Noise Vector Research Articles

Unsupervised co-generation of foreground–background segmentation from Text-to-Image synthesis

Text-to-Image (T2I) synthesis is a challenging task requiring modelling both textual and image domains and their relationship. The substantial improvement in image quality achieved by recent works has paved the way for numerous applications such as language-aided image editing, computer-aided design, text-based image retrieval, and training data augmentation. In this work, we ask a simple question: Along with realistic images, can we obtain any useful by-product (e.g. foreground/background or multi-class segmentation masks, detection labels) in an unsupervised way that will also benefit other computer vision tasks and applications?. In an attempt to answer this question, we explore generating realistic images and their corresponding foreground/background segmentation masks from the given text. To achieve this, we experiment the concept of co-segmentation along with GAN. Specifically, a novel GAN architecture called Co-Segmentation Inspired GAN (COS-GAN) is proposed that generates two or more images simultaneously from different noise vectors and utilises a spatial co-attention mechanism between the image features to produce realistic segmentation masks for each of the generated images. The advantages of such an architecture are two-fold: (1) The generated segmentation masks can be used to focus on foreground and background exclusively to improve the quality of generated images, and (2) the segmentation masks can be used as a training target for other tasks, such as object localisation and segmentation. Extensive experiments conducted on CUB, Oxford-102, and COCO datasets show that COS-GAN is able to improve visual quality and generate reliable foreground/background masks for the generated images.

Machine learning approach to flare-up detection and clustering in chronic obstructive pulmonary disease (COPD) patients.

Chronic obstructive pulmonary disease (COPD) is a prevalent and preventable condition that typically worsens over time. Acute exacerbations of COPD significantly impact disease progression, underscoring the importance of prevention efforts. This observational study aimed to achieve two main objectives: (1) identify patients at risk of exacerbations using an ensemble of clustering algorithms, and (2) classify patients into distinct clusters based on disease severity. Data from portable medical devices were analyzed post-hoc using hyperparameter optimization with Self-Organizing Maps (SOM), Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Isolation Forest, and Support Vector Machine (SVM) algorithms, to detect flare-ups. Principal Component Analysis (PCA) followed by KMeans clustering was applied to categorize patients by severity. 25 patients were included within the study population, data from 17 patients had the required reliability. Five patients were identified in the highest deterioration group, with one clinically confirmed exacerbation accurately detected by our ensemble algorithm. Then, PCA and KMeans clustering grouped patients into three clusters based on severity: Cluster 0 started with the least severe characteristics but experienced decline, Cluster 1 consistently showed the most severe characteristics, and Cluster 2 showed slight improvement. Our approach effectively identified patients at risk of exacerbations and classified them by disease severity. Although promising, the approach would need to be verified on a larger sample with a larger number of recorded clinically verified exacerbations.

Identification methodology for MIMO Hammerstein nonlinear model with process noise

In this paper, we present a methodology for identifying the multi-input–multi-output (MIMO) Hammerstein nonlinear model under colored noise. The Hammerstein model presented comprises neural fuzzy models (NFMs) as its static nonlinear block and rational transfer functions (RTF) model as its dynamic linear block. The hybrid signals consisting of separable signals and random signals are utilized to deal with the MIMO Hammerstein model identification issue, and the separable signals to implement separation identification of MIMO Hammerstein model is introduced, that is, the two blocks are separately identified. First, parameters of the linear block are estimated applying correlation function-based least squares method in the presence of measurable input–output of Gaussian signals, which can efficiently weaken the process noise interference. Second, estimate of noise parameters vector is introduced to solve the unknown noise vector in the information matrix, then a recursive extended least squares method is developed for identifying parameters of nonlinear block and colored noise model based on available input–output of random signals. The validity and precision of the presented methodology are demonstrated applying a numerical simulation and a nonlinear process, and it is known from the research results that compared with existing identification techniques, the methodology utilized achieved higher identification accuracy.

