Noise Bias Research Articles

A hybrid variational level set model based on double Gaussian distribution fitting energy for image segmentation and bias correction

AbstractThe variational level set model has been widely used in image segmentation. However, its performance is significantly hindered by bias fields and noise within the images. To address these limitations, we introduce a novel hybrid variational level set model based on dual Gaussian distribution fitting (DGDF) energy in this paper. The DGDF energy integrates both local and global Gaussian distributions. The local energy is derived from the original image, while the global energy employs the corrected image, enabling effective segmentation of images with intensity inhomogeneity. Furthermore, the model demonstrates low sensitivity to weighting parameters and robust performance for noisy images. We develop an alternating iteration algorithm that combines variational methods with gradient descent to efficiently solve the proposed model. Experimental results validate the effectiveness of the model and the algorithm. In addition, the proposed model shows competitiveness on test images and three datasets compared to several state‐of‐the‐art models, including other variational level set models and deep learning‐based techniques.

Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications

Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications

Output feedback fault-tolerant Q-learning for discrete-time linear systems with actuator faults

This paper presents an innovative output feedback fault-tolerant Q-learning algorithm that can be implemented online without relying on explicit system models or fault details. In the face of actuator faults, finding optimal Fault-Tolerant Control (FTC) solutions that can stabilize the faulty system poses significant challenges. The proposed approach is implemented online without the need for system dynamics and actuator fault information. Furthermore, it operates without relying on full state measurements, utilizing only the input-output data of the faulty system. An innovative representation of the output feedback Fault-Tolerant Q-function (FTQF) is established using input-output data. Subsequently, a model-free optimal output feedback FTC policy is obtained from the developed FTQF. Then, a fault-tolerant Q-learning algorithm is formulated to iteratively acquire the optimal FTC policy in real-time, eliminating the necessity for system dynamics and actuator fault information. The proposed algorithm exhibits immunity to excitation noise bias, even without considering a discounting factor. Furthermore, the proposed Q-learning approach is proven to be effective in stabilizing faulty closed-loop system. Finally, the proposed algorithm's efficiency is validated through numerical simulations of F-16 autopilot aircraft dynamics.

Bias and multiscale correction methods for variational state estimation

Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this paper employs variational state estimation using the so-called parametrized-background data-weak method. This approach relies on a background manifold parametrized by a set of constraints, enabling the state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. The proposed formulation incorporates a novel bias correction mechanism and a manifold decomposition that handles rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The method is validated in different examples, including the assimilation of biased synthetic data, discontinuous signals, and Doppler ultrasound data obtained from experimental measurements.

Validation of an ultrahigh contrast divided subtracted inversion recovery technique using a standard T1 phantom.

The divided subtracted inversion recovery (dSIR) is a high T1 contrast technique that shows changes in white matter in patients with traumatic brain injury and hypoxic injury. The changes can be explained by small differences in T1; however, to date, there has been no independent validation of the technique using a standard reference. The present study develops the theory of the dSIR signal and performs validation using the NIST/ISMRM T1 phantom. Non-idealities are explored, including the influence of noise bias and finite repetition time (TR), which leads to the introduction of an optimally efficient TR for inversion recovery acquisitions. Results show excellent agreement with theoretical calculations.

Progress and opportunities of foundation models in bioinformatics.

Bioinformatics has undergone a paradigm shift in artificial intelligence (AI), particularly through foundation models (FMs), which address longstanding challenges in bioinformatics such as limited annotated data and data noise. These AI techniques have demonstrated remarkable efficacy across various downstream validation tasks, effectively representing diverse biological entities and heralding a new era in computational biology. The primary goal of this survey is to conduct a general investigation and summary of FMs in bioinformatics, tracing their evolutionary trajectory, current research landscape, and methodological frameworks. Our primary focus is on elucidating the application of FMs to specific biological problems, offering insights to guide the research community in choosing appropriate FMs for tasks like sequence analysis, structure prediction, and function annotation. Each section delves into the intricacies of the targeted challenges, contrasting the architectures and advancements of FMs with conventional methods and showcasing their utility across different biological domains. Further, this review scrutinizes the hurdles and constraints encountered by FMs in biology, including issues of data noise, model interpretability, and potential biases. This analysis provides a theoretical groundwork for understanding the circumstances under which certain FMs may exhibit suboptimal performance. Lastly, we outline prospective pathways and methodologies for the future development of FMs in biological research, facilitating ongoing innovation in the field. This comprehensive examination not only serves as an academic reference but also as a roadmap for forthcoming explorations and applications of FMs in biology.

