Estimation Algorithm Research Articles

Evaluation of compressive strength of concrete modified with admixtures using arithmetic optimization-based estimation algorithms

Evaluation of compressive strength of concrete modified with admixtures using arithmetic optimization-based estimation algorithms

Triple-diode solar cell current optimization – An analytical solution based on the Lambert W function

A novel mathematical modeling approach for the Triple-Diode Model (TDM) and its parameter estimation is introduced in this paper. For the first time in the literature, this paper presents two analytical solutions for calculating the current in TDM solar cells using the Lambert W function. Additionally, a new metaheuristic algorithm, the Adaptive Evaporation Rate Water Cycle Algorithm (Adaptive ERWCA), is proposed for estimating TDM solar cell parameters. The proposed algorithm is tested using both the new analytical solutions and a well-known iterative approach for the current-voltage characteristics of the TDM solar cells model. Extensive testing is conducted on three well-known solar cells/modules and a panel under various weather conditions. The results demonstrate that the proposed analytical expressions for the current-voltage characteristics are accurate and highly effective for representing TDM solar cell current. The accuracy of the parameter estimates obtained with the application of the proposed algorithm, considering both analytical solutions and the iterative approach, is compared with existing literature results. It is shown that the proposed algorithm outperforms existing algorithms in solar cell parameter estimation across both the analytical and iterative approaches for current-voltage characteristics. Remarkably, for the RTC France solar cell, the SOLAREX MSX 60 solar module, and the PHOTOWATT-PWP 201 solar module, the obtained Root Mean Square Errors (RMSE) are 0.00075141, 0.01157153, and 0.0010578, respectively. These results are currently the best reported in the literature.

A Complex-Valued Stationary Kalman Filter for Positive and Negative Sequence Estimation in DER Systems

In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized with the positive sequence voltage. However, positive and negative sequences are conventionally defined in a steady state and are not directly observed from the instantaneous voltage and current measurements at the DER unit’s point of connection. In this article, an estimation algorithm for sequence separation based on the Kalman filter is proposed. Furthermore, the proposed filter uses a complex vector representation of the asymmetric three-phase signals in synchronous coordinates to allow for the implementation of the Kalman filter in its stationary form, resulting in a simple dynamic filter able to estimate positive and negative sequences even during transient operation. The proposed stationary complex Kalman filter performs better than state-of-the-art techniques like DSOGI and very similarly to other Kalman filter implementations found in the literature but at a fraction of its computational cost (23.5%).

Pose Estimation Algorithm for Construction Workers

In order to solve the problem of difficulty in judging the human posture of construction workers in complex environments, this paper uses the method based on bone points to identify the human posture, first produces a video dataset of construction workers, and then compares the two algorithms, and selects a suitable pose estimation algorithm for construction site scenarios, which contributes to the pose estimation of construction workers.

FFT-Based Probability Density Imaging of Euler Solutions.

When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming "tail"-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with only the structural index. The nonparametric estimation method based on the normalized B-spline probability density (BSS) is used to separate the Euler solution clusters and mark different anomaly sources according to the similarity and density characteristics of the Euler solutions. For display purposes, the BSS needs to map the samples onto the estimation grid at the points where density will be estimated in order to obtain the probability density distribution. However, if the size of the samples or the estimation grid is too large, this process can lead to high levels of memory consumption and excessive computation times. To address this issue, a fast linear binning approximation algorithm is introduced in the BSS to speed up the computation process and save time. Subsequently, the sample data are quickly projected onto the estimation grid to facilitate the discrete convolution between the grid and the density function using a fast Fourier transform. A method involving multivariate B-spline probability density estimation based on the FFT (BSSFFT), in conjunction with fast linear binning appropriation, is proposed in this paper. The results of two random normal distributions show the correctness of the BSS and BSSFFT algorithms, which is verified via a comparison with the true probability density function (pdf) and Gaussian kernel smoothing estimation algorithms. Then, the Euler solutions of the two synthetic models are analyzed using the BSS and BSSFFT algorithms. The results are consistent with their theoretical values, which verify their correctness regarding Euler solutions. Finally, the BSSFFT is applied to Bishop 5X data, and the numerical results show that the comprehensive analysis of the 3D probability density distributions using the BSSFFT algorithm, derived from the Euler solution subset of x0,y0,z0, can effectively separate and locate adjacent anomaly sources, demonstrating strong adaptability.