Text-Driven Video Prediction

Current video generation models usually convert signals indicating appearance and motion received from inputs (e.g., image and text) or latent spaces (e.g., noise vectors) into consecutive frames, fulfilling a stochastic generation process for the uncertainty introduced by latent code sampling. However, this generation pattern lacks deterministic constraints for both appearance and motion, leading to uncontrollable and undesirable outcomes. To this end, we propose a new task called Text-driven Video Prediction (TVP). Taking the first frame and text caption as inputs, this task aims to synthesize the following frames. Specifically, appearance and motion components are provided by the image and caption separately. The key to addressing the TVP task depends on fully exploring the underlying motion information in text descriptions, thus facilitating plausible video generation. In fact, this task is intrinsically a cause-and-effect problem, as the text content directly influences the motion changes of frames. To investigate the capability of text in causal inference for progressive motion information, our TVP framework contains a Text Inference Module (TIM), producing step-wise embeddings to regulate motion inference for subsequent frames. In particular, a refinement mechanism incorporating global motion semantics guarantees coherent generation. Extensive experiments are conducted on Something-Something V2 and Single Moving MNIST datasets. Experimental results demonstrate that our model achieves better results over other baselines, verifying the effectiveness of the proposed framework.

Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise.

Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian with rates, when [Formula: see text] data points are i.i.d. sampled from a general [Formula: see text]-dimensional manifold embedded in a possibly high-dimensional space. Under certain joint limit of [Formula: see text] and kernel bandwidth [Formula: see text], the point-wise convergence rate of the graph Laplacian operator (under 2-norm) is proved to be [Formula: see text] at finite large [Formula: see text] up to log factors, achieved at the scaling of [Formula: see text]. When the manifold data are corrupted by outlier noise, we theoretically prove the graph Laplacian point-wise consistency which matches the rate for clean manifold data plus an additional term proportional to the boundedness of the inner-products of the noise vectors among themselves and with data vectors. Motivated by our analysis, which suggests that not exact bi-stochastic normalization but an approximate one will achieve the same consistency rate, we propose an approximate and constrained matrix scaling problem that can be solved by SK iterations with early termination. Numerical experiments support our theoretical results and show the robustness of bi-stochastically normalized graph Laplacian to high-dimensional outlier noise.

Self-supervised graph representations with generative adversarial learning

Graph Neural Networks (GNNs) are powerful neural models for representation learning on graphs. In this work we study a self-supervised learning GNN method GraphSSGAN (Graph Self-Supervised Generative Adversarial Network) that learns generalized node representations using only unlabeled data. The core idea lies in learning representations that capture both the local information of the links and the global information of the plausibility of the subgraph samples. Specifically, node features of the original graph are first encoded into latent representations by optimizing a link prediction objective. Then the generator converts noise vectors to node representations in the latent space and predicts the link probabilities from the generated node representations. The discriminator leverages the graph convolutional network (GCN) architecture to produce permutation-invariant graph-level embeddings, and the intermediate node representations are used by simple classifiers in the downstream tasks. In addition, we introduce several technical tricks including Gumbel-Top-k trick, Gumbel-Softmax trick and mini-batch training via subgraph sampling to improve the training process. Through extensive experiments on node classification and link prediction tasks, we demonstrate the effectiveness of the proposed model and the contribution of GAN framework on graph representation learning.

Three-Dimensional Signal Source Localization with Angle-Only Measurements in Passive Sensor Networks

Some passive sensors can provide only relative angles of a signal source. To obtain the signal source location, multiple passive sensors can be constructed into a passive sensor network through communication links. This paper investigates the source localization problem with angle-only measurements in three-dimensional space. First, we present an intersection localization method, which estimates the target position by minimizing the sum of distances between lines formed by angle-only measurements. It has the same target position estimate as the widely used least-squares (LS) method, but with a lower computational cost. Furthermore, considering the differences in measurement accuracy of sensors, the weighted least-squares (WLS) algorithm can achieve better localization performance than the LS method. Unfortunately, since the coefficient matrix and the noise vector are correlated, the WLS method is biased. The bias-compensation WLS (BCWLS) method is also presented in this paper to reduce the bias by estimating the correlation between the coefficient matrix and the pseudolinear noise vector. To evaluate the performance of the presented algorithms, numerical simulations are conducted, indicating that the superiority of the intersection localization method in computational cost and the superiority of the BCWLS method in localization accuracy.