Domain Wall Color Code.

We introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a two-dimensional color code decouples into a series of repetition codes, resulting in an error-correcting threshold of 50%. Interestingly, at finite bias, our color code demonstrates thresholds identical to those of the noise-tailored XZZX surface code for all single-qubit Pauli noise channels. The design principle of the code is that it introduces domain walls which permute the code's excitations upon domain crossing. For practical implementation, we supplement the domain wall code with a scalable restriction decoder based on a matching algorithm. The proposed code is identified as a comparably resource-efficient quantum error-correcting code highly suitable for realistic noise.

Exact results on finite size corrections for surface codes tailored to biased noise

Exact results on finite size corrections for surface codes tailored to biased noise

CMB lensing power spectrum without noise bias

CMB lensing power spectrum without noise bias

Topoisomerase-modulated genome-wide DNA supercoiling domains colocalize with nuclear compartments and regulate human gene expression.

DNA supercoiling is a biophysical feature of the double helix with a pivotal role in biological processes. However, understanding of DNA supercoiling in the chromatin remains limited. Here, we developed azide-trimethylpsoralen sequencing (ATMP-seq), a DNA supercoiling assay offering quantitative accuracy while minimizing genomic bias and background noise. Using ATMP-seq, we directly visualized transcription-dependent negative and positive twin-supercoiled domains around genes and mapped kilobase-resolution DNA supercoiling throughout the human genome. Remarkably, we discovered megabase-scale supercoiling domains (SDs) across all chromosomes that are modulated mainly by topoisomerases I and IIβ. Transcription activities, but not the consequent supercoiling accumulation in the local region, contribute to SD formation, indicating the long-range propagation of transcription-generated supercoiling. Genome-wide SDs colocalize with A/B compartments in both human and Drosophila cells but are distinct from topologically associating domains (TADs), with negative supercoiling accumulation at TAD boundaries. Furthermore, genome-wide DNA supercoiling varies between cell states and types and regulates human gene expression, underscoring the importance of supercoiling dynamics in chromatin regulation and function.

Single-Image-Based Deep Learning for Precise Atomic Defect Identification.

Defect engineering is widely used to impart the desired functionalities on materials. Despite the widespread application of atomic-resolution scanning transmission electron microscopy (STEM), traditional methods for defect analysis are highly sensitive to random noise and human bias. While deep learning (DL) presents a viable alternative, it requires extensive amounts of training data with labeled ground truth. Herein, employing cycle generative adversarial networks (CycleGAN) and U-Nets, we propose a method based on a single experimental STEM image to tackle high annotation costs and image noise for defect detection. Not only atomic defects but also oxygen dopants in monolayer MoS2 are visualized. The method can be readily extended to other two-dimensional systems, as the training is based on unit-cell-level images. Therefore, our results outline novel ways to train the model with minimal data sets, offering great opportunities to fully exploit the power of DL in the materials science community.

Cubature Kalman fusion filtering under stochastic communication protocol: Tackling dynamical bias, scheduling probability and channel noise

The paper addresses the problem of cubature Kalman fusion filtering (CKFF) for nonlinear systems subject to dynamical bias and stochastic communication protocol (SCP). To account for the engineering practice of networked environment, the channels from sensors to filters, affected by Gaussian channel noise, are considered in the system model incorporating dynamical bias. With the purpose of reducing communication load and enhancing resource utilization efficiency, the SCP is adopted for information transmissions, where the scheduling probability is allowed to deviate within bounds from its designated value owing to possible implementation errors. The objective of this paper is to design a CKFF algorithm in spite of the presence of dynamical bias, channel noise and SCP with uncertain scheduling probability. Specifically, the local filter is constructed such that an upper bound on the filtering error covariance (FEC) is calculated through the resolution of matrix difference equations, and the filter gain is subsequently designed to minimize this upper bound. Then, the local filters are fused by utilizing the inverse covariance intersection fusion rule. Moreover, the boundedness of the FEC’s upper bound is also investigated using the matrix theory. The feasibility and effectiveness of the proposed CKFF approach are demonstrated through two simulation experiments.