An immune-related eleven-RNA signature-drived risk score model for prognosis of osteosarcoma metastasis

This study aimed to determine an immune-related RNA signature as a prognostic marker, in this study, we developed a risk score model for predicting the prognosis of osteosarcoma metastasis. We first downloaded the clinical information and expression data of osteosarcoma samples from the UCSC Xena and GEO databases, of which the former was the training set and the latter was the validation set. Immune infiltration was assessed using the ssGSEA and ESTIMATE algorithms, and the osteosarcoma samples were divided into the Immunity_L and Immunity_H groups. Then, eleven RNAs were identified as the optimal prognostic RNA signatures using LASSO Cox regression analysis for establishing a risk score (RS) model. Kaplan–Meier approach indicated the high-risk group exhibited a shorter survival. Furthermore, we analyzed the tumor metastasis, age, and RS model status were determined to be independent clinical prognostic factors using Cox regression analysis. Decision curve analysis (DCA) indicated that the prognostic factor + RS model had the best net benefit. Finally, nine tumor-infiltrating immune cells (TIICs) showed significant differences in abundance between high- and low-risk groups via CIBERSORT deconvolution algorithm. In conclusion, the immune-related eleven-RNA signature be could served as a potential prognostic biomarker for osteosarcoma metastasis.

Joint parameter estimation algorithm for polarization-sensitive channel compression arrays based on atomic norm minimization

To reduce the complexity of direction-of-arrival (DOA) algorithms in polarization-sensitive arrays and maintain high estimation accuracy while decreasing runtime, this paper proposes a channel compression model based on orthogonal dipole arrays. In addition, a DOA estimation algorithm using atomic norm minimization (ANM) is introduced for this model. This algorithm performs eigenvalue decomposition on the covariance matrix of the data received from the polarization-sensitive channel compressed array. A new observation vector is constructed for the ANM problem under the channel compression model using the obtained eigenvalues and eigenvectors. Subsequently, a Toeplitz matrix is constructed from the optimal solution of the semi-positive definite programming (SDP) problem. The Vandermonde decomposition of the Toeplitz matrix provides estimates of the signal DOA parameters. By combining the vectorization result of the covariance matrix and the least-squares calculation, the polarization auxiliary angle and polarization phase angle information of the incident source are also obtained. Simulation experiments compare the root-mean-squared error (RMSE) of each algorithm at different angular intervals and signal-to-noise ratios (SNR) to confirm the validity of estimating DOA and polarization parameters.

Human action recognition with transformer based on convolutional features

As one of the key research directions in the field of computer vision, human action recognition has a wide range of practical application values and prospects. In the fields of video surveillance, human-computer interaction, sports analysis, and healthcare, human action recognition technology shows a broad application prospect and potential. However, the diversity and complexity of human actions bring many challenges, such as handling complex actions, distinguishing similar actions, coping with changes in viewing angle, and overcoming occlusion problems. To address the challenges, this paper proposes an innovative framework for human action recognition. The framework combines the latest pose estimation algorithms, pre-trained CNN models, and a Vision Transformer to build an efficient system. The first step involves utilizing the latest pose estimation algorithm to accurately extract human pose information from real RGB image frames. Then, a pre-trained CNN model is used to perform feature extraction on the extracted pose information. Finally, the Vision Transformer model is applied for fusion and classification operations on the extracted features. Experimental validation is conducted on two benchmark datasets, UCF 50 and UCF 101, to demonstrate the effectiveness and efficiency of the proposed framework. The applicability and limitations of the framework in different scenarios are further explored through quantitative and qualitative experiments, providing valuable insights and inspiration for future research.

Pan-Cancer Analysis and Experimental Validation of CEND1 as a Prognostic and Immune Infiltration-Associated Biomarker for Gliomas.

