Estimation for the bivariate quantile varying coefficient model with application to diffusion tensor imaging data analysis.

Despite interest in the joint modeling of multiple functional responses such as diffusion properties in neuroimaging, robust statistical methods appropriate for this task are lacking. To address this need, we propose a varying coefficient quantile regression model able to handle bivariate functional responses. Our work supports innovative insights into biomedical data by modeling the joint distribution of functional variables over their domains and across clinical covariates. We propose an estimation procedure based on the alternating direction method of multipliers and propagation separation algorithms to estimate varying coefficients using a B-spline basis and an $L_2$ smoothness penalty that encourages interpretability. A simulation study and an application to a real-world neurodevelopmental data set demonstrates the performance of our model and the insights provided by modeling functional fractional anisotropy and mean diffusivity jointly and their association with gestational age and sex.

Transient Interference Excision and Spectrum Reconstruction with Partial Samples Using Modified Alternating Direction Method of Multipliers-Net for the Over-the-Horizon Radar.

Transient interference often submerges the actual targets when employing over-the-horizon radar (OTHR) to detect targets. In addition, modern OTHR needs to carry out multi-target detection from sea to air, resulting in the sparse sampling of echo data. The sparse OTHR signal will raise serious grating lobes using conventional methods and thus degrade target detection performance. This article proposes a modified Alternating Direction Method of Multipliers (ADMM)-Net to reconstruct the target and clutter spectrum of sparse OTHR signals so that target detection can be performed normally. Firstly, transient interferences are identified based on the sparse basis representation and then excised. Therefore, the processed signal can be seen as a sparse OTHR signal. By solving the Doppler sparsity-constrained optimization with the trained network, the complete Doppler spectrum is reconstructed effectively for target detection. Compared with traditional sparse solution methods, the presented approach can balance the efficiency and accuracy of OTHR signal spectrum reconstruction. Both simulation and real-measured OTHR data proved the proposed approach's performance.

A Sparse Recovery Algorithm for Suppressing Multiple Linear Frequency Modulation Interference in the Synthetic Aperture Radar Image Domain.

In synthetic aperture radar (SAR) signal processing, compared with the raw data of level-0, level-1 SAR images are more readily accessible and available in larger quantities. However, an amount of level-1 images are affected by radio frequency interference (RFI), which typically originates from Linear Frequency Modulation (LFM) signals emitted by ground-based radars. Existing research on interference suppression in level-1 data has primarily focused on two methods: transforming SAR images into simulated echo data for interference suppression, or focusing interference in the frequency domain and applying notching filters to reduce interference energy. However, these methods overlook the effective utilization of the interference parameters or are confined to suppressing only one type of LFM interference at a time. In certain SAR images, multiple types of LFM interference manifest bright radiation artifacts that exhibit varying lengths along the range direction while remaining constant in the azimuth direction. It is necessary to suppress multiple LFM interference on SAR images when original echo data are unavailable. This article proposes a joint sparse recovery algorithm for interference suppression in the SAR image domain. In the SAR image domain, two-dimensional LFM interference typically exhibits differences in parameters such as frequency modulation rate and pulse width in the range direction, while maintaining consistency in the azimuth direction. Based on this observation, this article constructs a series of focusing operators for LFM interference in SAR images. These operators enable the sparse representation of dispersed LFM interference. Subsequently, an optimization model is developed that can effectively suppress multi-LFM interference and reduce image loss with the assistance of a regularization term in the image domain. Simulation experiments conducted in various scenarios validate the superior performance of the proposed method.

Tensor decomposition with relational constraints for predicting multiple types of microRNA-disease associations.

MicroRNAs (miRNAs) play crucial roles in multifarious biological processes associated with human diseases. Identifying potential miRNA-disease associations contributes to understanding the molecular mechanisms of miRNA-related diseases. Most of the existing computational methods mainly focus on predicting whether a miRNA-disease association exists or not. However, the roles of miRNAs in diseases are prominently diverged, for instance, Genetic variants of miRNA (mir-15) may affect the expression level of miRNAs leading to B cell chronic lymphocytic leukemia, while circulating miRNAs (including mir-1246, mir-1307-3p, etc.) have potentials to detecting breast cancer in the early stage. In this paper, we aim to predict multi-type miRNA-disease associations instead of taking them as binary. To this end, we innovatively represent miRNA-disease-type triples as a tensor and introduce tensor decomposition methods to solve the prediction task. Experimental results on two widely-adopted miRNA-disease datasets: HMDD v2.0 and HMDD v3.2 show that tensor decomposition methods improve a recent baseline in a large scale (up to $38\%$ in Top-1F1). We then propose a novel method, Tensor Decomposition with Relational Constraints (TDRC), which incorporates biological features as relational constraints to further the existing tensor decomposition methods. Compared with two existing tensor decomposition methods, TDRC can produce better performance while being more efficient.

