Total Least Squares Research Articles

Medical image fusion by sparse-based modified fusion framework using block total least-square update dictionary learning algorithm.

Purpose: The technique of fusing or integrating medical images collected from single and various modalities is known as medical image fusion. This is done to improve the quality of the images and combine information from several medical images. The whole procedure aids medical practitioners in gaining correct information from single images. Image fusion is one of the fastest-growing research topics in the medical imaging field. Sparse modeling is a popular signal representation technique used for image fusion with different dictionary learning approaches. We propose a medical image fusion with sparse representation (SR) and block total least-square (BLOTLESS) update dictionary learning. Approach: The domain of dictionary learning is the most significant research domain related to SR. An efficient dictionary increases the effectiveness of sparse modeling. Due to SR being an ongoing interesting research area, the medical image fusion process is done with a modified image fusion framework with recently developed BLOTLESS update dictionary learning. Results: The experimental results are compared for the image fusion process using other state-of-the-art dictionary learning algorithms, such as simultaneous codeword optimization, method of optimal directions, and K-singular value decomposition. The effectiveness of the algorithm is evaluated based on image fusion quantitative parameters. Results show that the BLOTLESS update dictionary algorithm is a promising modification for the sparse-based image fusion with its applicability in the fusion of images related to different diseases. Conclusions: The experiments and results show that the dictionary learning algorithm plays an important role in the sparse-based image fusion general framework. The fusion results also show that the proposed improved image fusion framework for medical images is promising compared with frameworks with other dictionary learning algorithms. As an application, it is also used as a tool for the fusion of different modularities of images related to brain tumor and glioma.

On the choice of TLS versus OLS in climate signal detection regression

Total least squares (TLS) or multivariate orthogonal regression is widely used as a remedy for attenuation bias in climate signal detection or “optimal fingerprinting” regression. But under some circumstances it overcorrects and imparts an upward bias, as well as generating extremely unstable and imprecise coefficient estimates. While there has been increasing attention paid recently to the validity of TLS-based confidence intervals, there has been no corresponding examination of coefficient bias problems. This note explains why they are pertinent and presents a Monte Carlo simulation to illustrate the hazards of using TLS in a signal detection application without testing whether the modeling context makes it a suitable choice. TLS is not automatically preferred over OLS even when explanatory variables are believed to contain random errors. Notably it can be sufficiently biased to cause false positives when explanatory signals are negatively correlated, and the bias gets worse as the signal-noise ratio on the explanatory variables rises. Additionally TLS should not be used on its own for climate signal detection inferences since if the no-signal null is true, TLS is generally inconsistent whereas OLS attenuation bias disappears.

Thoracopelvic Covariation Across Ontogeny in Humans

Clarifying human thoracopelvic covariation patterns can contribute to an understanding of body shape evolution. Previous research has shown that although adult human males and females share a common thoracopelvic covariation pattern, males tend to exhibit mediolaterally wide thoraces and narrow pelves, and females tend to exhibit mediolaterally narrow thoraces and wide pelves (2020 Am J Phys Anthropol 173(3) 514‐534). The current study tests for sex differences in thoracopelvic covariation across ontogeny.I analyzed decedent computed tomography data from the Center for Forensic Imaging at the University of New Mexico with a sample of 44 females and 48 males, aged 0‐21 years. I used SlicerMorph to collect three‐dimensional landmark coordinate data representing thoracic and pelvic shapes as well as R geomorph and Morpho for geometric morphometric analyses. After separate Generalized Procrustes Analyses on the pelvis and thorax, I analyzed thoracopelvic covariation with two‐block partial least squares analysis. To compare covariation magnitudes, I tested effect sizes of sex‐specific two‐block partial least squares. I assessed sex‐specific covariation patterns by projecting the male data into the female two‐block partial least squares analysis and then comparing the slopes of sex‐specific data via major axis regressions and the smatr R package.Results from the two‐block partial least squares analyses indicate significant covariation between the thorax and pelvis in females and males (p=0.001). The first latent variables explain 94.47% and 94.40% of the total covariation in the female and male samples, respectively. In both sexes, as the thorax becomes less pyramidal and more barrel‐shaped with development, the pelvis becomes more anteroposteriorly elongated. The sex‐specific two‐block partial least squares analyses do not exhibit significantly different magnitudes of thoracopelvic covariation. Slope comparison between sexes does not indicate significantly different patterns of thoracopelvic covariation.Previous research suggests that adult thoracopelvic covariation is driven by sex differences. The current study shows that subadult thoracopelvic covariation tracks with growth and development in both sexes, which is expected in the ontogenetic sample. Subadult females and males do not exhibit significantly different magnitudes nor patterns of thoracopelvic covariation. Processes such as sagittal balance of the upper body over the pelvis may influence thoracopelvic covariation.