Cell cycle exit and neuronal differentiation 1 (CEND1), highly expressed in the brain, is a specific transmembrane protein which plays a tumor suppressor role. This study is performed to investigate the role of CEND1 in various cancers through pan-cancer analysis, and further investigate its functions in gliomas by cell experiments. The expression and subcellular localization of CEND1 in different cancer types were analyzed utilizing the data from the GEPIA, UCSC, UALCAN and HPA databases. Relationships of CEND1 expression with prognosis, immunomodulation-related genes, immune checkpoint genes, microsatellite instability (MSI), tumor mutation burden (TMB) and RNA modifications were analyzed based on the TCGA database. The ESTIMATE algorithm was utilized to evaluate tumors' StromalScore, Immune Score, and ESTIMATES Score. The cBioPortal database was employed to analyze the categories and frequencies of CEND1 gene alterations. Biological functions and co-expression patterns of CEND1 in gliomas were explored using the LinkedOmics database, and Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses were conducted. The interactions between CEND1 and drugs were explored employing the Comparative Toxicogenomics Database and molecular docking technology. Cell experiments were conducted to analyze triptonide's effects on glioma cells through CCK-8, flow cytometry and qRT-PCR. CEND1 was lowly expressed in gliomas, and high CEND1 expression was correlated to better overall survival of glioma patients (HR = 0.65, P = 0.02). Deep deletion was the main type of hereditary change of CEND1 mutation. CEND1 expression was markedly associated with immune infiltration, TMB, MSI, and RNA modification in various tumors (r > 0.3, P < 0.05). CEND1 co-expressed genes in gliomas were markedly correlated with immune responses and cell cycle (FDR < 0.05). Triptonide could bind well to CEND1 (-5.0kcal/mol), and triptonide could facilitate CEND1 expression in glioma cells and cell apoptosis, and block the cell cycle progression (P < 0.05). CEND1 serves as a potential biomarker for pan-cancer. Particularly in gliomas, CEND1 is a key regulator of cell apoptosis and cell cycle, and a potential target for glioma treatment.

Identification of disulfidptosis-associated genes and characterization of immune cell infiltration in thyroid carcinoma.

The primary objective of this study is to conduct a comprehensive screening and analysis of differentially expressed genes related to disulfidoptosis (DEDRGs) in thyroid carcinoma (THCA). This entails delving into the intricate characterization of immune cell infiltration within the THCA context and subsequently formulating and validating a novel prognostic model. To achieve our objectives, we first delineated two distinct subtypes of disulfidoptosis-related genes (DRGs) via consensus clustering methodology. Subsequently, employing the limma R package, we identified the DEDRGs critical for our investigation. These DEDRGs underwent meticulous validation across various databases, alongside an in-depth analysis of gene regulation. Employing functional enrichment techniques, we explored the potential molecular mechanisms underlying disulfidoptosis in THCA. Furthermore, we scrutinized the immune landscape within the two identified subtypes utilizing CIBERSORT and ESTIMATE algorithms. The construction of the prognostic model for THCA entailed intricate methodologies including univariate, multivariate Cox regression, and LASSO regression algorithms. The validity and efficacy of our prognostic model were corroborated through Kaplan-Meier survival curves and ROC curves. Additionally, a nomogram was meticulously formulated to facilitate the prediction of patient prognosis. To fortify our findings, we conducted a comprehensive Bayesian co-localization analysis coupled with rigorous in vitro experimentation, aimed at unequivocally establishing the validity of the identified DEDRGs. Our analyses unveiled Cluster C1, characterized by elevated expression levels of DEDRGs, as harboring a favorable prognosis accompanied by abundant immune cell infiltration. Correlation analyses underscored predominantly positive associations among the DEDRGs, further affirming their significance in THCA. Differential expression patterns of DEDRGs between tumor samples and normal tissues were evident across the GEPIA and HPA databases. Insights from the TIMER database underscored a robust correlation between DEDRGs and immune cell infiltration. KEGG analysis elucidated the enrichment of DEDRGs primarily in pivotal pathways including MAPK, PPAR signaling pathway, and Proteoglycans in cancer. Furthermore, analyses using CIBERSORT and ESTIMATE algorithms shed light on the crucial role played by DEDRGs in shaping the immune microenvironment. The prognostic model, anchored by five genes intricately associated with THCA prognosis, exhibited commendable predictive accuracy and was intricately linked to the tumor immune microenvironment. Notably, patients categorized with low-risk scores stood to potentially benefit more from immunotherapy. The validation of DEDRGs unequivocally underscores the protective role of INF2 in THCA. In summary, our study delineates two discernible subtypes intricately associated with DRGs, revealing profound disparities in immune infiltration and survival prognosis within the THCA milieu. The implications of our findings extend to potential treatment strategies for THCA patients, which could entail targeted interventions directed towards DEDRGs and prognostic genes, thereby influencing disulfidptosis and the immune microenvironment. Moreover, the robust predictive capability demonstrated by our prognostic model, based on the five genes (ANGPTL7, FIRRE, ODAPH, PROKR1, SFRP5), underscores its potential clinical utility in guiding personalized therapeutic approaches for THCA patients.

