Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.
Ontology highlight
ABSTRACT:
SUBMITTER: Jon K
PROVIDER: S-EPMC8057597 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Immersed interface method (IIM) is a promising high-accuracy numerical scheme for the Poisson-Boltzmann model that has been widely used to study electrostatic interactions in biomolecules. However, the IIM suffers from instability and slow convergence for typical applications. In this study, we introduced both analytical interface and surface regulation into IIM to address these issues. The analytical interface setup leads to better accuracy and its convergence closely follows a quadratic manner as predicted by theory. The surface regulation further speeds up the convergence for nontrivial biomolecules. In addition, uncertainties of the numerical energies for tested systems are also reduced by about half. More interestingly, the analytical setup significantly improves the linear solver efficiency and stability by generating more precise and better-conditioned linear systems. Finally, we implemented the bottleneck linear system solver on GPUs to further improve the efficiency of the method, so it can be widely used for practical biomolecular applications. © 2019 Wiley Periodicals, Inc.
| S-EPMC6422926 | biostudies-literature
Project description:We investigate a second-order dynamical system with variable damping in connection with the minimization of a nonconvex differentiable function. The dynamical system is formulated in the spirit of the differential equation which models Nesterov's accelerated convex gradient method. We show that the generated trajectory converges to a critical point, if a regularization of the objective function satisfies the Kurdyka- Lojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the Lojasiewicz exponent.
| S-EPMC7077366 | biostudies-literature
Project description:The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements.
| S-EPMC3087981 | biostudies-literature
Project description:MotivationMultispectral biological fluorescence microscopy has enabled the identification of multiple targets in complex samples. The accuracy in the unmixing result degrades (i) as the number of fluorophores used in any experiment increases and (ii) as the signal-to-noise ratio in the recorded images decreases. Further, the availability of prior knowledge regarding the expected spatial distributions of fluorophores in images of labeled cells provides an opportunity to improve the accuracy of fluorophore identification and abundance.ResultsWe propose a regularized sparse and low-rank Poisson regression unmixing approach (SL-PRU) to deconvolve spectral images labeled with highly overlapping fluorophores which are recorded in low signal-to-noise regimes. First, SL-PRU implements multipenalty terms when pursuing sparseness and spatial correlation of the resulting abundances in small neighborhoods simultaneously. Second, SL-PRU makes use of Poisson regression for unmixing instead of least squares regression to better estimate photon abundance. Third, we propose a method to tune the SL-PRU parameters involved in the unmixing procedure in the absence of knowledge of the ground truth abundance information in a recorded image. By validating on simulated and real-world images, we show that our proposed method leads to improved accuracy in unmixing fluorophores with highly overlapping spectra.Availability and implementationThe source code used for this article was written in MATLAB and is available with the test data at https://github.com/WANGRUOGU/SL-PRU.
| S-EPMC10081874 | biostudies-literature
Project description:This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the theoretical support of this approach is still far from optimal in the noisy setting, falling short of explaining its empirical success. We make progress towards demystifying the practical efficacy of convex relaxation vis-à-vis random noise. When the rank and the condition number of the unknown matrix are bounded by a constant, we demonstrate that the convex programming approach achieves near-optimal estimation errors - in terms of the Euclidean loss, the entrywise loss, and the spectral norm loss - for a wide range of noise levels. All of this is enabled by bridging convex relaxation with the nonconvex Burer-Monteiro approach, a seemingly distinct algorithmic paradigm that is provably robust against noise. More specifically, we show that an approximate critical point of the nonconvex formulation serves as an extremely tight approximation of the convex solution, thus allowing us to transfer the desired statistical guarantees of the nonconvex approach to its convex counterpart.
| S-EPMC8300474 | biostudies-literature
Project description:Inferring causal structures of real world complex networks from measured time series signals remains an open issue. The current approaches are inadequate to discern between direct versus indirect influences (i.e., the presence or absence of a directed arc connecting two nodes) in the presence of noise, sparse interactions, as well as nonlinear and transient dynamics of real world processes. We report a sparse regression (referred to as the l1-min) approach with theoretical bounds on the constraints on the allowable perturbation to recover the network structure that guarantees sparsity and robustness to noise. We also introduce averaging and perturbation procedures to further enhance prediction scores (i.e., reduce inference errors), and the numerical stability of l1-min approach. Extensive investigations have been conducted with multiple benchmark simulated genetic regulatory network and Michaelis-Menten dynamics, as well as real world data sets from DREAM5 challenge. These investigations suggest that our approach can significantly improve, oftentimes by 5 orders of magnitude over the methods reported previously for inferring the structure of dynamic networks, such as Bayesian network, network deconvolution, silencing and modular response analysis methods based on optimizing for sparsity, transients, noise and high dimensionality issues.