Robust Kalman filter for fractional order systems with uncertain colored noise variance

For fractional order systems with colored process noise, the discretization fractional order system model is used to construct the augmented vector defined by the state vector and colored process noise vector. Based on the augmented equation of fractional order systems, the robust local Kalman filtering algorithm for fractional order systems with colored process noise is derived. The matrix weighted fusion, weighted measurement fusion and centralized fusion methods were used to fuse and estimate the state of multi-sensor fractional order system. Simulation results show the effectiveness of the proposed algorithm.

Frequency compensated diffusion model for real-scene dehazing

Due to distribution shift, deep learning based methods for image dehazing suffer from performance degradation when applied to real-world hazy images. In this paper, this study considers a dehazing framework based on conditional diffusion models for improved generalization to real haze. First, our work finds that optimizing the training objective of diffusion models, i.e., Gaussian noise vectors, is non-trivial. The spectral bias of deep networks hinders the higher frequency modes in Gaussian vectors from being learned and hence impairs the reconstruction of image details. To tackle this issue, this study designs a network unit, named Frequency Compensation block (FCB), with a bank of filters that jointly emphasize the mid-to-high frequencies of an input signal. Our work demonstrates that diffusion models with FCB achieve significant gains in both perceptual and distortion metrics. Second, to further boost the generalization performance, this study proposed a novel data synthesis pipeline, HazeAug, to augment haze in terms of degree and diversity. Within the framework, a solid baseline for blind dehazing is set up where models are trained on synthetic hazy-clean pairs, and directly generalize to real data. Extensive evaluations on real dehazing datasets demonstrate the superior performance of the proposed dehazing diffusion model in distortion metrics. Compared to recent methods pre-trained on large-scale, high-quality image datasets, our model achieves a significant PSNR improvement of over 1 dB on challenging databases such as Dense-Haze and Nh-Haze.

ACQ: Improving generative data-free quantization via attention correction

Data-free quantization aims to achieve model quantization without accessing any authentic sample. It is significant in an application-oriented context involving data privacy. Converting noise vectors into synthetic samples through a generator is a popular data-free quantization method, which is called generative data-free quantization. However, there is a difference in attention map between synthetic samples and authentic samples. This is always ignored and restricts the quantization performance. First, since synthetic samples of the same class are prone to have homogenous attention, the quantized network can only learn limited intra-class visual features. Second, synthetic samples in eval mode and training mode exhibit different attention. Hence, the statistical distribution matching tends to be inaccurate. ACQ is proposed in this paper to fix the attention of synthetic samples. Regarding intra-class attention homogeneity, we introduce an attention center matching loss aimed at achieving coarse-grained matching of attention of synthetic samples. Additionally, we have devised an adversarial loss based on pairs of samples with identical conditions. On one hand, this mechanism prevents the generator from mode collapse due to excessive attention on conditional information. On the other hand, it augments the separation between intra-class samples, thus further enhancing intra-class attention diversity. To improve the attention similarity of synthetic samples in different network modes, we introduce a consistency penalty to guarantee accurate statistical distribution matching. The experimental results demonstrate that ACQ effectively improves the attention problems of synthetic samples. Under various training settings, ACQ achieves the best quantization performance. For the 4-bit quantization of Resnet18 and Resnet50, ACQ reaches 67.55 % and 72.23 % accuracy, respectively.

Web Semantic-Based Robust Graph Contrastive Learning for Recommendation via Invariant Learning

The use of contrastive learning (CL) in recommendation has advanced significantly. Recently, some works use perturbations in the embedding space to obtain enhanced views of nodes. This makes the representation distribution of nodes more even and then improve recommendation effectiveness. In this article, the authors provide an explanation on the role of added noises in the embedding space from the perspective of invariant learning and feature selection. Guided by this thinking, the authors devise a more reasonable method for generating random noises and put forward web semantic based robust graph contrastive learning for recommendation via invariant learning, a novel graph CL-based recommendation model, named RobustGCL. RobustGCL, randomly zeros the values of certain dimensions in the noise vectors at a fixed ratio. In this way, RobustGCL can identify invariant and variant features and then learn invariant and variant representations. Tests on publicly available datasets show that our proposed approach can learn invariant representations and achieve better performance.