LiDAR-based SLAM pose estimation via GNSS graph optimization algorithm

LiDAR simultaneous localization and mapping (SLAM) is widely used in positioning and navigation. By illuminating a series of light spots on the surface of an object, orientation and pose information is obtained. However, improving the accuracy of the pose optimization algorithm without affecting the position information is difficult. Therefore, this study combines the graph optimization algorithm and the Global Navigation Satellite System (GNSS) to optimize the coordinates of the target object in the LiDAR SLAM pose. A GNSS pose estimation algorithm is proposed to show the relationship between positioning algorithms with and without GNSS pose optimization by analyzing the deviation of the distance, level, and height laser point cloud coordinates. The results show that with GNSS pose optimization, the deviations in distance, level, and height are 99% smaller than those without GNSS pose optimization. Furthermore, we demonstrate the effectiveness of the proposed graph optimization algorithm and GNSS optimization of LiDAR SLAM. Finally, this study highlights the directions for the application of wireless communication technology in the field of LiDAR SLAM.

Congruential Summation-Triggered Identification of FIR Systems under Binary Observations and Uncertain Communications

With the advancement of network technology, there has been an increase in the volume of data being transmitted across networks. Due to the bandwidth limitation of communication channels, data often need to be quantized or event-triggered mechanisms are introduced to conserve communication resources. On the other hand, network uncertainty can lead to data loss and destroy data integrity. This paper investigates the identification of finite impulse response (FIR) systems under the framework of stochastic noise and the combined effects of the event-triggered mechanism and uncertain communications. The study provides a reference for the application of remote system identification under transmission-constrained and packet loss scenarios. First, a congruential summation-triggered communication scheme (CSTCS) is introduced to lower the communication rate. Then, parameter estimation algorithms are designed for scenarios with known and unknown packet loss probabilities, respectively, and their strong convergence is proved. Furthermore, an approximate expression for the convergence rate is obtained by data fitting under the condition of uncertain packet loss probability, treating the trade-off between convergence performance and communication resource usage as a constrained optimization problem. Finally, the rationality and correctness of the algorithm are verified by numerical simulations.

Joint ABS-UKCGG-CanGene-CanVar consensus regarding the use of CanRisk in clinical practice.

The CanRisk tool, which operationalises the Breast and Ovarian Analysis of Disease Incidence and Carrier Estimation Algorithm (BOADICEA) is used by Clinical Geneticists, Genetic Counsellors, Breast Oncologists, Surgeons and Family History Nurses for breast cancer risk assessments both nationally and internationally. There are currently no guidelines with respect to the day-to-day clinical application of CanRisk and differing inputs to the model can result in different recommendations for practice. To address this gap, the UK Cancer Genetics Group in collaboration with the Association of Breast Surgery and the CanGene-CanVar programme held a workshop on 16th of May 2023, with the aim of establishing best practice guidelines. Using a pre-workshop survey followed by structured discussion and in-meeting polling, we achieved consensus for UK best practice in use of CanRisk in making recommendations for breast cancer surveillance, eligibility for genetic testing and the input of available information to undertake an individualised risk assessment. Whilst consensus recommendations were achieved,the meeting highlighted some of the barriers limiting the use of CanRisk in clinical practice and identified areas that require further work and collaboration with relevant national bodies and policy makers to incorporate wider use of CanRisk into routine breast cancer risk assessments.

