS, the SAME-ECOS method yields much more reliable T2 spectra in a dramatically shorter time, increasing the feasibility of multi-component T2 decay analysis in clinical settings.

Developments in waveform unfolding of PMT signals in future IceCube extensions

Waveform unfolding, in which photomultiplier tube signals are expressed as a linear combination of single-photoelectron waveforms, is a useful processing method both for analysis and for data compression in the IceCube Neutrino Observatory. This processing is currently only possible with a cluster of computers on the surface, but improvements in embedded technology will make it possible to move this unfolding inside the digital optical modules for planned extensions of IceCube such as IceCube-Gen2. In order to meet power constraints, waveform unfolding is most efficiently implemented with field programmable gate arrays (FPGA). A non-negative least squares (NNLS) algorithm developed for use with FPGAs was modified to reproduce the results of the Lawson-Hanson NNLS algorithm that is currently used for waveform unfolding in IceCube. High Level Synthesis (HLS) tools were used to synthesize firmware directly from C code. This proceeding discusses the structure and performance of the modified NNLS algorithm that was developed, and demonstrates what can be accomplished with new FPGA synthesis tools.

Strategies for cellular deconvolution in human brain RNA sequencing data

Background: Statistical deconvolution strategies have emerged over the past decade to estimate the proportion of various cell populations in homogenate tissue sources like brain using gene expression data. However, no study has been undertaken to assess the extent to which expression-based and DNAm-based cell type composition estimates agree. Results: Using estimated neuronal fractions from DNAm data, from the same brain region (i.e., matched) as our bulk RNA-Seq dataset, as proxies for the true unobserved cell-type fractions (i.e., as the gold standard), we assessed the accuracy (RMSE) and concordance (R2) of four reference-based deconvolution algorithms: Houseman, CIBERSORT, non-negative least squares (NNLS)/MIND, and MuSiC. We did this for two cell-type populations - neurons and non-neurons/glia - using matched single nuclei RNA-Seq and mismatched single cell RNA-Seq reference datasets. With the mismatched single cell RNA-Seq reference dataset, Houseman, MuSiC, and NNLS produced concordant (high correlation; Houseman R2 = 0.51, 95% CI [0.39, 0.65]; MuSiC R2 = 0.56, 95% CI [0.43, 0.69]; NNLS R2 = 0.54, 95% CI [0.32, 0.68]) but biased (high RMSE, >0.35) neuronal fraction estimates. CIBERSORT produced more discordant (moderate correlation; R2 = 0.25, 95% CI [0.15, 0.38]) neuronal fraction estimates, but with less bias (low RSME, 0.09). Using the matched single nuclei RNA-Seq reference dataset did not eliminate bias (MuSiC RMSE = 0.17). Conclusions: Our results together suggest that many existing RNA deconvolution algorithms estimate the RNA composition of homogenate tissue, e.g. the amount of RNA attributable to each cell type, and not the cellular composition, which relates to the underlying fraction of cells.

Continuous diffusion spectrum computation for diffusion-weighted magnetic resonance imaging of the kidney tubule system

The use of rigid multi-exponential models (with a priori predefined numbers of components) is common practice for diffusion-weighted MRI (DWI) analysis of the kidney. This approach may not accurately reflect renal microstructure, as the data are forced to conform to the a priori assumptions of simplified models. This work examines the feasibility of less constrained, data-driven non-negative least squares (NNLS) continuum modelling for DWI of the kidney tubule system in simulations that include emulations of pathophysiological conditions. Non-linear least squares (LS) fitting was used as reference for the simulations. For performance assessment, a threshold of 5% or 10% for the mean absolute percentage error (MAPE) of NNLS and LS results was used. As ground truth, a tri-exponential model using defined volume fractions and diffusion coefficients for each renal compartment (tubule system: Dtubules , ftubules ; renal tissue: Dtissue , ftissue ; renal blood: Dblood , fblood ;) was applied. The impact of: (I) signal-to-noise ratio (SNR) =40-1,000, (II) number of b-values (n=10-50), (III) diffusion weighting (b-rangesmall =0-800 up to b-rangelarge =0-2,180 s/mm2), and (IV) fixation of the diffusion coefficients Dtissue and Dblood was examined. NNLS was evaluated for baseline and pathophysiological conditions, namely increased tubular volume fraction (ITV) and renal fibrosis (10%: grade I, mild) and 30% (grade II, moderate). NNLS showed the same high degree of reliability as the non-linear LS. MAPE of the tubular volume fraction (ftubules ) decreased with increasing SNR. Increasing the number of b-values was beneficial for ftubules precision. Using the b-rangelarge led to a decrease in MAPE ftubules compared to b-rangesmall. The use of a medium b-value range of b=0-1,380 s/mm2 improved ftubules precision, and further bmax increases beyond this range yielded diminishing improvements. Fixing Dblood and Dtissue significantly reduced MAPE ftubules and provided near perfect distinction between baseline and ITV conditions. Without constraining the number of renal compartments in advance, NNLS was able to detect the (fourth) fibrotic compartment, to differentiate it from the other three diffusion components, and to distinguish between 10% vs. 30% fibrosis. This work demonstrates the feasibility of NNLS modelling for DWI of the kidney tubule system and shows its potential for examining diffusion compartments associated with renal pathophysiology including ITV fraction and different degrees of fibrosis.