An Innovative Approach for Removing Stripe Noise in Infrared Images.

The non-uniformity of infrared detectors' readout circuits can lead to stripe noise in infrared images, which affects their effective information and poses challenges for subsequent applications. Traditional denoising algorithms have limited effectiveness in maintaining effective information. This paper proposes a multi-level image decomposition method based on an improved LatLRR (MIDILatLRR). By utilizing the global low-rank structural characteristics of stripe noise, the noise and smooth information are decomposed into low-rank part images, and texture information is adaptively decomposed into several salient part images, thereby better preserving texture edge information in the image. Sparse terms are constructed according to the smoothness of the effective information in the final low-rank part of the image and the sparsity of the stripe noise direction. The modeling of stripe noise is achieved using multi-sparse constraint representation (MSCR), and the Alternating Direction Method of Multipliers (ADMM) is used for calculation. Extensive experiments demonstrated the proposed algorithm's effectiveness and compared it with state-of-the-art algorithms in subjective judgments and objective indicators. The experimental results fully demonstrate the proposed algorithm's superiority and efficacy.

Super-resolution image reconstruction from sparsity regularization and deep residual-learned priors.

BACKGROUND: Computed tomography (CT) plays an important role in the field of non-destructive testing. However, conventional CT images often have blurred edge and unclear texture, which is not conducive to the follow-up medical diagnosis and industrial testing work. OBJECTIVE: This study aims to generate high-resolution CT images using a new CT super-resolution reconstruction method combining with the sparsity regularization and deep learning prior. METHODS: The new method reconstructs CT images through a reconstruction model incorporating image gradient L0-norm minimization and deep image priors using a plug-and-play super-resolution framework. The deep learning priors are learned from a deep residual network and then plugged into the proposed new framework, and alternating direction method of multipliers is utilized to optimize the iterative solution of the model. RESULTS: The simulation data analysis results show that the new method improves the signal-to-noise ratio (PSNR) by 7% and the modulation transfer function (MTF) curves show that the value of MTF50 increases by 0.02 factors compared with the result of deep plug-and-play super-resolution. Additionally, the real CT image data analysis results show that the new method improves the PSNR by 5.1% and MTF50 by 0.11 factors. CONCLUSION: Both simulation and real data experiments prove that the proposed new CT super-resolution method using deep learning priors can reconstruct CT images with lower noise and better detail recovery. This method is flexible, effective and extensive for low-resolution CT image super-resolution.

Minimizing L 1 over L 2 norms on the gradient.

In this paper, we study the L 1 /L 2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L 1 /L 2 is better than the L 1 norm when approximating the L 0 norm to promote sparsity. Consequently, we postulate that applying L 1 /L 2 on the gradient is better than the classic total variation (the L 1 norm on the gradient) to enforce the sparsity of the image gradient. Numerically, we design a specific splitting scheme, under which we can prove subsequential and global convergence for the alternating direction method of multipliers (ADMM) under certain conditions. Experimentally, we demonstrate visible improvements of L 1 /L 2 over L 1 and other nonconvex regularizations for image recovery from low-frequency measurements and two medical applications of MRI and CT reconstruction. Finally, we reveal some empirical evidence on the superiority of L 1 /L 2 over L 1 when recovering piecewise constant signals from low-frequency measurements to shed light on future works.

A Novel Stripe Noise Removal Model for Infrared Images.

Infrared images often carry obvious streak noises due to the non-uniformity of the infrared detector and the readout circuit. These streak noises greatly affect the image quality, adding difficulty to subsequent image processing. Compared with current elimination algorithms for infrared stripe noises, our approach fully utilizes the difference between the stripe noise components and the actual information components, takes the gradient sparsity along the stripe direction and the global sparsity of the stripe noises as regular terms, and treats the sparsity of the components across the stripe direction as a fidelity term. On this basis, an adaptive edge-preserving operator (AEPO) based on edge contrast was proposed to protect the image edge and, thus, prevent the loss of edge details. The final solution was obtained by the alternating direction method of multipliers (ADMM). To verify the effectiveness of our approach, many real experiments were carried out to compare it with state-of-the-art methods in two aspects: subjective judgment and objective indices. Experimental results demonstrate the superiority of our approach.

A Combined Approach to Infrared Small-Target Detection with the Alternating Direction Method of Multipliers and an Improved Top-Hat Transformation.

