Maximum A Posteriori Research Articles

The Deep Generative Decoder: MAP estimation of representations improves modelling of single-cell RNA data.

Learning low-dimensional representations of single-cell transcriptomics has become instrumental to its downstream analysis. The state of the art is currently represented by neural network models, such as variational autoencoders, which use a variational approximation of the likelihood for inference. We here present the Deep Generative Decoder (DGD), a simple generative model that computes model parameters and representations directly via maximum a posteriori estimation. The DGD handles complex parameterized latent distributions naturally unlike variational autoencoders, which typically use a fixed Gaussian distribution, because of the complexity of adding other types. We first show its general functionality on a commonly used benchmark set, Fashion-MNIST. Secondly, we apply the model to multiple single-cell datasets. Here, the DGD learns low-dimensional, meaningful, and well-structured latent representations with sub-clustering beyond the provided labels. The advantages of this approach are its simplicity and its capability to provide representations of much smaller dimensionality than a comparable variational autoencoder. scDGD is available as a python package at https://github.com/Center-for-Health-Data-Science/scDGD. The remaining code is made available here: https://github.com/Center-for-Health-Data-Science/dgd.

Sample size reestimation and Bayesian predictive probability for single-arm clinical trials with a time-to-event endpoint using Weibull distribution with unknown shape parameter

ABSTRACT This manuscript consists of two topics. Firstly, we explore the utility of internal pilot study (IPS) approach for reestimating sample size at an interim stage when a reliable estimate of the nuisance shape parameter of the Weibull distribution for modeling survival data is unavailable during the planning phase of a study. Although IPS approach can help rescue the study power, it is noted that the adjusted sample size can be as much as twice the initially planned sample size, which may put substantial practical constraints to continue the study. Secondly, we discuss Bayesian predictive probability for conducting interim analyses to obtain preliminary evidence of efficacy or futility of an experimental treatment warranting early termination of a clinical trial. In the context of single-arm clinical trials with time-to-event endpoints following Weibull distribution, we present the calculation of the Bayesian predictive probability when the shape parameter of the Weibull distribution is unknown. Based on the data accumulated at the interim, we propose two approaches which rely on the posterior mode or the entire posterior distribution of the shape parameter. To account for uncertainty in the shape parameter, it is recommended to incorporate its entire posterior distribution in our calculation.

LVIF: a lightweight tightly coupled stereo-inertial SLAM with fisheye camera

To enhance the real-time performance and reduce CPU usage in feature-based visual SLAM, this paper introduces a lightweight tightly coupled stereo-inertial SLAM with fisheye cameras, incorporating several key innovations. First, the stereo-fisheye camera is treated as two independent monocular cameras, and the SE(3) transformation is computed between them to minimize the CPU burden during stereo feature matching and eliminate the need for camera rectification. Another important innovation is the application of maximum-a-posteriori (MAP) estimation for the inertial measurement unit (IMU), which effectively reduces inertial bias and noise in a short time frame. By optimizing the system’s parameters, the constant-velocity model is replaced from the beginning, resulting in improved tracking efficiency. Furthermore, the system incorporates the inertial data in the loop closure thread. The IMU data are employed to determine the translation direction relative to world coordinates and utilized as a necessary condition for loop detection. Experimental results demonstrate that the proposed system achieves superior real-time performance and lower CPU usage compared to the majority of other SLAM systems.

MAP estimation using two temporally consecutive data for ultrasonic sensor arrays

This paper proposes MAP estimation using two temporally consecutive data using signals from eight ultrasonic sensors forming a linear array. First, we estimate the distance to the obstacle from the time difference between the eight received signals. Then, assuming that the ranging error follows a Gaussian distribution and that each of the eight ranging values is independent, we can get the existence probability of the obstacle’s position by a pair of two obtained distances. Finally, we estimate the position of the obstacle by multiplying 28 (8C2) existence probabilities obtained. The conventional method estimates the position of an obstacle by the above procedure. However, the estimation accuracy in the angular direction was poor, resulting in the spread of the existence probability in the horizontal direction. In the proposed MAP estimation using two temporally consecutive data, we obtain the existence probability of an obstacle by the procedure shown above, and then use it as a prior probability of the obstacle’s estimated position. Furthermore, we recursively perform the same process to obtain the existence probability of the obstacle. In this way, we improve the accuracy of the estimation of the position of the obstacle by the existence probability. We present the experiment results to show the effectiveness of the proposed method.