Influence of Leaf Age on the Scaling Relationships of Lamina Mass vs. Area.

Leaf lamina mass and area are closely correlated with the photosynthetic capacity and competitive ability of plants, whereas leaf age has been demonstrated to affect physiological processes such as photosynthesis. However, it remains unknown whether the lamina mass vs. area scaling relationship is influenced by leaf age, which is important for understanding plant adaptive strategies and, more broadly, resource utilization and growth. We measured the leaf functional traits of five leaf-age groups of Photinia × fraseri for a total of 1,736 leaves. ANOVA followed by Tukey’s honestly significant difference test was used to compare the functional traits among the five leaf-age groups. Reduced major axis regression protocols were used to fit the scaling relationship between lamina mass and area, and the bootstrap percentile method was used to compare the lamina mass vs. area scaling relationships among the leaf-age groups. Lamina area, and the ratio of lamina dry mass to lamina fresh mass increased with increasing leaf age. Lamina fresh mass per unit area, and lamina dry mass per unit area both exhibited a parabolic-like trend as leaf age increased, i.e., at the leaf maturation stage, it showed a slight but significant decline. The phenomenon called diminishing returns were confirmed by each of the five leaf-age groups, i.e., all of the numerical values of the scaling exponents of lamina mass vs. area were significantly greater than 1. There were significant differences in the scaling exponents of lamina mass vs. area for the leaves across different sampling times. The scaling exponents were lower at the early rapid growth stage, indicating a lower cost for increasing leaf area compared to the leaf maturation stage. These data are consistent with leaves undergoing a transition from resource acquisition to resource conservation in the process of their development and growth.

Improvement in fatigue and sleep measures with the dual orexin receptor antagonist lemborexant in adults with insomnia disorder

ABSTRACT Objective Fatigue is a common symptom in patients with insomnia. This analysis evaluated whether treatment of nighttime symptoms of insomnia with a dual orexin receptor antagonist, lemborexant, might also reduce fatigue. Methods Analyses were conducted of two phase 3 studies of subjects with insomnia disorder. Subjects received placebo, lemborexant 5 mg, or lemborexant 10 mg in the 12-month (6 months placebo-controlled) Study E2006-G000-303 (Study 303: SUNRISE-2) of adults (N = 949; full analysis set [FAS]), and the 1-month, placebo- and active-controlled Study E2006-G000-304 (Study 304; SUNRISE-1) of older adults (females ≥55 years, males ≥65 years) (N = 1006; FAS). Fatigue was assessed using the Fatigue Severity Scale (FSS). Patient-reported sleep onset and maintenance endpoints were analyzed using data from electronic sleep diaries. Results Lemborexant significantly reduced subject-reported fatigue versus placebo over a 6-month treatment period (FSS total score least-squares mean treatment difference of −2.50 for 5 mg and −2.56 for 10 mg of lemborexant; p < 0.05 for both). This reduction was sustained over 12 months of lemborexant in both the overall population and in subjects with clinically meaningful fatigue (FSS total score ≥36) at baseline. Improvements in fatigue over time positively correlated with improvements in sleep onset and maintenance parameters. Improvements in sleep quality were evident as early as 1 week after lemborexant treatment, whereas longer-term treatment (>1 month) may be needed for improvements in insomnia-related fatigue. Conclusions In addition to improving sleep onset and sleep maintenance in subjects with insomnia disorder, lemborexant provides further benefit by reducing daytime fatigue. Clinical trial registration https://clinicaltrials.gov/ct2/show/NCT02952820 and https://clinicaltrials.gov/ct2/show/NCT02783729 Abbreviations DSM-5 = Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition; FSS = Fatigue Severity Scale; ICSD-3 = International Classification of Sleep Disorders, Third Edition; LSM = least squares mean; sSE = subjective sleep efficiency; sSOL = subjective sleep onset latency; sTST = subjective total sleep time; sWASO = subjective sleep after wake onset.