A multi-inversion-recovery magnetic resonance fingerprinting for multi-compartment water mapping

PurposeThis study aimed at introducing short-T1/T2 compartment to MR fingerprinting (MRF) at 3 T. Water that is bound to myelin macromolecules have significantly shorter T1 and T2 than free water and can be distinguished from free water by multi-compartment analysis. MethodsWe developed a new multi-inversion-recovery (mIR) water mapping-MRF based on an unbalanced steady-state coherent sequence (FISP). mIR pulses with an interval of 400 or 500 repetition times (TRs) were inserted into the conventional FISP MRF sequence. Data from our proposed mIR MRF was used to quantify different compartments, including myelin water, gray matter free water, and white matter free water, of brain water by virtue of the iterative non-negative least square (NNLS) with reweighting. Three healthy volunteers were scanned with mIR MRF on a clinical 3 T MRI. ResultsUsing an extended phase graph simulation, we found that our proposed mIR scheme with four IR pulses allowed differentiation between short and long T1/T2 components. For in vivo experiments, we achieved the quantification of myelin water, gray matter water, and white matter water at an image resolution of 1.17 × 1.17 × 5 mm3/pixel. As compared to the conventional MRF technique with single IR, our proposed mIR improved the detection of myelin water content. In addition, mIR MRF using spiral-in/out trajectory provided a higher signal level compared with that with spiral-out trajectory. Myelin water quantification using mIR MRF with 4 IR and 5 IR pulses were qualitatively similar. Meanwhile, 5 IR MRF showed fewer artifacts in myelin water detection. ConclusionWe developed a new mIR MRF sequence for the rapid quantification of brain water compartments.

Compact computational spectrometer using a solid wedged low finesse etalon.

A novel, to the best of our knowledge, two-layer hybrid solid wedged etalon was fabricated and combined with a traditional imager to make a compact computational spectrometer. The hybrid wedge, comprised of ${{\rm Nb}_2}{{\rm O}_5}$ and Infrasil 302, was designed to operate from 0.4-2.4 µm. Initial demonstrations, however, used a complementary metal-oxide semiconductor (CMOS) imager and demonstrated operation from 0.4-0.9 µm with spectral resolutions ${\lt}\;{30}\;{{\rm cm}^{- 1}}$ from single snapshots. The computational spectrometer itself operates similarly to a spatial Fourier transform spectrometer (FTIR), but rather than use conventional Fourier-based methods or assumptions, the spectral reconstruction used a non-negative least-squares fitting algorithm based on analytically computed wavelength response vectors determined from extracted physical thicknesses across the entire two-dimensional wedge. This new computational technique resulted in performance and spectral resolutions exceeding those that could be achieved from Fourier processing techniques applied to this wedge etalon. With an additional imaging lens and translational scanning, the system can be converted into a hyperspectral imager.

Inverse Problem Analysis in Magnetic Nanoparticle Tomography Using Minimum Variance Spatial Filter

In magnetic nanoparticle tomography (MNT), the reduction of artifacts and the calculation time can be used to estimate the position of magnetic nanoparticles (MNPs). A non-negative least-squares (NNLS) inverse problem analysis has been used in MNT systems for this task. However, due to the presence of measurement noise and the high sensitivity of the NNLS method, it often estimates certain MNPs inaccurately, i.e., it generates artifacts. In addition, its calculation time is very high. In this study, we applied the minimum variance spatial filter (MV-SF) inverse problem analysis to MNT and estimated the position of an MNP sample containing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\mu \text{g}$ </tex-math></inline-formula> of Fe. Using the MV-SF method, MNP samples placed at a depth of 25–40 mm were observed to have no artifacts. Moreover, the MV-SF method was also observed to be faster than the NNLS method by a factor of approximately 20. These results verify the feasibility of the MV-SF method for estimating the MNP positions in an MNT system.

