Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.

Epidemiologists and social scientists have used the Network Scale-Up Method (NSUM) for over thirty years to estimate the size of a hidden sub-population within a social network. This method involves querying a subset of network nodes about the number of their neighbors belonging to the hidden sub-population. In general, NSUM assumes that the social network topology and the hidden sub-population distribution are well-behaved; hence, the NSUM estimate is close to the actual value. However, bounds on NSUM estimation errors have not been analytically proven. This paper provides analytical bounds on the error incurred by the two most popular NSUM estimators. These bounds assume that the queried nodes accurately provide their degree and the number of neighbors belonging to the hidden sub-population. Our key findings are twofold. First, we show that when an adversary designs the network and places the hidden sub-population, then the estimate can be a factor of Ω(√n) off from the real value (in a network with n nodes). Second, we also prove error bounds when the underlying network is randomly generated, showing that a small constant factor can be achieved with high probability using samples of logarithmic size O(log n). We present improved analytical bounds for Erdős-Rényi and Scale-Free networks. Our theoretical analysis is supported by an extensive set of numerical experiments designed to determine the effect of the sample size on the accuracy of the estimates in both synthetic and real networks.

Indirect surveys, in which respondents provide information about other people they know, have been proposed for estimating (nowcasting) the size of a hidden population where privacy is important or the hidden population is hard to reach. Examples include estimating casualties in an earthquake, conditions among female sex workers, and the prevalence of drug use and infectious diseases. The Network Scale-up Method (NSUM) is the classical approach to developing estimates from indirect surveys, but it was designed for one-shot surveys. Further, it requires certain assumptions and asking for or estimating the number of individuals in each respondent's network. In recent years, surveys have been increasingly deployed online and can collect data continuously (e.g., COVID-19 surveys on Facebook during much of the pandemic). Conventional NSUM can be applied to these scenarios by analyzing the data independently at each point in time, but this misses the opportunity of leveraging the temporal dimension. We propose to use the responses from indirect surveys collected over time and develop analytical tools (i) to prove that indirect surveys can provide better estimates for the trends of the hidden population over time, as compared to direct surveys and (ii) to identify appropriate temporal aggregations to improve the estimates. We demonstrate through extensive simulations that our approach outperforms traditional NSUM and direct surveying methods. We also empirically demonstrate the superiority of our approach on a real indirect survey dataset of COVID-19 cases.

The COVID-19 pandemic exposed the importance of research on the spread of epidemic diseases. In the case of COVID-19, official data about infection prevalence was based on PCR and antigen tests reports, which can be unreliable. In our work, we construct prediction models based on Genetic Programming to estimate the SARS-Co V-2 seroprevalence of a given population from multiple estimates of the COVID-19 prevalence (official prevalence data, estimates derived from wastewater data, and estimates obtained from massive surveys with different rules and ML methods). To do that, we propose the use of stacking techniques based on Genetic Programming to obtain Machine Learning Ensemble Methods. Our approach produces more accurate prediction models than conventional stacking techniques based on Linear Regression.

The COVID-19 pandemic exposed the importance of research on the spread of epidemic diseases. In this paper, we apply Artificial Intelligence and statistics techniques to build prediction models to estimate the SARS-CoV-2 seroprevalence in the United States, using multiple estimates of COVID-19 prevalence and other explanatory variables. We propose the use of stacking techniques based on multiple model building techniques (Linear and Beta Regression, Genetic Programming and Neural Networks) to obtain Predictive Ensemble Models. There has been extensive research on this field, but there has not been in-depth research on the application of stacking methods to estimate and forecast seroprevalence in the USA specifically. This paper provides a novel comparison of the behaviour and performance of different building techniques for stacking ensemble models and presents which methods are better for different scenarios. We find that Genetic Programming and Neural Networks are the best models with trained data within single states, and when multiple states are considered Genetic Programming is still better than the Regression models, but Neural Networks fail to estimate the seroprevalence accurately. Another novelty of our work is the use of cross-state validation to evaluate the models with new data, as well as temporal forecasting. Depending on how the data is processed, Linear Regression performs very well with cross-state validation and temporal forecasting, and Genetic Programming is very accurate with the former while Neural Networks work better with the latter.