Ground Maneuvering Target Focusing via High-Order Phase Correction in High-Squint Synthetic Aperture Radar

Moving target imaging in high-squint synthetic aperture radar (SAR) shows great potential for reconnaissance and surveillance tasks. For the desired resolution, high-squint SAR has a long-time coherent processing interval (CPI). In this case, the maneuvering motion of the moving target usually causes high-order phase terms in the echoed data, which cannot be neglected for precise focusing. Many ground moving target imaging (GMTIm) algorithms have been proposed in the literature, but some high-order phase terms remain uncompensated in high-squint SAR. For this problem, a high-order phase correction-based GMTIm (HPC-GMTIm) method is proposed in this paper. We assumed that the target of interest has a constant velocity in the subaperture CPI, but maneuvering motion parameters for the whole CPI. Within the short subaperture CPI, the target signal can be simplified as a three-order phase expression, and the instantaneous Doppler frequency (DF) was estimated by some time–frequency analysis tools, including the Hough transform and the fractional Fourier transform. For the whole CPI, the subaperture, the instantaneous DF was combined to form a total least-squares problem, outputting the undetermined phase coefficients. Using the proposed local-to-global processing chain, all high-order phase terms can be estimated and corrected, which outperforms existing methods. The effectiveness of the HPC-GMTIm method is demonstrated by real measured high-squint SAR data.

A DOA Tracking Method Based on Offset Compensation Using Nested Array

In this brief, DOA tracking using a nested array (NA) is discussed and a modified tracking method is proposed. Discrete Fourier transform (DFT) is firstly used to estimate DOAs at the beginning moment. Thereafter, we realize DOA tracking through compensating offsets of adjacent moments. Offsets can be obtained by total least squares (TLS), which is constructed via first-order Taylor expansion. Meanwhile, the noise component is taken into account to strengthen the robustness to noise influence, whose power can be estimated as a by-product. The proposed method is simple to implement and requires no data association operation with multiple DOAs. Compared with other state-of-art DOA tracking methods, it has much better DOA tracking performance while with medium complexity, which achieves a good compromise between performance and computational complexity. The feasibility of this approach is verified by experimental simulations.

Diminishing returns among lamina fresh and dry mass, surface area, and petiole fresh mass among nine Lauraceae species.

The phenomenon called "diminishing returns" refers to a scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ Aα>1 , where α is the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM). For each of 3268 leaves from nine Lauraceae species, FM, DM, A, and PFM were measured, and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species. The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r2 -values. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship. "Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more strongly with lamina mass than with area, suggesting that static (self) loading takes precedence over dynamic (wind) loading.

Rhizome trait scaling relationships are modulated by growth conditions and are linked to plant fitness.

Rhizomes are important organs allowing many clonal plants to persist and reproduce under stressful climates with longer rhizomes, indicating enhanced ability of the plants to spread vegetatively. We do not, however, know either how rhizome construction costs change with increasing length or how they vary with environmental conditions. We analysed the rhizome length vs. mass scaling relationship, the plasticity in the scaling relationships, their genetic basis and how scaling relationships are linked to plant fitness. We used data from 275 genotypes of a clonal grass Festuca rubra originating from 11 localities and cultivated under four contrasting climates. Data were analysed using standard major axis regression, mixed-effect regression models and a structural equation model. Rhizome construction costs increased (i.e. lower specific rhizome length) with increasing length. The trait scaling relationships were modulated by cultivation climate, and its effects also interacted with the climate of origin of the experimental plants. With increasing length, increasing moisture led to a greater increase in rhizome construction costs. Plants with lower rhizome construction costs showed significantly higher fitness. This study suggests that rhizome scaling relationships are plastic, but also show genetic differentiation and are linked to plant fitness. Therefore, to persist under variable environments, modulation in scaling relationships could be an important plant strategy.

A simple iterative algorithm based on weighted least-squares for errors-in-variables models: Examples of coordinate transformations

Abstract Although weighted total least-squares (WTLS) adjustment within the errors-in-variables (EIV) model is a rigorous method developed for parameter estimation, its exact solution is complicated since the matrix operations are extremely time-consuming in the whole repeated iteration process, especially when dealing with large data sets. This paper rewrites the EIV model to a similar Gauss–Markov model by taking the random error of the design matrix and observations into account, and reformulates it as an iterative weighted least-squares (IWLS) method without complicated theoretical derivation. IWLS approximates the “exact solution” of the general WTLS and provides a good balance between computational efficiency and estimation accuracy. Because weighted LS (WLS) method has a natural advantage in solving the EIV model, we also investigate whether WLS can directly replace IWLS and WTLS to implement the EIV model when the parameters in the EIV model are small. The results of numerical experiments confirmed that IWLS can obtain almost the same solution as the general WTLS solution of Jazaeri [21] and WLS can achieve the same accuracy as the general WTLS when the parameters are small.