In infrared small target detection, the infrared patch image (IPI)-model-based methods produce better results than other popular approaches (such as max-mean, top-hat, and human visual system) but in some extreme cases it suffers from long processing times and inconsistent performance. In order to overcome these issues, we propose a novel approach of dividing the traditional target detection process into two steps: suppression of background noise and elimination of clutter. The workflow consists of four steps: after importing the images, the second step applies the alternating direction multiplier method to preliminarily remove the background. Comparatively to the IPI model, this step does not require sliding patches, resulting in a significant reduction in processing time. To eliminate residual noise and clutter, the interim results from morphological filtering are then processed in step 3 through an improved new top-hat transformation, using a threefold structuring element. The final step is thresholding segmentation, which uses an adaptive threshold algorithm. Compared with IPI and the new top-hat methods, as well as some other widely used methods, our approach was able to detect infrared targets more efficiently (90% less computational time) and consistently (no sudden performance drop).

VERTICOX: Vertically Distributed Cox Proportional Hazards Model Using the Alternating Direction Method of Multipliers.

The Cox proportional hazards model is a popular semi-parametric model for survival analysis. In this paper, we aim at developing a federated algorithm for the Cox proportional hazards model over vertically partitioned data (i.e., data from the same patient are stored at different institutions). We propose a novel algorithm, namely VERTICOX, to obtain the global model parameters in a distributed fashion based on the Alternating Direction Method of Multipliers (ADMM) framework. The proposed model computes intermediary statistics and exchanges them to calculate the global model without collecting individual patient-level data. We demonstrate that our algorithm achieves equivalent accuracy for the estimation of model parameters and statistics to that of its centralized realization. The proposed algorithm converges linearly under the ADMM framework. Its computational complexity and communication costs are polynomially and linearly associated with the number of subjects, respectively. Experimental results show that VERTICOX can achieve accurate model parameter estimation to support federated survival analysis over vertically distributed data by saving bandwidth and avoiding exchange of information about individual patients. The source code for VERTICOX is available at: https://github.com/daiwenrui/VERTICOX.

Total variation combining nonlocal means filtration for image reconstruction in X-ray computed tomography.

BACKGROUND: Image reconstruction for realistic medical images under incomplete observation is still one of the core tasks for computed tomography (CT). However, the stair-case artifacts of Total variation (TV) based ones have restricted the usage of the reconstructed images. OBJECTIVE: This work aims to propose and test an accurate and efficient algorithm to improve reconstruction quality under the idea of synergy between local and nonlocal regularizations. METHODS: The total variation combining the nonlocal means filtration is proposed and the alternating direction method of multipliers is utilized to develop an efficient algorithm. The first order approximation of linear expansion at intermediate point is applied to overcome the computation of the huge CT system matrix. RESULTS: The proposed method improves root mean squared error by 25.6% compared to the recent block-matching sparsity regularization (BMSR) on simulation dataset of 19 views. The structure similarities of image of the new method is higher than 0.95, while that of BMSR is about 0.92. Moreover, on real rabbit dataset of 20 views, the peak signal-to-noise ratio (PSNR) of the new method is 36.84, while using other methods PSNR are lower than 35.81. CONCLUSIONS: The proposed method shows advantages on noise suppression and detail preservations over the competing algorithms used in CT image reconstruction.

Robust AOA-Based Target Localization for Uniformly Distributed Noise via ℓp-ℓ1 Optimization.

This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓp-norm with 0≤p<2 as the measurement error and the ℓ1-norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1≤p<2. However, when 0≤p<1, the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise.

Comparison of parameter optimization methods for quantitative susceptibility mapping.

PURPOSE: Quantitative Susceptibility Mapping (QSM) is usually performed by minimizing a functional with data fidelity and regularization terms. A weighting parameter controls the balance between these terms. There is a need for techniques to find the proper balance that avoids artifact propagation and loss of details. Finding the point of maximum curvature in the L-curve is a popular choice, although it is slow, often unreliable when using variational penalties, and has a tendency to yield overregularized results. METHODS: We propose 2 alternative approaches to control the balance between the data fidelity and regularization terms: 1) searching for an inflection point in the log-log domain of the L-curve, and 2) comparing frequency components of QSM reconstructions. We compare these methods against the conventional L-curve and U-curve approaches. RESULTS: Our methods achieve predicted parameters that are better correlated with RMS error, high-frequency error norm, and structural similarity metric-based parameter optimizations than those obtained with traditional methods. The inflection point yields less overregularization and lower errors than traditional alternatives. The frequency analysis yields more visually appealing results, although with larger RMS error. CONCLUSION: Our methods provide a robust parameter optimization framework for variational penalties in QSM reconstruction. The L-curve-based zero-curvature search produced almost optimal results for typical QSM acquisition settings. The frequency analysis method may use a 1.5 to 2.0 correction factor to apply it as a stand-alone method for a wider range of signal-to-noise-ratio settings. This approach may also benefit from fast search algorithms such as the binary search to speed up the process.