Underwater image dehazing using a novel color channel based dual transmission map estimation

Underwater image dehazing using a novel color channel based dual transmission map estimation

Alzheimer's Disease Genetic Influences Impact the Associations between Diet and Resting-State Functional Connectivity: A Study from the UK Biobank.

Red wine and dairy products have been staples in human diets for a long period. However, the impact of red wine and dairy intake on brain network activity remains ambiguous and requires further investigation. This study investigated the associations between dairy and red wine consumption and seven neural networks' connectivity with functional magnetic resonance imaging (fMRI) data from a sub-cohort of the UK Biobank database. Linear mixed models were employed to regress dairy and red wine consumption against the intrinsic functional connectivity for each neural network. Interactions with Alzheimer's disease (AD) risk factors, including apolipoprotein E4 (APOE4) genotype, TOMM40 genotype, and family history of AD, were also assessed. More red wine consumption was associated with enhanced connectivity in the central executive function network and posterior default mode network. Greater milk intake was correlated with more left executive function network connectivity, while higher cheese consumption was linked to reduced posterior default mode network connectivity. For participants without a family history of Alzheimer's disease (AD), increased red wine consumption was positively correlated with enhanced left executive function network connectivity. In contrast, participants with a family history of AD displayed diminished network connectivity in relation to their red wine consumption. The association between cheese consumption and neural network connectivity was influenced by APOE4 status, TOMM40 status, and family history, exhibiting contrasting patterns across different subgroups. The findings of this study indicate that family history modifies the relationship between red wine consumption and network strength. The interaction effects between cheese intake and network connectivity may vary depending on the presence of different genetic factors.

Joint channel estimation and data detection for high rate orthogonal time frequency space systems

SummaryThis paper proposes a new pilot pattern in the delay‐Doppler (DD) domain for the orthogonal time frequency space (OTFS) system. In contrast to the embedded‐pilot schemes, guard intervals are not used so as increase the spectral efficiency. Also, compared to the superimposed design where data symbols and pilots are arranged on the entire DD grid, in the proposed rearrangement, the number of pilots used is only spread over a subgrid of the DD grid. Hence, the interference of pilots with data symbols is reduced. Afterwards, an algorithm for channel estimation (CE) and symbol detection in the DD domain benefiting from the sparsity of the DD channel is designed. The sparse CE step is formulated as a specific marginalization of the maximum a posteriori (MAP) criterion by providing a Bayesian approach via the mean‐field approximation that involves the variational Bayesian expectation maximization (VB‐EM) algorithm. Detection of data symbols is done using a low complexity MP algorithm. We also propose an interference cancellation (IC) scheme to mitigate contamination of data by pilots that is run after each CE step. To achieve a high CE accuracy, based on the mean mutual incoherence property (MIP), a pilot optimization problem for OTFS is formulated and develop a simulated annealing‐based algorithm to solve it. Finally, simulation results show that the proposed scheme achieves a good compromise between spectral efficiency, complexity, and performance in terms of bit error rate (BER) and normalized mean square error (NMSE) when compared to literature benchmarks.

Saliva as a noninvasive sampling matrix for therapeutic drug monitoring of intravenous busulfan in Chinese patients undergoing hematopoietic stem cell transplantation: A prospective population pharmacokinetic and simulation study.

Therapeutic drug monitoring (TDM) of busulfan (BU) is currently performed by plasma sampling in patients undergoing hematopoietic stem cell transplantation (HSCT). Saliva samples are considered a noninvasive TDM matrix. Currently, no salivary population pharmacokinetics (PopPKs) model for BU available. This study aimed to develop a PopPK model that can describe the relationship between plasma and saliva kinetics in patients receiving intravenous BU. The performance of the model in predicting the area under the concentration-time curve at steady state (AUCss ) based on saliva samples is evaluated. Sixty-six patients with HSCT were recruited and administered 0.8 mg/kg BU intravenously. A PopPK model for saliva and plasma was developed using the nonlinear mixed effects model. Bayesian maximum a posteriori (MAP) optimization was used to estimate the model's predictive performance. Plasma and saliva PKs were adequately described with a one-compartment model and a scaled central compartment. Body surface area correlated positively with both clearance and apparent volume of distribution (Vd), whereas alkaline phosphatase correlated negatively with Vd. Simulations demonstrated that the percentage root mean squared prediction error and lower and upper limits of agreements reduced to 10.02% and -16.96% to 22.86% based on five saliva samples. Saliva can be used as an alternative matrix to plasmain TDM of BU. The AUCss can be predicted from saliva concentration by Bayesian MAP optimization, which can be used to design personalized dosing for BU.