| S-EPMC4768174 | biostudies-literature
Project description:We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.
| S-EPMC10438917 | biostudies-literature
Project description:Particle tracking in living systems requires low light exposure and short exposure times to avoid phototoxicity and photobleaching and to fully capture particle motion with high-speed imaging. Low-excitation light comes at the expense of tracking accuracy. Image restoration methods based on deep learning dramatically improve the signal-to-noise ratio in low-exposure data sets, qualitatively improving the images. However, it is not clear whether images generated by these methods yield accurate quantitative measurements such as diffusion parameters in (single) particle tracking experiments. Here, we evaluate the performance of two popular deep learning denoising software packages for particle tracking, using synthetic data sets and movies of diffusing chromatin as biological examples. With synthetic data, both supervised and unsupervised deep learning restored particle motions with high accuracy in two-dimensional data sets, whereas artifacts were introduced by the denoisers in three-dimensional data sets. Experimentally, we found that, while both supervised and unsupervised approaches improved tracking results compared with the original noisy images, supervised learning generally outperformed the unsupervised approach. We find that nicer-looking image sequences are not synonymous with more precise tracking results and highlight that deep learning algorithms can produce deceiving artifacts with extremely noisy images. Finally, we address the challenge of selecting parameters to train convolutional neural networks by implementing a frugal Bayesian optimizer that rapidly explores multidimensional parameter spaces, identifying networks yielding optimal particle tracking accuracy. Our study provides quantitative outcome measures of image restoration using deep learning. We anticipate broad application of this approach to critically evaluate artificial intelligence solutions for quantitative microscopy.
| S-EPMC8108534 | biostudies-literature
Project description:We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. In this paper, we propose an approximate regularization path-following method for solving a variety of learning problems with nonconvex objective functions. Under a unified analytic framework, we simultaneously provide explicit statistical and computational rates of convergence for any local solution attained by the algorithm. Computationally, our algorithm attains a global geometric rate of convergence for calculating the full regularization path, which is optimal among all first-order algorithms. Unlike most existing methods that only attain geometric rates of convergence for one single regularization parameter, our algorithm calculates the full regularization path with the same iteration complexity. In particular, we provide a refined iteration complexity bound to sharply characterize the performance of each stage along the regularization path. Statistically, we provide sharp sample complexity analysis for all the approximate local solutions along the regularization path. In particular, our analysis improves upon existing results by providing a more refined sample complexity bound as well as an exact support recovery result for the final estimator. These results show that the final estimator attains an oracle statistical property due to the usage of nonconvex penalty.
| S-EPMC4276088 | biostudies-literature
Project description:Abstract. Significance: Functional near-infrared spectroscopy (fNIRS) is a noninvasive technology that uses low levels of nonionizing light in the range of red and near-infrared to record changes in the optical absorption and scattering of the underlying tissue that can be used to infer blood flow and oxygen changes during brain activity. The challenges and difficulties of reconstructing spatial images of hemoglobin changes from fNIRS data are mainly caused by the illposed nature of the optical inverse model. Aim: We describe a Bayesian approach combining several lasso-based regularizations to apply anatomy-prior information to solving the inverse model. Approach: We built a Bayesian hierarchical model to solve the Bayesian adaptive fused sparse overlapping group lasso (Ba-FSOGL) model. The method is evaluated and validated using simulation and experimental datasets. Results: We apply this approach to the simulation and experimental datasets to reconstruct a known brain activity. The reconstructed images and statistical plots are shown. Conclusion: We discuss the adaptation of this method to fNIRS data and demonstrate that this approach provides accurate image reconstruction with a low false-positive rate, through numerical simulations and application to experimental data collected during motor and sensory tasks.
| S-EPMC9912979 | biostudies-literature