Joint total variation-based reconstruction of multiparametric magnetic resonance images for mapping tissue types.

Multispectral analysis of coregistered multiparametric magnetic resonance (MR) images provides a powerful method for tissue phenotyping and segmentation. Acquisition of a sufficiently varied set of multicontrast MR images and parameter maps to objectively define multiple normal and pathologic tissue types can require long scan times. Accelerated MRI on clinical scanners with multichannel receivers exploits techniques such as parallel imaging, while accelerated preclinical MRI scanning must rely on alternate approaches. In this work, tumor-bearing mice were imaged at 7 T to acquire k-space data corresponding to a series of images with varying T1-, T2- and T2*-weighting. A joint reconstruction framework is proposed to reconstruct a series of T1-weighted images and corresponding T1 maps simultaneously from undersampled Cartesian k-space data. The ambiguity introduced by undersampling was resolved by using model-based constraints and structural information from a reference fully sampled image as the joint total variation prior. This process was repeated to reconstruct T2-weighted and T2*-weighted images and corresponding maps of T2 and T2* from undersampled Cartesian k-space data. Validation of the reconstructed images and parameter maps was carried out by computing tissue-type maps, as well as maps of the proton density fat fraction (PDFF), proton density water fraction (PDwF), fat relaxation rate ( R2f*) and water relaxation rate ( R2w*) from the reconstructed data, and comparing them with ground truth (GT) equivalents. Tissue-type maps computed using 18% k-space data were visually similar to GT tissue-type maps, with dice coefficients ranging from 0.43 to 0.73 for tumor, fluid adipose and muscle tissue types. The mean T1 and T2 values within each tissue type computed using only 18% k-space data were within 8%-10% of the GT values from fully sampled data. The PDFF and PDwF maps computed using 27% k-space data were within 3%-15% of GT values and showed good agreement with the expected values for the four tissue types.

Sequence Set Design for a New LFM-PC Hybrid Modulated Radar Signal.

In this paper we study the code design problem of a new form of linear frequency modulation phase-coded (LFM-PC) hybrid signal with wide Doppler tolerance based on a range-Doppler discrete ambiguity function (DAF) to get better detection performance and anti-jamming capability. The DAF of the LFM-PC inter pulse signal is derived within the Doppler tolerance. Two optimization models are established. One is single pulse sequence design (SSD) for Doppler tolerance extension based on minimum integral normalized sidelobe level (INSL); the other is multi pulse sequence set design (MSSD) for signal orthogonality based on the minimizing sum of the normalized DAF sidelobe (NDAFSL) and discrete cross ambiguity function (DCAF). Two low-complexity signal optimization methods based on alternating direction method of multiplier (ADMM) are proposed, respectively. The simulation results show that the optimized signals have either wide Doppler tolerance or good orthogonal performance, and the optimization methods (i.e., SSD-ADMM and MSSD-ADMM) have the characteristics of fast convergence speed and low operation amount.

Parameter Estimation for Interrupted Sampling Repeater Jamming Based on ADMM.

By repeatedly sampling, storing, and retransmitting parts of the radar signal, interrupted sampling repeater jamming (ISRJ) based on digital radio frequency memory (DRFM) can produce a train of secondary false targets symmetrical to the main false target, threatening to mislead or deceive the victim radar system. This paper proposes a computationally-effective method to estimating the parameters for ISRJ by resorting to the framework of alternating direction method of multipliers (ADMM). Firstly, the analytical form of pulse compression is derived. Then, for the purpose of estimating the parameters of ISRJ, the original problem is transformed into a nonlinear integer optimization model with respect to a window vector. On this basis, the ADMM is introduced to decompose the nonlinear integer optimization model into a series of sub-problems to estimate the width and number of ISRJ's sample slices. Finally, the numerical simulation results show that, compared with the traditional time-frequency (TF) method, the proposed method exhibits much better performance in accuracy and stability.

Using multivariate mixed-effects selection models for analyzing batch-processed proteomics data with non-ignorable missingness.