The association between the essential metal mixture and fasting plasma glucose in Chinese community-dwelling elderly people

BackgroundEpidemiological studies about the effect of essential metal mixture on fasting plasma glucose (FPG) levels among elderly people are sparse. The object of this study was to examine the associations of single essential metals and essential metal mixture with FPG levels in Chinese community-dwelling elderly people. MethodsThe study recruited 2348 community-dwelling elderly people in total. Inductively coupled plasma-mass spectrometry was adopted to detect the levels of vanadium (V), selenium (Se), magnesium (Mg), cobalt (Co), calcium (Ca), and molybdenum (Mo) in urine. The relationships between single essential metals and essential metal mixture and FPG levels were evaluated by linear regression and Bayesian kernel machine regression (BKMR) models, respectively. ResultsIn multiple-metal linear regression models, urine V and Mg were negatively related to the FPG levels (β = − 0.016, 95 % CI: − 0.030 to − 0.003 for V; β = − 0.021, 95 % CI: − 0.033 to − 0.009 for Mg), and urine Se was positively related to the FPG levels (β = 0.024, 95 % CI: 0.014–0.034). In BKMR model, the significant relationships of Se and Mg with the FPG levels were also found. The essential metal mixture was negatively associated with FPG levels in a dose-response pattern, and Mg had the maximum posterior inclusion probability (PIP) value (PIP = 1.0000), followed by Se (PIP = 0.9968). Besides, Co showed a significant association with decreased FPG levels in older adults without hyperlipemia and in women. ConclusionsBoth Mg and Se were associated with FPG levels, individually and as a mixture. The essential metal mixture displayed a linear dose-response relationship with reduced FPG levels, with Mg having the largest contribution to FPG levels, followed by Se. Further prospective investigations are necessary to validate these exploratory findings.

Application of traditional manual measurements and remote sensing technologies in monitoring natural disasters

Natural disasters have occurred frequently worldwide. Some manual measurements and remote sensing technologies are widely believed to be effective and convenient in hazard monitoring. This study illustrates the causes and impacts of three natural disasters including floods, wildfires and earthquakes, and analyzes the application of traditional and remote sensing technologies in monitoring these natural disasters. In flood monitoring, traditional tools include meteorological and hydrological detection facilities and equipment could obtain rainfall and water level. Remote sensing technologies could extract water bodies and make disaster evaluation. In wildfire monitoring, traditional tools include the standard equipment of urban fire departments, portable pumps, tank trucks, and earth-moving equipment. Remote sensing technologies could be applied to fuel mapping and fire estimates. In earthquake monitoring, traditional tools include seismic measurement, crustal deformation observation, geomagnetic measurement, telluric observation, gravity observation, in-situ stress observation, and groundwater dynamic observation. Remote sensing technologies could help monitor through house images and thermal data. Remote sensing technologies bring natural disaster monitoring systems a great revolution, both in data acquisition and processing methods.

Covariance structure estimation with Laplace approximation

The Gaussian covariance graph model is popular for revealing the underlying dependency structures among random variables. In this paper, we consider a spike and slab prior, which is a mixture of point-mass and normal distribution, on the off-diagonal entries. The spike and slab prior naturally introduces sparsity to the covariance structure so that the resulting posterior renders covariance structure learning. Under the spike and slab prior, we calculate the posterior model probabilities of covariance structures and natural Bayesian quantities for model selection using the Laplace approximation. We show that the error due to the Laplace approximation becomes asymptotically marginal at a rate that depends on the posterior convergence rate of the covariance matrix under the Frobenius norm. We propose a covariance structure estimation method based on the approximated posterior model probabilities. We also propose a block coordinate descent algorithm to determine the mode of the posterior density conditional on the structure of the covariance. The posterior mode is an estimate of the covariance matrix once the structure is chosen and the Laplace approximation is computed around it. Through a simulation study based on five numerical models, we demonstrate that the proposed method outperforms its competitors. The proposed method is applied to the breast cancer and Parkinson’s disease datasets, as well as the prediction of telephone call counts using telephone call center data, and compared with its competitors in terms of the linear discriminant analysis classification accuracy.