A variational Bayesian based robust filter for unknown measurement bias and inaccurate noise statistics

In many practical fields, the unknown time-varying measurement biases (additive and multiplicative bias) and heavy-tailed measurement noise caused by some unpredictable anomalous behaviors may degrade the performance of conventional Kalman filter seriously. To solve the state estimation problem of systems with time-varying measurement biases and heavy-tailed measurement noise, this paper proposes a new variational Bayesian (VB) based robust filter. Firstly, the non-Gaussian measurement likelihood probability density function (ML-PDF) with multiplicative and additive measurement bias is built. Then, the conjugate prior distributions for unknown bias and noise scale parameters are selected, and the VB method is utilized to jointly infer the system state, unknown measurement biases and inaccurate measurement noise covariance matrix. Finally, a VB based robust filter is derived and its effectiveness is verified by the numerical simulations.

Unscented Schmidt-Kalman filter on Lie groups with application to spacecraft attitude estimation

This paper addresses the estimation problem of nonlinear systems evolving on Lie groups with unknown parameters. More precisely, some parameters in the equations of motion or sensor measurements are unknown, such as gravitational anomalies and measurement biases, and are infeasible to estimate with available observations. The unscented Schmidt-Kalman filter (USKF) approach in Euclidean space is incorporated with exponential maps from Lie algebra to Lie groups, to develop USKF algorithms on Lie groups. Two types of USKFs are derived, respectively, from left-invariant and right-invariant state estimation errors. The two USKFs, not only account for the effect of unknown parameters but also provide estimates preserving the geometry of state manifold. They are advantageous over the extended Schmidt-Kalman filter for nonlinear systems in the sense of avoiding the computation of Jacobian and achieving higher or comparable estimation accuracy depending on the magnitude of parameters uncertainties. The proposed method is then applied to a spacecraft attitude estimation problem based on quaternion representation, where the magnitude of the gyroscope bias noise is unknown. Simulations are conducted to illustrate the effectiveness of the proposed algorithms in comparison with other methods.

A Low-Cost Redundant Attitude System for Small Satellites, Based on Strap-Down Inertial Techniques and Gyro Sensors Linear Clustering

The significant technological changes related to the manufacturing of the miniaturized sensors produced a higher impact at the level of the detection units equipping the strap-down inertial navigation systems (INSs). Together with miniaturization, many more advantages are brought by these technologies, related to low costs, low necessary energy, high robustness and high potential for adapting the design solutions. However, reducing the dimensions and weight of the sensors is reflected by a decrease in their performance in terms of sensitivity, noise and the possibility of controlling sensitive elements. On the other hand, there is a permanent increase in the need to have in-space applications of miniaturized systems with a high degree of redundancy and to equip miniaturized satellites, miniaturized space robots or space rovers. The paper proposes a new methodology to increase the quality of the signals received from the miniaturized inertial measurement units (IMUs), but also to increase the degree of redundancy, by using low-cost sensors arranged in redundant linear configurations. The presentation is focused on the development of an attitude system based on strap-down inertial techniques which uses a redundant IMU equipped with three linear clusters of miniaturized gyros. For each of the three clusters, a data fusion mechanism based on the maximal ratio combining method is applied. This fusion mechanism reduces the noise power and bias of the signal delivered to the navigation processor. Shown are the theory, software modeling and experimentation results for the attitude algorithm, for the data fusion method, and for the integrated system.