A Golden Ratio Primal–Dual Algorithm for Structured Convex Optimization

We design, analyze and test a golden ratio primal–dual algorithm (GRPDA) for solving structured convex optimization problem, where the objective function is the sum of two closed proper convex functions, one of which involves a composition with a linear transform. GRPDA preserves all the favorable features of the classical primal–dual algorithm (PDA), i.e., the primal and the dual variables are updated in a Gauss–Seidel manner, and the per iteration cost is dominated by the evaluation of the proximal point mappings of the two component functions and two matrix-vector multiplications. Compared with the classical PDA, which takes an extrapolation step, the novelty of GRPDA is that it is constructed based on a convex combination of essentially the whole iteration trajectory. We show that GRPDA converges within a broader range of parameters than the classical PDA, provided that the reciprocal of the convex combination parameter is bounded above by the golden ratio, which explains the name of the algorithm. An $$\mathcal {O}(1/N)$$ ergodic convergence rate result is also established based on the primal–dual gap function, where N denotes the number of iterations. When either the primal or the dual problem is strongly convex, an accelerated GRPDA is constructed to improve the ergodic convergence rate from $$\mathcal {O}(1/N)$$ to $$\mathcal {O}(1/N^2)$$ . Moreover, we show for regularized least-squares and linear equality constrained problems that the reciprocal of the convex combination parameter can be extended from the golden ratio to 2 and meanwhile a relaxation step can be taken. Our preliminary numerical results on LASSO, nonnegative least-squares and minimax matrix game problems, with comparisons to some state-of-the-art relative algorithms, demonstrate the efficiency of the proposed algorithms.

Non-Bayesian Activity Detection, Large-Scale Fading Coefficient Estimation, and Unsourced Random Access With a Massive MIMO Receiver

In this paper, we study the problem of user activity detection and large-scale fading coefficient estimation in a random access wireless uplink with a massive MIMO base station with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$-dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_\text{tot}$ is much larger than $L$ but at each time slot only $K_a<<K_\text{tot}$ of them are active. Previous results, based on compressed sensing, require that $K_a\leq L$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and unsourced random access. In this work we show that such limitation can be overcome when the number of base station antennas $M$ is sufficiently large. We also provide two algorithms. One is based on Non-Negative Least-Squares, for which the above scaling result can be rigorously proved. The other consists of a low-complexity iterative componentwise minimization of the likelihood function of the underlying problem. Finally, we use the discussed approximated ML algorithm as the decoder for the inner code in a concatenated coding scheme for unsourced random access, a grant-free uncoordinated multiple access scheme where all users make use of the same codebook, and the massive MIMO base station must come up with the list of transmitted messages irrespectively of the identity of the transmitters. We show that reliable communication is possible at any $E_b/N_0$ provided that a sufficiently large number of base station antennas is used, and that a sum spectral efficiency in the order of $\mathcal{O}(L\log(L))$ is achievable.

Monitoring Changes in Biochemical and Biomechanical Properties of Collagenous Tissues Using Label-Free and Nondestructive Optical Imaging Techniques

We demonstrate the ability of nondestructive optical imaging techniques such as second-harmonic generation (SHG), two-photon fluorescence (TPF), fluorescence lifetime imaging (FLIM), and Raman spectroscopy (RS) to monitor biochemical and mechanical alterations in tissues upon collagen degradation. Decellularized equine pericardium (EP) was treated with 50 μg/mL bacterial collagenase at 37 °C for 8, 16, 24, and 32 h. The SHG ratio (defined as the normalized ratio between SHG and TPF signals) remained unchanged for untreated EP (stored in phosphate-buffered solution (PBS)), whereas treated EP showed a trend of a decreasing SHG ratio with increasing collagen degradation. In the fluorescence domain, treated EP experienced a red-shifted emission and the fluorescence lifetime had a trend of decreasing lifetime with increasing collagen digestion. RS monitors collagen degradation, the spectra had less intense Raman bands at 814, 852, 938, 1242, and 1270 cm-1. Non-negative least-squares (NNLS) modeling quantifies collagen loss and relative increase of elastin. The Young's modulus, derived from atomic force microscope-based nanoindentation experiments, showed a rapid decrease within the first 8 h of collagen degradation, whereas more gradual changes were observed for optical modalities. We conclude that optical imaging techniques like SHG, RS, and FLIM can monitor collagen degradation in a label-free manner and coarsely access mechanical properties in a nondestructive manner.