Single-Point Least Square Matching Embedded Method for Improving Visual SLAM

Visual simultaneous location and mapping (VSLAM) has been widely used today, but for some tough cases with insufficient feature points (such as weak texture and motion blur), it is still an ongoing challenge to further boost the corresponding robustness and accuracy. In this paper, to address the problem of inadequate feature points, for conventional visual SLAM, we improve the original feature matching mechanism by providing more correspondences with higher position precision. Firstly, based on the original feature matching results in the map initialization stage, a single-point least square matching (LSM) which iteratively refines position of the matching points by considering geometric and photometric consistency, is presented to improve the map initialization result. Secondly, to improve the tracking performance, given the motion model, the single-point LSM is again used to yield new correspondences from the unsuccessfully matched features of original matching mechanism between current frame and previous frame in the tracking thread, and these extra correspondences participate in and boost the subsequent pose optimization. Lastly, for newly inserted keyframe, we focus on identifying the corresponding 3D map points’ reprojections on relevant local neighbor keyframes, these reprojections are added in the local bundle adjustment (BA) optimization for further improving the estimation of camera pose and local map. The popular VSLAM package, ORB-SLAM2, is used to demonstrate the efficacy of the proposed improvements. An ablation study on accuracy and tracking stability on public datasets are reported, furthermore, the comparisons with several state of the arts (namely, VINS-Mono, ORB-SLAM3, DSO, PL-SLAM) are investigated. The experimental results show that our approach can improve accuracy in weak texture scenes and motion blur cases, reduce the number of tracking loss and improve tracking robustness.

Mapping estimates of vascular permeability with a clinical indocyanine green fluorescence imaging system in experimental pancreatic adenocarcinoma tumors.

Pancreatic cancer tumors are known to be avascular, but their neovascular capillaries are still chaotic leaky vessels. Capillary permeability could have significant value for therapy assessment, and its quantification might be possible with macroscopic imaging of indocyanine green (ICG) kinetics in tissue. The capacity of using standard fluorescence surgical systems for ICG kinetic imaging as a probe for capillary leakage was evaluated using a clinical surgical fluorescence imaging system, as interpreted through vascular permeability modeling. Xenograft pancreatic adenocarcinoma models were imaged in mice during bolus injection of ICG to capture the kinetics of uptake. Image analysis included ratiometric data, normalization, and match to theoretical modeling. Kinetic data were converted into the extraction fraction of the capillary leakage. Pancreatic tumors were usually less fluorescent than the surrounding healthy tissues, but still the rate of tumor perfusion could be assessed to quantify capillary extraction. Model simulations showed that flow kinetics stabilized after about 1min beyond the initial bolus injection and that the relative extraction fraction model estimates matched the experimental data of normalized uptake within the tissue. The kinetics in the time period of 1 to 2min post-injection provided optimal differential data between AsPC1 and BxPC3 tumors, although high individual variation exists between tumors. ICG kinetic imaging during the initial leakage phase was diagnostic for quantitative vascular permeability within pancreatic tumors. Methods for autogain correction and normalized model-based interpretation allowed for quantification of extraction fraction and difference identification between tumor types in early timepoints.

An Hybrid Integration Method-Based Track-before-Detect for High-Speed and High-Maneuvering Targets in Ubiquitous Radar