Bigger cities better climate? Results from an analysis of urban areas in China

Continued urban population expansion will be a defining challenge for climate change mitigation, and global sustainability more generally, over the coming decades. In this context, an important but underexplored issue concerns the relationship between the scale of urban areas and their carbon emissions. This paper employs the urban Kaya relation and Reduced Major Axis regression to look at urban emission patterns in China from 2000 to 2016. Our results reveal that larger cities tend to have lower per capita emissions. Thus, population agglomeration may be able to contribute to climate change mitigation and a wider transition to sustainability. The inverse-U shape between carbon emissions and population size is found. In addition, we observe unique scaling patterns in different regions, revealing how the relationship between emissions and population can be influenced by economic geography. City consumption weakens the role of population agglomeration in reducing carbon emissions in the East region, therefore it should be placed top priority in carbon emissions mitigation. These findings are important for China which looks to achieve carbon neutrality by 2060 against the backdrop of intertwined interplay between population agglomeration and city consumption.

Semi-Passive Elements Assisted Channel Estimation for Intelligent Reflecting Surface-Aided Communications

In this paper, we propose a novel semi-passive elements-aided channel estimation framework for intelligent reflecting surface (IRS), where a small portion of IRS reflecting elements are able to process the received signal for facilitating the channel estimation. Specifically, the BS-IRS channel is estimated by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), while the user-IRS channels are estimated by combining the use of total least square (TLS) ESPRIT and multiple signal classification (MUSIC) methods. The required training time of the proposed channel estimation scheme is irrelevant to the number of IRS reflecting elements, thus substantially reducing the training overhead. Simulation results show the great advantages of our proposed scheme over both the conventional compressed sensing (CS)-based channel estimation and cascaded channel estimation schemes.

Comparison of pretreatment, preservation and determination methods for foliar pH of plant samples

Abstract To compare current methods of pretreatment/determination for plant foliar pH, we proposed a method for long-period sample preservation with little interference with the stability of foliar pH. Four hundred leaf samples from 20 species were collected and four methods of pH determination were used: refrigerated (stored at 4 °C for 4 days), frozen (stored at −16 °C for 4 days), oven-dried and fresh green-leaf pH (control). To explore the effects of different leaf:water mixing ratio on the pH determination results, we measured oven-dried green-leaf pH by leaf:water volume ratio of 1:8 and mass ratio of 1:10, and measured frozen senesced-leaf pH by mass ratio of 1:10 and 1:15. The standard major axis regression was used to analyze the relationship and the conversion equation between the measured pH with different methods. Foliar pH of refrigerated and frozen green leaves did not significantly differ from that of fresh green-leaf, but drying always overrated fresh green-leaf pH. During the field sampling, cryopreservation with a portable refrigerator was an advisable choice to get a precise pH. For long-duration field sampling, freezing was the optimal choice, and refrigeration is the best choice for the short-time preservation. The different leaf:water mixing ratio significantly influenced the measured foliar pH. High dilution reduced the proton concentration and increased the measured pH. Our findings provide the conversion relationships between the existing pretreatment and measurement methods, and establish a connection among pH determined by different methods. Our study can facilitate foliar pH measurement, thus contributing to understanding of this interesting plant functional trait.

Pansharpening based on total least squares regression and ratio enhancement

ABSTRACT The key of ratio enhancement (RE) is to synthesize a low-resolution panchromatic image. The grey-level distortion of the synthesized low-resolution image can distort a fused image. To tackle this problem, we propose a pansharpening method based on total least-squares regression and ratio enhancement (TLSR-RE). This method can correct the grey-level distortion in the low-resolution panchromatic synthetic image for different ground objects. The normalized difference vegetation index (NDVI) and normalized difference water index (NDWI) are adopted to classify the pixels into different classes. Then, we employe total least squares (TLS) regression to obtain the error-free panchromatic and multispectral image of each class. The low-resolution panchromatic image is synthesized by weighted summation of the error-free multispectral image. In addition, the grey-level distorted pixels are extracted for further correction. Finally, the multispectral image is sharpened by the ratio enhancement method. The experimental results reveal that the proposed algorithm achieves high-fidelity in spatial details and spectrum.