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing and communications applications, including denoising, spectrum sensing, and compression. Notice that estimating the covariance matrix from compressive samples leads to ill-posed minimizations with severe performance loss at high compression rates. In this regard, a regularization term is typically aggregated to the cost function to consider prior information about a particular property of the covariance matrix. Hence, this paper proposes an algorithm based on the projected gradient method to recover low-rank or Toeplitz approximations of the covariance matrix from compressive measurements. The proposed algorithm divides the compressive measurements into data subsets projected onto different subspaces and accurately estimates the covariance matrix by solving a single optimization problem assuming that each data subset contains an approximation of the signal statistics. Furthermore, gradient filtering is included at every iteration of the proposed algorithm to minimize the estimation error. The error induced by the proposed splitting approach is analytically derived along with the convergence guarantees of the proposed method. The proposed algorithm estimates the covariance matrix of hyperspectral images from synthetic and real compressive samples. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images from compressive measurements with high compression ratios ( 8-15% approx) in noisy scenarios. Moreover, simulations and theoretical results show that the filtering step reduces the recovery error up to twice the number of eigenvectors. Finally, an optical implementation is proposed, and real measurements are used to validate the theoretical findings.

In remote sensing, hyperspectral (HS) and multispectral (MS) image fusion have emerged as a synthesis tool to improve the data set resolution. However, conventional image fusion methods typically degrade the performance of the land cover classification. In this paper, a feature fusion method from HS and MS images for pixel-based classification is proposed. More precisely, the proposed method first extracts spatial features from the MS image using morphological profiles. Then, the feature fusion model assumes that both the extracted morphological profiles and the HS image can be described as a feature matrix lying in different subspaces. An algorithm based on combining alternating optimization (AO) and the alternating direction method of multipliers (ADMM) is developed to solve efficiently the feature fusion problem. Finally, extensive simulations were run to evaluate the performance of the proposed feature fusion approach for two data sets. In general, the proposed approach exhibits a competitive performance compared to other feature extraction methods.

Image fusion aims at estimating a high-resolution spectral image from a low-spatial-resolution hyperspectral image and a low-spectral-resolution multispectral image. In this regard, compressive spectral imaging (CSI) has emerged as an acquisition framework that captures the relevant information of spectral images using a reduced number of measurements. Recently, various image fusion methods from CSI measurements have been proposed. However, these methods exhibit high running times and face the challenging task of choosing sparsity-inducing bases. In this paper, a deep network under the algorithm unrolling approach is proposed for fusing spectral images from compressive measurements. This architecture, dubbed LADMM-Net, casts each iteration of a linearized version of the alternating direction method of multipliers into a processing layer whose concatenation deploys a deep network. The linearized approach enables obtaining fusion estimates without resorting to costly matrix inversions. Furthermore, this approach exploits the benefits of learnable transforms to estimate the image details included in both the auxiliary variable and the Lagrange multiplier. Finally, the performance of the proposed technique is evaluated on two spectral image databases and one dataset captured at the laboratory. Extensive simulations show that the proposed method outperforms the state-of-the-art approaches that fuse spectral images from compressive measurements.

Spectral Videos (SV) are datasets containing spatial-spectral-and-temporal information of a moving scene and this kind of information have been successfully used in medicine, remote sensing, and military application. However, expensive acquisition processes and difficulties in equipment manufacture lead to low-resolution datasets. Therefore, super-resolution (SR) techniques have emerged as a processing tool that recovers a high-resolution dataset by expressing the measurements as compressed versions of the desired data. Furthermore, the Convolutional Sparse Coding (CSC) has been developed as a signal model that learns a dictionary directly from the target signal, improving the reconstruction quality. This work proposes to extend the CSC formulation to consider temporal correlations in SVs, exploiting the shifting invariance property of the CSC model. The simulation results show a PSNR improvement in up to 2.5dB with respect to the state-of-the-art methods, preserving the edges and textures of the spectral video frames.