Zonotopic state estimation and sensor fault detection for a wastewater treatment bioprocess

AbstractIn this paper, a fault diagnosis method for the basic process of microbial growth in wastewater treatment based on interval estimation technology is proposed. First, a nonlinear microbial growth model is converted into a linear time‐varying system. A time‐varying observer is then designed for the generated system, which takes into account an performance. Furthermore, a zonotope‐based set‐membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault diagnosis is performed for a wastewater treatment bioprocess with sensor fault signals. Finally, the feasibility of the proposed fault diagnosis strategy for the wastewater treatment bioprocess is illustrated through numerical simulations.

A Stochastic-Geometrical Framework for Object Pose Estimation Based on Mixture Models Avoiding the Correspondence Problem

AbstractPose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple feature points. This framework utilizes mixture models for feature point densities in object space and for interpreting real measurements. Advantages are the avoidance to resolve individual feature correspondences and to incorporate correct stochastic dependencies in multi-view applications. First, the general modeling framework is presented, second, a general algorithm for pose estimation is derived, and third, two example models (camera and lateration setup) are presented. Numerical experiments show the effectiveness of this modeling and general algorithm by presenting four simulation scenarios for three observation systems, including the dependence on measurement resolution, object deformations and measurement noise. Probabilistic modeling utilizing mixture models shows the potential for accurate and robust pose estimations while avoiding the correspondence problem.

Linear System Identification-Oriented Optimal Tampering Attack Strategy and Implementation Based on Information Entropy with Multiple Binary Observations

With the rapid development of computer technology, communication technology, and control technology, cyber-physical systems (CPSs) have been widely used and developed. However, there are massive information interactions in CPSs, which lead to an increase in the amount of data transmitted over the network. The data communication, once attacked by the network, will seriously affect the security and stability of the system. In this paper, for the data tampering attack existing in the linear system with multiple binary observations, in the case where the estimation algorithm of the defender is unknown, the optimization index is constructed based on information entropy from the attacker’s point of view, and the problem is modeled. For the problem of the multi-parameter optimization with energy constraints, this paper uses particle swarm optimization (PSO) to obtain the optimal data tampering attack solution set, and gives the estimation method of unknown parameters in the case of unknown parameters. To implement the real-time improvement of online implementation, the BP neural network is designed. Finally, the validity of the conclusions is verified through numerical simulation. This means that the attacker can construct effective metrics based on information entropy without the knowledge of the defense’s discrimination algorithm. In addition, the optimal attack strategy implementation based on PSO and BP is also effective.

Direction of Arrival (DOA) Estimation using Switched Beam Antenna with Butler Matrix at mm-Wave Frequency

This paper presents a butler matrix-based microstrip hexagonal patch antenna with a direction of arrival (DOA) estimation approach for mm-wave application. The hexagonal-shaped patch antenna had been designed with a Z-shaped slot with an eight-port butler matrix. The DOA estimation is also done for the switched beam antenna using a novel direction of arrival (DOA) estimation algorithm known as Cramer-Rao lower bound (CRLB). The proposed design leads to significant size reduction and loss minimization. In addition to this, the design had the advantages of being low-cost, lightweight, and small-volume. The entire proposed design provides an operating frequency range of 28 GHz to 39 GHz with a center frequency of 33 GHz. The proposed work makes use of two butler matrices with two 45° phase shifters and 120° phase shifters. The effectiveness of the proposed algorithm and antenna design using the Butler matrix is evaluated for various performance metrics separately. The antenna is designed using Rogers RT/duroid 5880(tm) substrate, and the fabricated prototype is studied. The designed antenna attains high radiation efficiency, and it ranges between 97 to 98% under both the measures and simulated scenarios under the operating frequency range of 28 GHz to 39 GHz.