Total Least Squares Phase Retrieval

We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this approach to handle errors in the sensing vectors by adopting the total least squares (TLS) framework that is used in linear inverse problems with operator errors. We show how gradient descent and the specific geometry of the phase retrieval problem can be used to obtain a simple and efficient TLS solution. Additionally, we derive the gradients of the TLS and LS solutions with respect to the sensing vectors and measurements which enables us to calculate the solution errors. By analyzing these error expressions we determine conditions under which each method should outperform the other. We run simulations to demonstrate that our method can lead to more accurate solutions. We further demonstrate the effectiveness of our approach by performing phase retrieval experiments on real optical hardware which naturally contains both sensing vector and measurement errors.

Maximum Total Quaternion Correntropy for Adaptive Filtering

Quaternion adaptive filters have been widely used in processing three-dimensional ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {3}$</tex-math></inline-formula> -D) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {4}$</tex-math></inline-formula> -D signals. However, the performance of existing quaternion adaptive filtering algorithms will be deteriorated when both the input and output signals are disturbed by noises. To solve this problem, this paper first proposes a quaternion error-in-variables (QEIV) model in which the input and output signals are disturbed by noises, and develops a maximum total quaternion correntropy (MTQC) criterion to resist non-Gaussian noises. Then, combined with the total least squares (TLS) method, an MTQC algorithm is proposed based on the stochastic gradient method and quaternion generalized Hamilton-real (GHR) calculus for the proposed QEIV model. Furthermore, a variable kernel width strategy is given to avoid the problem of kernel width selection and a variable kernel width MTQC (VKWMTQC) algorithm is therefore proposed, simultaneously. More importantly, the local stability, the convergence condition, and steady-state performance of the proposed MTQC algorithm are theoretically analyzed by the quaternion calculus and quaternion matrix theories. Finally, simulation results verify the correctness of the theoretical analysis and demonstrate the superiority of the proposed MTQC algorithm for the QEIV model.

A contribution to the conditioning of the mixed least-squares scaled total least-squares problem

A contribution to the conditioning of the mixed least-squares scaled total least-squares problem

Comparison of Posterior Precision Estimation Methods of Weighted Total Least-Squares Solution in Errors-in-Variables Model with Analytical Form

Comparison of Posterior Precision Estimation Methods of Weighted Total Least-Squares Solution in Errors-in-Variables Model with Analytical Form

STLS-LADMM-Net: A Deep Network for SAR Autofocus Imaging

Synthetic aperture radar (SAR) can provide high-resolution electromagnetic backscattering images of the illuminated area, playing a significant role in various applications. However, achieving focused SAR images is challenging under sparse sampling and phase error conditions. By exploiting the sparsity or compressibility priors, the state-of-the-art sparsity-driven SAR imaging methods can reconstruct images under the condition of sparse sampling. However, the handcrafted priors used in these methods limit the imaging performance, and the iterative solution schemes reduce the computational efficiency. Besides, the measurement inaccuracy introduced by the phase error also degrades the reconstruction performance of the sparsity-driven imaging methods. To address these issues, a deep network for SAR autofocus imaging is proposed, which alternately performs image reconstruction and phase error estimation. When performing image reconstruction, the sparsity-cognizant total least-square (S-TLS) model is introduced to handle the problem of measurement inaccuracy, contributing to robust reconstruction performance under the condition of phase error. During the implementation of the deep network, a feature transform operator is used to realize data-driven prior knowledge learning and overcome the limitations of handcrafted priors. Moreover, the deep network approach can significantly improve computational efficiency. Experiments on simulated and real data verify the effectiveness and efficiency of the proposed method.

Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares

This paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A total least squares problem is often ill-conditioned. To solve a TLS problem, a classical algorithm based on finding the right singular vector or an algorithm based on an augmented system of equations with complex coefficients can be applied. In this paper, a new augmented system of equations with real coefficients is proposed to solve TLS problems. A symmetrical augmented system of equations was applied to the parameter identification of discrete fractional systems. The simulation results showed that the use of the proposed symmetrical augmented system of equations can shorten the time for solving such problems. It was also shown that the proposed system can have a smaller condition number.