Spectral diffusion analysis of kidney intravoxel incoherent motion MRI in healthy volunteers and patients with renal pathologies.

To assess the feasibility of measuring tubular and vascular signal fractions in the human kidney using nonnegative least-square (NNLS) analysis of intravoxel incoherent motion data collected in healthy volunteers and patients with renal pathologies. MR imaging was performed at 3 Tesla in 12 healthy subjects and 3 patients with various kidney pathologies (fibrotic kidney disease, failed renal graft, and renal masses). Relative signal fractions f and mean diffusivities of the diffusion components in the cortex, medulla, and renal lesions were obtained using the regularized NNLS fitting of the intravoxel incoherent motion data. Test-retest repeatability of the NNLS approach was tested in 5 volunteers scanned twice. In the healthy kidneys, the NNLS method yielded diffusion spectra with 3 distinguishable components that may be linked to the slow tissue water diffusion, intermediate tubular and vascular flow, and fast blood flow in larger vessels with the relative signal fractions, fslow , finterm and ffast , respectively. In the pathological kidneys, the diffusion spectra varied substantially from those acquired in the healthy kidneys. Overall, the renal cyst showed substantially higher finterm and lower fslow , whereas the fibrotic kidney, failed renal graft, and renal cell carcinoma demonstrated the opposite trend. NNLS-based intravoxel incoherent motion could potentially become a valuable tool in assessing changes in tubular and vascular volume fractions under pathophysiological conditions.

Dwell Time Algorithm Based on Bounded Constrained Least Squares Under Dynamic Performance Constraints of Machine Tool in Deterministic Optical Finishing

The dwell time algorithm is one of the most important techniques within the deterministic optical surfacing technologies. The existing dwell time algorithms are generally based on non-negative least squares (NNLS) without considering the dynamic performance constraints of machine tools. This is a circumstance that leads to poor convergence accuracy. In this paper, a dwell time algorithm, based on bounded constrained least-squares (BCLS) under dynamic performance constraints of the machine tool, has been developed. The upper and lower constraints of the dwell time model could be derived through the acceleration and deceleration mechanism of the CNC (Computer Numerical Control) machine tools. A two-metric projection Newton iteration algorithm was used to solve the large-scale dwell time model, which greatly improved the computation efficiency. The results of the experiments and simulations showed that the proposed algorithm will give a very high convergence accuracy for optical finishing with machine tools with different dynamic performances. When the machine acceleration was set to a value as low as 0.1 g, the accuracies of the surface figures PV (Peak-to-Valley) and RMS (Root Mean Square) till improved by 40.8% and 55.2%, respectively, when using the BCLS algorithm. The influences of different dynamic performances of the machine tools on the dwell time solutions have also been investigated, which will provide a good guidance in the design of deterministic polishing machine tools.

Comparison of non-parametric T2 relaxometry methods for myelin water quantification

Multi-component T2 relaxometry allows probing tissue microstructure by assessing compartment-specific T2 relaxation times and water fractions, including the myelin water fraction. Non-negative least squares (NNLS) with zero-order Tikhonov regularization is the conventional method for estimating smooth T2 distributions. Despite the improved estimation provided by this method compared to non-regularized NNLS, the solution is still sensitive to the underlying noise and the regularization weight. This is especially relevant for clinically achievable signal-to-noise ratios. In the literature of inverse problems, various well-established approaches to promote smooth solutions, including first-order and second-order Tikhonov regularization, and different criteria for estimating the regularization weight have been proposed, such as L-curve, Generalized Cross-Validation, and Chi-square residual fitting. However, quantitative comparisons between the available reconstruction methods for computing the T2 distribution, and between different approaches for selecting the optimal regularization weight, are lacking. In this study, we implemented and evaluated ten reconstruction algorithms, resulting from the individual combinations of three penalty terms with three criteria to estimate the regularization weight, plus non-regularized NNLS. Their performance was evaluated both in simulated data and real brain MRI data acquired from healthy volunteers through a scan-rescan repeatability analysis. Our findings demonstrate the need for regularization. As a result of this work, we provide a list of recommendations for selecting the optimal reconstruction algorithms based on the acquired data. Moreover, the implemented methods were packaged in a freely distributed toolbox to promote reproducible research, and to facilitate further research and the use of this promising quantitative technique in clinical practice.