Due to the limited transmission gain of ubiquitous radar systems, it has become necessary to use a long-time coherent integration method for range-Doppler (RD) analysis. However, when the target exhibits high-speed and high-maneuver capabilities, it introduces challenges, such as range migration (RM), Doppler frequency migration (DFM), and velocity ambiguity (VA) in the RD domain, thus posing significant difficulties in target detection and tracking. Moreover, the presence of VA further complicates the problem. To address these complexities while maintaining integration efficiency, this study proposes a hybrid integration approach. First, methods called Keystone-transform (KT) and matched filtering processing (MFP) are proposed for compensating for range migration (RM) and velocity ambiguity (VA) in Radar Detection (RD) images. The KT approach is employed to compensate for RM, followed by the generation of matched filters with varying ambiguity numbers. Subsequently, MFP enables the production of multiple RD images covering different but contiguous Doppler frequency ranges. These RD images can be compiled into an extended RD (ERD) image that exhibits an expanded Doppler frequency range. Second, an improved particle-filter (IPF) algorithm is raised to perform incoherent integration among ERD images and to achieve track-before-detect (TBD) for a target. In the IPF, the target state vector is augmented with ambiguous numbers, which are estimated via maximum posterior probability estimation. Then, to compensate for the DFM, a line spread model (LSM) is proposed instead of the point spread model (PSM) used in traditional PF. To evaluate the efficacy of the proposed method, a radar simulator is devised, encompassing comprehensive radar signal processing. The findings demonstrate that the proposed approach achieves a harmonious equilibrium between integration efficiency and computational complexity when it comes to detecting and tracking high-speed and high-maneuvering targets with intricate maneuvers. Furthermore, the algorithm’s effectiveness is authenticated by exploiting ubiquitous radar data.

Deep Bayesian-Assisted Keypoint Detection for Pose Estimation in Assembly Automation

Pose estimation is crucial for automating assembly tasks, yet achieving sufficient accuracy for assembly automation remains challenging and part-specific. This paper presents a novel, streamlined approach to pose estimation that facilitates automation of assembly tasks. Our proposed method employs deep learning on a limited number of annotated images to identify a set of keypoints on the parts of interest. To compensate for network shortcomings and enhance accuracy we incorporated a Bayesian updating stage that leverages our detailed knowledge of the assembly part design. This Bayesian updating step refines the network output, significantly improving pose estimation accuracy. For this purpose, we utilized a subset of network-generated keypoint positions with higher quality as measurements, while for the remaining keypoints, the network outputs only serve as priors. The geometry data aid in constructing likelihood functions, which in turn result in enhanced posterior distributions of keypoint pixel positions. We then employed the maximum a posteriori (MAP) estimates of keypoint locations to obtain a final pose, allowing for an update to the nominal assembly trajectory. We evaluated our method on a 14-point snap-fit dash trim assembly for a Ford Mustang dashboard, demonstrating promising results. Our approach does not require tailoring to new applications, nor does it rely on extensive machine learning expertise or large amounts of training data. This makes our method a scalable and adaptable solution for the production floors.

Turbo encoder and decoder chip design and FPGA device analysis for communication system

<p>Turbo codes are error-correcting codes with performance that is close to the Shannon theoretical limit (SHA). The motivation for using turbo codes is that the codes are an appealing mix of a random appearance on the channel and a physically realizable decoding structure. The communication systems have the problem of latency, fast switching, and reliable data transfer. The objective of the research paper is to design and turbo encoder and decoder hardware chip and analyze its performance. Two convolutional codes are concatenated concurrently and detached by an interleaver or permuter in the turbo encoder. The expected data from the channel is interpreted iteratively using the two related decoders. The soft (probabilistic) data about an individual bit of the decoded structure is passed in each cycle from one elementary decoder to the next, and this information is updated regularly. The performance of the chip is also verified using the maximum a posteriori (MAP) method in the decoder chip. The performance of field-programmable gate array (FPGA) hardware is evaluated using hardware and timing parameters extracted from Xilinx ISE 14.7. The parallel concatenation offers a better global rate for the same component code performance, and reduced delay, low hardware complexity, and higher frequency support.</p>

Dual-View Noise Correction for Crowdsourcing

In crowdsourcing scenarios, each instance obtains a multiple noisy label set from different crowd workers on the Internet and then gets its integrated label via label integration. Although label integration algorithms are often effective, a certain level of noise still remains in the integrated labels. To reduce the impact of noise on label quality, many noise correction algorithms have been proposed in recent years. However, most of them are hard to fully utilize the joint information of the original attribute view and multiple noisy label view. Motivated by multi-view learning, in this paper, we propose a dual-view noise correction (DVNC) algorithm. Benefiting from the complementary and consensus principle, DVNC can fully utilize the joint information of two views and thus enhance the effect of noise correction. In DVNC, we at first construct the original attribute view and multiple noisy label view for each instance and respectively train a classifier on each view. Then, we use the trained two classifiers to filter each noise instance and thus obtain a clean set and noise set. Finally, we train a classifier on the clean set to correct each instance in the noise set via reclassifying it as the class with the maximum posterior probability. The experimental results on simulated and real-world datasets indicate that DVNC significantly outperforms all the other noise correction algorithms used for comparison.