In quantitative proteomics, mass tag labeling techniques have been widely adopted in mass spectrometry experiments. These techniques allow peptides (short amino acid sequences) and proteins from multiple samples of a batch being detected and quantified in a single experiment, and as such greatly improve the efficiency of protein profiling. However, the batch-processing of samples also results in severe batch effects and non-ignorable missing data occurring at the batch level. Motivated by the breast cancer proteomic data from the Clinical Proteomic Tumor Analysis Consortium, in this work, we developed two tailored multivariate MIxed-effects SElection models (mvMISE) to jointly analyze multiple correlated peptides/proteins in labeled proteomics data, considering the batch effects and the non-ignorable missingness. By taking a multivariate approach, we can borrow information across multiple peptides of the same protein or multiple proteins from the same biological pathway, and thus achieve better statistical efficiency and biological interpretation. These two different models account for different correlation structures among a group of peptides or proteins. Specifically, to model multiple peptides from the same protein, we employed a factor-analytic random effects structure to characterize the high and similar correlations among peptides. To model biological dependence among multiple proteins in a functional pathway, we introduced a graphical lasso penalty on the error precision matrix, and implemented an efficient algorithm based on the alternating direction method of multipliers. Simulations demonstrated the advantages of the proposed models. Applying the proposed methods to the motivating data set, we identified phosphoproteins and biological pathways that showed different activity patterns in triple negative breast tumors versus other breast tumors. The proposed methods can also be applied to other high-dimensional multivariate analyses based on clustered data with or without non-ignorable missingness.

Application of Blind Deconvolution Based on the New Weighted L1-norm Regularization with Alternating Direction Method of Multipliers in Light Microscopy Images.

This study aimed to develop and evaluate a blind-deconvolution framework using the alternating direction method of multipliers (ADMMs) incorporated with weighted L1-norm regularization for light microscopy (LM) images. A presimulation study was performed using the Siemens star phantom prior to conducting the actual experiments. Subsequently, the proposed algorithm and a total generalized variation-based (TGV-based) method were applied to cross-sectional images of a mouse molar captured at 40× and 400× on-microscope magnifications and the results compared, and the resulting images were compared. Both simulation and experimental results confirmed that the proposed deblurring algorithm effectively restored the LM images, as evidenced by the quantitative evaluation metrics. In conclusion, this study demonstrated that the proposed deblurring algorithm can efficiently improve the quality of LM images.

Weak-harmonic regularization for quantitative susceptibility mapping.

PURPOSE: Background-field removal is a crucial preprocessing step for quantitative susceptibility mapping (QSM). Remnants from this step often contaminate the estimated local field, which in turn leads to erroneous tissue-susceptibility reconstructions. The present work aimed to mitigate this undesirable behavior with the development of a new approach that simultaneously decouples background contributions and local susceptibility sources on QSM inversion. METHODS: Input phase data for QSM can be seen as a composite scalar field of local effects and residual background components. We developed a new weak-harmonic regularizer to constrain the latter and to separate the 2 components. The resulting optimization problem was solved with the alternating directions of multipliers method framework to achieve fast convergence. In addition, for convenience, a new alternating directions of multipliers method-based preconditioned nonlinear projection onto dipole fields solver was developed to enable initializations with wrapped-phase distributions. Weak-harmonic QSM, with and without nonlinear projection onto dipole fields preconditioning, was compared with the original (alternating directions of multipliers method-based) total variation QSM algorithm in phantom and in vivo experiments. RESULTS: Weak-harmonic QSM returned improved reconstructions regardless of the method used for background-field removal, although the proposed nonlinear projection onto dipole fields method often obtained better results. Streaking and shadowing artifacts were substantially suppressed, and residual background components were effectively removed. CONCLUSION: Weak-harmonic QSM with field preconditioning is a robust dipole inversion technique and has the potential to be extended as a single-step formulation for initialization with uncombined multi-echo data.

Spectral Estimation Using Multitaper Whittle Methods with a Lasso Penalty.

Spectral estimation provides key insights into the frequency domain characteristics of a time series. Naive non-parametric estimates of the spectral density, such as the periodogram, are inconsistent, and the more advanced lag window or multitaper estimators are often still too noisy. We propose an L 1 penalized quasi-likelihood Whittle framework based on multitaper spectral estimates which performs semiparametric spectral estimation for regularly sampled univariate stationary time series. Our new approach circumvents the problematic Gaussianity assumption required by least square approaches and achieves sparsity for a wide variety of basis functions. We present an alternating direction method of multipliers (ADMM) algorithm to efficiently solve the optimization problem, and develop universal threshold and generalized information criterion (GIC) strategies for efficient tuning parameter selection that outperform cross-validation methods. Theoretically, a fast convergence rate for the proposed spectral estimator is established. We demonstrate the utility of our methodology on simulated series and to the spectral analysis of electroencephalogram (EEG) data.