Spectral image classification is an active research topic in remote sensing. In this sense, various multi-sensor spectral image fusion algorithms have been recently evaluated via pixel-based classification. In general, the sizes of multi-sensor images challenge the storing and processing capabilities of sensing systems. Therefore, different image fusion algorithms from measurements captured by multi-resolution compressive spectral imaging (CSI) sensors have been proposed. However, the computational costs for reconstructing and fusing spectral images from compressive measurements are high, and these approaches do not consider the huge amount of information embedded in acquired data. In this article, a spectral image classification scheme from multi-sensor CSI projections is developed. Specifically, this scheme includes a feature extraction procedure that exploits the fact that CSI data contain relevant information of the spectral image, and therefore, low-dimensional features can be obtained from measurements. Furthermore, a fusion model is presented to combine the information of the extracted features with the aim of estimating high-resolution classification attributes. Then, a pixel-based classifier is applied to the fused features with the goal of labeling the corresponding high-resolution spectral image. The performance of the proposed classification scheme is compared to other methods on the Salinas Valley data set for different supervised classifiers and various downsampling settings. Extensive simulations on the Pavia University data set are also shown, where the proposed method outperforms other classification approaches that reconstruct and fuse from compressive measurements. Finally, the effectiveness of the proposed classification approach is validated in real multi-sensor data.

Compressive spectral imaging (CSI) acquires coded projections of a spectral image by performing a modulation of the data cube followed by a spectral-wise integration. To avoid the spectral image reconstruction procedure, this paper proposes a classification approach that extracts features directly from multi-sensor CSI measurements. Particularly, the proposed method obtains the features by considering the spectral information extracted from Hyperspectral CSI measurements, and the local spatial information extracted by clustering the Multispectral CSI measurements using a superpixel algorithm. This approach is evaluated on Pavia University and Salinas Valley datasets. Extensive simulations show that considering the local spatial information boosts the overall accuracy up to 3% in comparison with traditional approaches that only uses the spectral information. Furthermore, the computation time of the approach that reconstructs, fuses and classifies takes approximately 87.43 [s], while classifying directly from multi-sensor compressive measurements takes only 0.74 [s], achieving similar classification results.

Compressive spectral imaging (CSI) has emerged as an alternative acquisition framework that simultaneously senses and compresses spectral images. In this context, the spectral image classification from CSI compressive measurements has become a challenging task since the feature extraction stage usually requires reconstructing the spectral image. Moreover, most approaches do not consider multi-sensor compressive measurements. In this paper, an approach for fusing features obtained from multi-sensor compressive measurements is proposed for spectral image classification. To this end, linear models describing low-resolution features as degraded versions of the high-resolution features are developed. Furthermore, an inverse problem is formulated aiming at estimating high-resolution features including both a sparsity-inducing term and a total variation (TV) regularization term to exploit the correlation between neighboring pixels of the spectral image, and therefore, to improve the performance of pixel-based classifiers. An algorithm based on the alternating direction method of multipliers (ADMM) is described for solving the fusion problem. The proposed feature fusion approach is tested for two CSI architectures: three-dimensional coded aperture snapshot spectral imaging (3D-CASSI) and colored CASSI (C-CASSI). Extensive simulations on various spectral image data sets show that the proposed approach outperforms other classification approaches under different performance criteria.

In this letter, we propose a robust algorithm for determining a unitary transform of a discrete-time signal, whose samples are sensed in impulsive noise environments. The proposed algorithm estimates the transformed signal coefficients by solving an$\ellb _{\bf 1}$-regularized least absolute deviation ($\ellb_{\bf 1}$-LAD) regression problem, leading to the weighted median (WM) as the optimal operator for computing each transform coefficient. Numerical simulations on synthetic data are presented in order to compare the performance of the proposed algorithm to those yielded by previously reported methods. Furthermore, an example of audio denoising using the short time Fourier transform of a digital audio record, in the presence of impulsive noise, is also shown.

In this paper, we present a robust approach to estimate communications channel in OFDM systems exploiting the sparsity of the channel impulse response (CIR) commonly found in multi-path channels. The CIR is found as the solution of a regularized optimization problem where we minimize the least absolute deviation of a residual signal while, at the same time, encourage sparsity in the solution by an ℓ0pseudo-norm regularization term. The proposed approach reduces to estimate iteratively each tap of the CIR using a complex median based operator followed by a relevance test that forces sparsity in the solution. A blanking filter at the front end of the receiver is used to further mitigate the impact of the impulsive noise. Extensive simulations show that the proposed approach performs better than conventional approaches for AWGN channels and for situations where the additive noise follows a heavier-than-Gaussian tail distribution.