Effective resting-state connectivity in severe unipolar depression before and after electroconvulsive therapy

BackgroundElectroconvulsive therapy (ECT) is one of the most effective treatments for severe depressive disorders. A recent multi-center study found no consistent changes in correlation-based (undirected) resting-state connectivity after ECT. Effective (directed) connectivity may provide more insight into the working mechanism of ECT. ObjectiveWe investigated whether there are consistent changes in effective resting-state connectivity. MethodsThis multi-center study included data from 189 patients suffering from severe unipolar depression and 59 healthy control participants. Longitudinal data were available for 81 patients and 24 healthy controls. We used dynamic causal modeling for resting-state functional magnetic resonance imaging to determine effective connectivity in the default mode, salience and central executive networks before and after a course of ECT. Bayesian general linear models were used to examine differences in baseline and longitudinal effective connectivity effects associated with ECT and its effectiveness. ResultsCompared to controls, depressed patients showed many differences in effective connectivity at baseline, which varied according to the presence of psychotic features and later treatment outcome. Additionally, effective connectivity changed after ECT, which was related to ECT effectiveness. Notably, treatment effectiveness was associated with decreasing and increasing effective connectivity from the posterior default mode network to the left and right insula, respectively. No effects were found using correlation-based (undirected) connectivity. ConclusionsA beneficial response to ECT may depend on how brain regions influence each other in networks important for emotion and cognition. These findings further elucidate the working mechanisms of ECT and may provide directions for future non-invasive brain stimulation research.

Underwater Image Enhancement Based on Zero-Reference Deep Network

Due to underwater light absorption and scattering, underwater images usually suffer from severe color attenuation and contrast reduction. Most mainstream underwater image processing methods based on deep learning require a large amount of underwater paired training data, leading to a complex network structure, longer training time, and higher computational cost. To address this problem, a novel Zero-Reference Deep Network for Underwater Image Enhancement (Zero-UIE) is proposed in this paper, which transforms the enhancement of an underwater image into a specific parameter map estimation by using a deep network. The underwater curve model based on the classical haze image formation principle is specially designed to remove underwater color dispersion and cast. A lightweight deep network is designed to estimate the dynamic adjustment parameters of the underwater curve model, and then adjust the dynamic range of the given image pixels according to the model. A set of non-reference loss functions are designed according to the characteristics of underwater images, which can implicitly drive the network learning. In addition, adaptive color compensation can be optionally used as the pre-processing step to further improve the robustness and visual performance. The significant contribution of the proposed method is zero reference, i.e., it does not require any paired or unpaired reference data for training. Extensive experiments on various benchmarks demonstrate that the proposed method is superior to state-of-the-art methods subjectively and objectively, which is competitive and applicable to diverse underwater conditions. Most importantly, it is an innovative exploration of zero reference for underwater image enhancement.

VLSI Design of Saturation-Based Image Dehazing Algorithm

Hazy weather degrades the vividness of the images captured by real-time systems for applications such as object detection, remote sensing, and surveillance systems. This affects the performance of such real-time systems. The hardware implementation of a real-time haze removal system is imperative to solve these problems. Such a solution is proposed in this article. Here, the saturation-based hardware implementation of an image dehazing system is presented. To estimate atmospheric light more precisely, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$15\ttimes 15$</tex-math> </inline-formula> window minimum filter is implemented, which uses the downsampled hazy image to estimate the atmospheric light. Furthermore, we have employed saturation-based transmission map estimation, which makes our approach pixel-based rather than patch-based. Unlike existing patch-based methods, the proposed method requires neither an edge detection unit nor an image filtering unit to suppress halo artifacts around edges. The VLSI architecture of the proposed dehazing system comprises seven pipelined stages. It is implemented on FPGA as well as ASIC (65-nm technology node) platforms. The ASIC implementation of the proposed dehazing system yielded a maximum throughput of 624 Mpixels/s, which is fast enough to process <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3840\ttimes 2160$</tex-math> </inline-formula> resolution at a rate higher than 70 fps with only 13.2k logic gates count.