Machine learning applications for anomaly detection in Smart Water Metering Networks: A systematic review

The digitization of the water sector has led to the emergence of Smart Water Metering Networks (SWMNs), which enable automated and continuous water consumption measurement. However, challenges persist in efficiently managing and transmitting the vast amount of data generated by these networks. To address this, researchers have proposed anomaly detection techniques to identify and detect anomalies within SWMNs. In the realm of anomaly detection, a substantial body of research has emerged. However, there is a notable gap in the literature on a comprehensive synthesis of Machine Learning (ML) applications for anomaly detection in SWMNs. To bridge this knowledge gap, this study evaluated thirty-two research papers written between 2016 and 2023, focusing on ML applications for anomaly detection in smart water systems, smart water grids, water distribution networks, and water networks. From an initial pool of 725 research papers, those directly related to ML-based anomaly detection techniques were selected and analysed using both quantitative and qualitative data analysis. The study revealed that ML techniques such as k-Nearest Neighbors (kNN), Autoencoders, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Random Forest, Decision Trees, and Support Vector Machines (SVM) have made significant contributions to anomaly detection within these networks. Notably, researchers frequently employed multiple ML techniques to enhance accuracy. Performance metrics analysis demonstrated that F1 score, precision, accuracy, and recall were commonly used to assess the quality of ML anomaly detection techniques. This review aims to provide researchers with recommendations for selecting suitable ML anomaly detection techniques in SWMNs. The findings underscore the promising nature of ML applications for anomaly detection in SWMNs and highlight the need for further research in this area.

On the correlation between the noise and a priori error vectors for standard and augmented affine projection algorithms

This paper analyzes the correlation matrix between the a priori error and measurement noise vectors for standard and augmented affine projection algorithms using a unified approach. This correlation stems from the dependence between the filter tap estimates and the noise samples, and has a strong influence on the mean square behavior of the algorithm. We show that the correlation matrix is upper triangular, and compute the diagonal elements in closed form, showing that they are independent of the input process statistics. Also, for white inputs we show that the matrix is fully diagonal. These results are valid in the transient and steady states, considering a possibly variable step-size. Our only assumption is that the filter order is large compared to its projection order and that the input signal is stationary. Using these results, we perform a steady-state analysis for small step size and provide a new simple closed-form expression for the mean-square error, which has comparable or better accuracy to many preexisting expressions, and is much simpler to compute. Finally, we also obtain expressions for the steady-state energy of the other components of the error vector.

The performance of the amplitude-based model for complex phase retrieval

Abstract This paper aims to study the performance of the amplitude-based model $\widehat{{\boldsymbol x}} \in \mathop{\mathrm{argmin}}\limits _{{\boldsymbol x}\in \mathbb{C}^{d}}\sum _{j=1}^{m}\left (|\langle{\boldsymbol a}_{j},{\boldsymbol x}\rangle |-b_{j}\right )^{2}$, where $b_{j}:=|\langle{\boldsymbol a}_{j},{\boldsymbol x}_{0}\rangle |+\eta _{j}$ and ${\boldsymbol x}_{0}\in \mathbb{C}^{d}$ is a target signal. The model is raised in phase retrieval as well as in absolute value rectification neural networks. Many efficient algorithms have been developed to solve it in the past decades. However, there are very few results available regarding the estimation performance in the complex case under noisy conditions. In this paper, we present a theoretical guarantee on the amplitude-based model for the noisy complex phase retrieval problem. Specifically, we show that $\min _{\theta \in [0,2\pi )}\|\widehat{{\boldsymbol x}}-\exp (\mathrm{i}\theta )\cdot{\boldsymbol x}_{0}\|_{2} \lesssim \frac{\|{\boldsymbol \eta }\|_{2}}{\sqrt{m}}$ holds with high probability provided the measurement vectors ${\boldsymbol a}_{j}\in \mathbb{C}^{d},$ $j=1,\ldots ,m,$ are i.i.d. complex sub-Gaussian random vectors and $m\gtrsim d$. Here ${\boldsymbol \eta }=(\eta _{1},\ldots ,\eta _{m})\in \mathbb{R}^{m}$ is the noise vector without any assumption on the distribution. Furthermore, we prove that the reconstruction error is sharp. For the case where the target signal ${\boldsymbol x}_{0}\in \mathbb{C}^{d}$ is sparse, we establish a similar result for the nonlinear constrained $\ell _{1}$ minimization model. To accomplish this, we leverage a strong version of restricted isometry property for an operator on the space of simultaneous low-rank and sparse matrices.