Denoising diffusion post-processing for low-light image enhancement

Low-light image enhancement (LLIE) techniques attempt to increase the visibility of images captured in low-light scenarios. However, as a result of enhancement, a variety of image degradations such as noise and color bias are revealed. Furthermore, each particular LLIE approach may introduce a different form of flaw within its enhanced results. To combat these image degradations, post-processing denoisers have widely been used, which often yield oversmoothed results lacking detail. We propose using a diffusion model as a post-processing approach, and we introduce Low-light Post-processing Diffusion Model (LPDM) in order to model the conditional distribution between under-exposed and normally-exposed images. We apply LPDM in a manner which avoids the computationally expensive generative reverse process of typical diffusion models, and post-process images in one pass through LPDM. Extensive experiments demonstrate that our approach outperforms competing post-processing denoisers by increasing the perceptual quality of enhanced low-light images on a variety of challenging low-light datasets. Source code is available at https://github.com/savvaki/LPDM.

Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model.

Cat-state qubits formed by photonic cat states have a biased noise channel, i.e., one type of error dominates over all the others. We demonstrate that such biased-noise qubits are also promising for error-tolerant simulations of the quantum Rabi model (and its varieties) by coupling a cat-state qubit to an optical cavity. Using the cat-state qubit can effectively enhance the counterrotating coupling, allowing us to explore several fascinating quantum phenomena relying on the counterrotating interaction. Moreover, another benefit from biased-noise cat qubits is that the two main error channels (frequency and amplitude mismatches) are both exponentially suppressed. Therefore, the simulation protocols are robust against parameter errors of the parametric drive that determines the projection subspace. We analyze three examples: (i)collapse and revivals of quantum states; (ii)hidden symmetry and tunneling dynamics; and (iii)pair-cat-code computation.

Swap-test interferometry with biased qubit noise

The Mach-Zehnder interferometer is a powerful device for detecting small phase shifts between two light beams. Simple input states, such as coherent states or single photons, can reach the standard quantum limit of phase estimation, while more complex states can be used to reach Heisenberg scaling; the latter, however, require challenging preparation and measurement strategies. The quest for highly sensitive phase estimation therefore calls for interferometers with nonlinear devices which would make the preparation of these complex states more efficient. Here, we show that the Heisenberg scaling can be recovered with simple input states (including Fock and coherent states) when the linear mirrors in the interferometer are replaced with controlled-swap gates and measurements on auxiliary qubits. These swap tests project the input Fock and coherent states onto NOON and entangled coherent states, respectively, and allow optimal or near-optimal measurements, leading to improved sensitivity to small phase shifts in one of the interferometer arms. We analyze auxiliary qubit errors in detail, showing that biasing the qubit towards phase flips offers a great advantage, and perform thorough numerical simulations of a possible implementation in circuit quantum electrodynamics with an auxiliary Kerr-cat qubit. Our results thus present a viable approach to phase estimation approaching Heisenberg-limited sensitivity and demonstrate potential advantages of using biased-noise qubits in quantum metrology. Published by the American Physical Society 2024

Accurate isoform quantification by joint short- and long-read RNA-sequencing.

Accurate quantification of transcript isoforms is crucial for understanding gene regulation, functional diversity, and cellular behavior. Existing RNA sequencing methods have significant limitations: short-read (SR) sequencing provides high depth but struggles with isoform deconvolution, whereas long-read (LR) sequencing offers isoform resolution at the cost of lower depth, higher noise, and technical biases. Addressing this gap, we introduce Multi-Platform Aggregation and Quantification of Transcripts (MPAQT), a generative model that combines the complementary strengths of different sequencing platforms to achieve state-of-the-art isoform-resolved transcript quantification, as demonstrated by extensive simulations and experimental benchmarks. By applying MPAQT to an in vitro model of human embryonic stem cell differentiation into cortical neurons, followed by machine learning-based modeling of transcript abundances, we show that untranslated regions (UTRs) are major determinants of isoform proportion and exon usage; this effect is mediated through isoform-specific sequence features embedded in UTRs, which likely interact with RNA-binding proteins that modulate mRNA stability. These findings highlight MPAQT's potential to enhance our understanding of transcriptomic complexity and underline the role of splicing-independent post-transcriptional mechanisms in shaping the isoform and exon usage landscape of the cell.

Mitigating Temporal Fragility in the XY Surface Code

An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure O(n) high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement. Published by the American Physical Society 2024