Comparing the allometric model to machine learning algorithms for aboveground biomass estimation in tropical forests

Estimating aboveground biomass (AGB) pools is critical for understanding the structural characteristics of forest ecosystems, as the quantitative analysis of biomass contributes to a better understanding of carbon sequestration and in studying the productivity within forest ecosystems. A more precise estimation of AGB is necessary for the estimation of the amount of carbon stored in an ecosystem that is needed for the valuation of the ecosystem services. Though regression models have been used previously for both tree-level and stand-level biomass estimations, supervised machine learning models have rarely been put to test in field-based estimations of AGB. This study was done in the tropical forests of Northeast India (two reserve forests in Tripura) to compare the allometric performance of weighted nonlinear regression model (NLM) to random forest regression (RFR), extreme gradient boost regression (XGB), and support vector machine regression (SVR) in estimating tree-level AGB. Due to their ease of measurement in field conditions and ensuring practical use, tree diameter at breast height (DBH) and tree height (H) were used as the independent variables to train the models. 506 trees representing 21 local tree species were inventoried. Then, the four models (NLM, RFR, XGB, and SVM) were trained separately on the data and compared to find an optimal method to estimate AGB using modeling efficiency of fit (MEfit) and Root Mean Squared Error (RMSE). The models were then validated using the predicted residual error sum of squares (PRESS) statistics. The best fit model in our study was using RFR, with a high MEfit (0.95–0.99), low RMSE (63.10–132.39 kg), and outperforming all other methods in the PRESS statistics, with the highest modeling efficiency of prediction (0.94–0.99) and lowest mean of absolute PRESS residuals (34.99–78.23). The results from Northeast India presented here provide preliminary evidence that RFR could be a reliable method for determining the field-level carbon stock and understanding the biomass dynamics for evergreen and moist deciduous tropical forests. The model accuracy may be constrained by a limited number of variables chosen to suit practical use in the field, and incorporating additional tree-level or stand-level variables such as crown diameter and stand basal area could enhance the robustness and generalizability of AGB estimation.

Operational Angular Track Reconstruction in Space Surveillance Radars through an Adaptive Beamforming Approach

In the last few years, many space surveillance initiatives have started to consider the problem represented by resident space object overpopulation. In particular, the European Space Surveillance and Tracking (EUSST) consortium is in charge of providing services like collision avoidance, fragmentation analysis, and re-entry, which rely on measurements obtained through ground-based sensors. BIRALES is an Italian survey radar belonging to the EUSST framework and is capable of providing measurements including Doppler shift, slant range, and angular profile. In recent years, the Music Approach for Track Estimate and Refinement (MATER) algorithm has been developed to retrieve angular tracks through an adaptive beamforming technique, guaranteeing the generation of more accurate and robust measurements with respect to the previous static beamforming approach. This work presents the design of a new data processing chain to be used by BIRALES to compute the angular track. The signal acquired by the BIRALES receiver array is down-converted and the receiver bandwidth is split into multiple channels, in order to maximize the signal-to-noise ratio of the measurements. Then, the signal passes through a detection block, where an isolation procedure creates, for each epoch, signal correlation matrices (CMs) related to the channels involved in the detection and then processes them to isolate the data stream related to a single detected source. Consequently, for each epoch and for each detected source, just the CM featuring the largest signal contribution is kept, allowing deriving the Doppler shift measurement from the channel illumination sequence. The MATER algorithm is applied to each CM stream, first estimating the signal directions of arrival, then grouping them in the observation time window, and eventually returning the target angular track. Ambiguous estimates may be present due to the configuration of the receiver array, which cause spatial aliasing phenomena. This problem can be addressed by either exploiting transit prediction (in the case of cataloged objects), or by applying tailored criteria (for uncatalogued objects). The performance of the new architecture was assessed in real operational scenarios, demonstrating the enhancement represented by the implementation of the channelization strategy, as well as the angular measurement accuracy returned by MATER, in both nominal and off-nominal scenarios.

Simultaneous Activity and Attenuation Estimation in TOF-PET With TV-Constrained Nonconvex Optimization.

An alternating direction method of multipliers (ADMM) framework is developed for nonsmooth biconvex optimization for inverse problems in imaging. In particular, the simultaneous estimation of activity and attenuation (SAA) problem in time-of-flight positron emission tomography (TOF-PET) has such a structure when maximum likelihood estimation (MLE) is employed. The ADMM framework is applied to MLE for SAA in TOF-PET, resulting in the ADMM-SAA algorithm. This algorithm is extended by imposing total variation (TV) constraints on both the activity and attenuation map, resulting in the ADMM-TVSAA algorithm. The performance of this algorithm is illustrated using the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm as a reference.