Verification of Parametric Properties of Linear Discrete-time Stochastic Systems

We study the problem of verifying parametric properties of linear discrete-time stochastic systems (linear DTSSs) over bounded and unbounded time horizons. A linear DTSS captures random processes, where the one-step transition relation between the current random vector X and the next-step random vector X’ is linear and is given by X’ = AX + W, where A is an n x n matrix and W is a random noise vector. We assume that the initial and noise random vectors are multivariate normal, each of which is expressed as a pair of two parameters, namely, mean and covariance. We are interested in verifying whether the system always satisfies a given parametric property specified as a subset of the parameters’ space over bounded or unbounded time horizons. For bounded time steps, we reduce the problem to the satisfiability of a semidefinite programming problem. For the unbounded time steps, we propose a novel abstraction procedure to reduce the verification problem to that of a finite graph, wherein, the nodes of the graph correspond to the regions of a partition of the random vector space, in contrast to existing works that partition the state-space. More precisely, we partition the parameter space of normal random vectors, namely, the space of means and covariance matrices, and apply semi-definite programming to compute the edges. We show that our abstraction procedure is sound. Our experiments with varying number of vehicle dynamics and different dimensions of random models show that our methods are reasonably scalable.

Towards Benchmarking for Evaluating Machine Learning Methods in Detecting Outliers in Process Datasets

Within the integration and development of data-driven process models, the underlying process is digitally mapped in a model through sensory data acquisition and subsequent modelling. In this process, challenges of different types and degrees of severity arise in each modelling step, according to the Cross-Industry Standard Process for Data Mining (CRISP-DM). Particularly in the context of data acquisition and integration into the process model, it can be assumed with a sufficiently high degree of probability that the acquired data contain anomalies of various kinds. The outliers must be detected in the data preparation and processing phase and dealt with accordingly. If this is sufficiently implemented, it will positively impact the subsequent modelling in terms of accuracy and precision. Therefore, this paper shows how outliers can be identified using the unsupervised machine learning methods autoencoder, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Isolation Forest (iForest), and One-Class Support Vector Machine (OCSVM). Following implementing these methods, we compared them by applying the Numenta Anomaly Benchmark (NAB) and sufficiently presented the individual strengths and disadvantages. Evaluating the correctness, distinctiveness and robustness criteria described in the paper showed that the One-Class Support Vector Machine was outstanding among the methods considered. This is because the OCSVM achieved acceptable anomaly detections on the available process datasets with comparatively little effort.

A novel homomorphic polynomial public key encapsulation algorithm

Background: One of the primary drivers in development of novel quantum-safe cryptography techniques is the ongoing National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) competition, which aims to identify quantum-safe algorithms for standardization. Although NIST has recently announced candidates to be standardized, the development of novel PQC algorithms remains desirable to address the challenges of quantum computing. Furthermore, to enhance security and improve performance. Methods: This paper introduces a novel public key encapsulation algorithm that incorporates an additional layer of encryption during key construction procedure, through a hidden ring. This encryption involves modular multiplication over the hidden ring using a homomorphism operator that is closed under addition and scalar multiplication. The homomorphic encryption key is comprised of two values - one used to create the hidden ring and the other to form an encryption operator. This homomorphic encryption can be applied to any polynomials during key construction over a finite field with their coefficients considered private. Particularly, the proposed homomorphic encryption operator can be applied to the public key of the Multivariate Public Key Cryptography schemes (MPKC) to hide the structure of its central map construction. Results: This paper presents a new variant of the MPKC with its public key encrypted using the proposed homomorphic operator. This novel scheme is called the Homomorphic Polynomial Public Key (HPPK) algorithm, which simplifies MPKC central map to two multivariate polynomials constructed from polynomial multiplications. The HPPK algorithm employs a single polynomial vector for the plaintext and a multi-variate noise vector associated with the central map. In contrast, in MPKC, a single multivariate vector is created by segmenting the secret plaintext over a small finite field. The HPPK algorithm is Indistinguishability Under Chosen-Plaintext Attack (IND-CPA) secure, and its classical complexity for cracking is exponential in the size of the prime field GF(p).

FontFusionGAN: Refinement of Handwritten Fonts by Font Fusion

Handwritten fonts possess unique expressive qualities; however, their clarity often suffers because of inconsistent handwriting. This study introduces FontFusionGAN (FFGAN), a novel method that enhances handwritten fonts by mixing them with printed fonts. The proposed approach leverages a generative adversarial network (GAN) to synthesize fonts that combine the desirable features of both handwritten and printed font styles. Training a GAN on a comprehensive dataset of handwritten and printed fonts enables it to produce legible and visually appealing font samples. The methodology was applied to a dataset of handwriting fonts, showing substantial enhancements in the legibility of the original fonts, while retaining their unique aesthetic essence. Unlike the original GAN setting where a single noise vector is used to generate a sample image, we randomly selected two noise vectors, z1 and z2, from a Gaussian distribution to train the generator. Simultaneously, we input a real image into the fusion encoder for exact reconstruction. This technique ensured the learning of style mixing during training. During inference, we provided the encoder with two font images, one handwritten and the other printed font, to obtain their respective latent vectors. Subsequently, the latent vector of the handwritten font image was injected into the first five layers of the generator, whereas the latent vector of the printed font image was injected into the last two layers to obtain a refined handwritten font image. The proposed method has the potential to improve the readability of handwritten fonts, offering benefits across diverse applications, such as document composition, letter writing, and assisting individuals with reading and writing difficulties.

Digital Filtering Techniques Using Fuzzy-Rules Based Logic Control.

This paper discusses current formulations based on fuzzy-logic control concepts as applied to the removal of impulsive noise from digital images. We also discuss the various principles related to fuzzy-ruled based logic control techniques, aiming at preserving edges and digital image details efficiently. Detailed descriptions of a number of formulations for recently developed fuzzy-rule logic controlled filters are provided, highlighting the merit of each filter. Fuzzy-rule based filtering algorithms may be designed assuming the tailoring of specific functional sub-modules: (a) logical controlled variable selection, (b) the consideration of different methods for the generation of fuzzy rules and membership functions, (c) the integration of the logical rules for detecting and filtering impulse noise from digital images. More specifically, we discuss impulse noise models and window-based filtering using fuzzy inference based on vector directional filters as associated with the filtering of RGB color images and then explain how fuzzy vector fields can be generated using standard operations on fuzzy sets taking into consideration fixed or random valued impulse noise and fuzzy vector partitioning. We also discuss how fuzzy cellular automata may be used for noise removal by adopting a Moore neighbourhood architecture. We also explain the potential merits of adopting a fuzzy rule based deep learning ensemble classifier which is composed of a convolutional neural network (CNN), a recurrent neural networks (RNN), a long short term memory neural network (LSTM) and a gated recurrent unit (GRU) approaches, all within a fuzzy min-max (FMM) ensemble. Fuzzy non-local mean filter approaches are also considered. A comparison of various performance metrics for conventional and fuzzy logic based filters as well as deep learning filters is provided. The algorhitms discussed have the following advantageous properties: high quality of edge preservation, high quality of spatial noise suppression capability especially for complex images, sound properties of noise removal (in cases when both mixed additive and impulse noise are present), and very fast computational implementation.

A ReLU-based hard-thresholding algorithm for non-negative sparse signal recovery

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K-sparse signal x from an underdetermined linear model y=Ax+v, where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms.