Hassan Mansour

Michael P. Friedlander, Hassan Mansour, Rayan Saab et al.

In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.

Hanfeng Zhai, Hongtao Qiao, Hassan Mansour et al. · stanford

We present a scalable, data-driven simulation framework for large-scale heating, ventilation, and air conditioning (HVAC) systems that couples physics-informed neural ordinary differential equations (PINODEs) with differential-algebraic equation (DAE) solvers. At the component level, we learn heat-exchanger dynamics using an implicit PINODE formulation that predicts conserved quantities (refrigerant mass $M_r$ and internal energy $E_\text{hx}$) as outputs, enabling physics-informed training via automatic differentiation of mass/energy balances. Stable long-horizon prediction is achieved through gradient-stabilized latent evolution with gated architectures and layer normalization. At the system level, we integrate learned components with DAE solvers (IDA and DASSL) that explicitly enforce junction constraints (pressure equilibrium and mass-flow consistency), and we use Bayesian optimization to tune solver parameters for accuracy--efficiency trade-offs. To reduce residual system-level bias, we introduce a lightweight corrector network trained on short trajectory segments. Across dual-compressor and scaled network studies, the proposed approach attains multi-fold speedups over high-fidelity simulation while keeping errors low (MAPE below a few percent) and scales to systems with up to 32 compressor--condenser pairs.

Yuying Liu, Aleksei Sholokhov, Hassan Mansour et al.

Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate arbitrarily complex functions. However, despite their great potential, they typically require large training data-sets either from measurements of a real system or from high-fidelity simulations. In this work, we propose a novel architecture inspired by physics-informed neural networks, which leverage automatic differentiation to impose the underlying physical laws via soft penalty constraints during model training. We demonstrate that it not only reduces the need of large training data-sets, but also maintains high effectiveness in approximating Koopman eigenfunctions.

Hassan Mansour

This note presents a more efficient formulation of the robust online subspace estimation and tracking algorithm (ROSETA) that is capable of identifying and tracking a time-varying low dimensional subspace from incomplete measurements and in the presence of sparse outliers. The algorithm minimizes a robust l1 norm cost function between the observed measurements and their projection onto the estimated subspace. The projection coefficients and sparse outliers are computed using a LASSO solver and the subspace estimate is updated using a proximal point iteration with adaptive parameter selection.

Vineet R Shenoy, Suhas Lohit, Hassan Mansour et al.

Camera-based monitoring of vital signs, also known as imaging photoplethysmography (iPPG), has seen applications in driver-monitoring, perfusion assessment in surgical settings, affective computing, and more. iPPG involves sensing the underlying cardiac pulse from video of the skin and estimating vital signs such as the heart rate or a full pulse waveform. Some previous iPPG methods impose model-based sparse priors on the pulse signals and use iterative optimization for pulse wave recovery, while others use end-to-end black-box deep learning methods. In contrast, we introduce methods that combine signal processing and deep learning methods in an inverse problem framework. Our methods estimate the underlying pulse signal and heart rate from facial video by learning deep-network-based denoising operators that leverage deep algorithm unfolding and deep equilibrium models. Experiments show that our methods can denoise an acquired signal from the face and infer the correct underlying pulse rate, achieving state-of-the-art heart rate estimation performance on well-known benchmarks, all with less than one-fifth the number of learnable parameters as the closest competing method.

Arjun Teh, Wael H. Ali, Joshua Rapp et al.

We develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using background-oriented schlieren (BOS) measurements and physics-informed reconstruction. Our framework utilizes a light projector that projects a pattern onto a target back-wall and a camera that observes small distortions in the light pattern. While the single-view BOS tomography problem is severely ill-posed, our proposed framework addresses this using: (1) improved ray tracing, (2) a physics-based light rendering approach and loss formulation, and (3) a physics-based regularization using a physics-informed neural network (PINN) to ensure that the reconstructed airflow is consistent with the governing equations for buoyancy-driven flows.

Jing Liu, Toshiaki Koike-Akino, Ye Wang et al.

To address the enormous size of Large Language Models (LLMs), model compression methods, such as quantization and pruning, are often deployed, especially on edge devices. In this work, we focus on layer-wise post-training quantization and pruning. Drawing connections between activation-aware weight pruning and sparse approximation problems, and motivated by the success of Iterative Hard Thresholding (IHT), we propose a unified method for Activation-aware Weight pruning and quantization via Projected gradient descent (AWP). Our experiments demonstrate that AWP outperforms state-of-the-art LLM pruning and quantization methods. Theoretical convergence guarantees of the proposed method for pruning are also provided.

Vineet R. Shenoy, Shaoju Wu, Armand Comas et al.

Remote estimation of vital signs enables health monitoring for situations in which contact-based devices are either not available, too intrusive, or too expensive. In this paper, we present a modular, interpretable pipeline for pulse signal estimation from video of the face that achieves state-of-the-art results on publicly available datasets.Our imaging photoplethysmography (iPPG) system consists of three modules: face and landmark detection, time-series extraction, and pulse signal/pulse rate estimation. Unlike many deep learning methods that make use of a single black-box model that maps directly from input video to output signal or heart rate, our modular approach enables each of the three parts of the pipeline to be interpreted individually. The pulse signal estimation module, which we call TURNIP (Time-Series U-Net with Recurrence for Noise-Robust Imaging Photoplethysmography), allows the system to faithfully reconstruct the underlying pulse signal waveform and uses it to measure heart rate and pulse rate variability metrics, even in the presence of motion. When parts of the face are occluded due to extreme head poses, our system explicitly detects such "self-occluded" regions and maintains estimation robustness despite the missing information. Our algorithm provides reliable heart rate estimates without the need for specialized sensors or contact with the skin, outperforming previous iPPG methods on both color (RGB) and near-infrared (NIR) datasets.

Lantao Yu, Dehong Liu, Hassan Mansour et al.

Blind pansharpening addresses the problem of generating a high spatial-resolution multi-spectral (HRMS) image given a low spatial-resolution multi-spectral (LRMS) image with the guidance of its associated spatially misaligned high spatial-resolution panchromatic (PAN) image without parametric side information. In this paper, we propose a fast approach to blind pansharpening and achieve state-of-the-art image reconstruction quality. Typical blind pansharpening algorithms are often computationally intensive since the blur kernel and the target HRMS image are often computed using iterative solvers and in an alternating fashion. To achieve fast blind pansharpening, we decouple the solution of the blur kernel and of the HRMS image. First, we estimate the blur kernel by computing the kernel coefficients with minimum total generalized variation that blur a downsampled version of the PAN image to approximate a linear combination of the LRMS image channels. Then, we estimate each channel of the HRMS image using local Laplacian prior to regularize the relationship between each HRMS channel and the PAN image. Solving the HRMS image is accelerated by both parallelizing across the channels and by fast numerical algorithms for each channel. Due to the fast scheme and the powerful priors we used on the blur kernel coefficients (total generalized variation) and on the cross-channel relationship (local Laplacian prior), numerical experiments demonstrate that our algorithm outperforms state-of-the-art model-based counterparts in terms of both computational time and reconstruction quality of the HRMS images.

Yanting Ma, Petros T. Boufounos, Hassan Mansour et al.

In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations. In this paper we take a fresh look at this problem through the lens of optimal transport (OT). In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others. We exploit this by introducing a regularization function that promotes the more likely permutations in the solution. We show that, even though the general problem is not convex, an appropriate relaxation of the resulting regularized problem allows us to exploit the well-developed machinery of OT and develop a tractable algorithm.

Ajinkya Kadu, Hassan Mansour, Petros T. Boufounos

Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects that commonly occurs in ground-penetrating radar, exploration geophysics, terahertz imaging, ultrasound, and electron microscopy. Unlike conventional transmission tomography, the reflection regime is severely ill-posed since the measured wavefields contain far less spatial frequency information of the target object. We propose a constrained incremental frequency inversion framework that requires no side information from a background model of the object. Our framework solves a sequence of regularized least-squares subproblems that ensure consistency with the measured scattered wavefield while imposing total-variation and non-negativity constraints. We propose a proximal Quasi-Newton method to solve the resulting subproblem and devise an automatic parameter selection routine to determine the constraint of each subproblem. We validate the performance of our approach on synthetic low-resolution phantoms and with a mismatched forward model test on a high-resolution phantom.

Yanting Ma, Shuchin Aeron, Hassan Mansour

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence only occurs after some sufficiently large number of iterations. This is in contrast to the claim in Mertikopoulos et al. of monotone convergence of OMD with exact gradients for coherent saddle point problems. Besides highlighting this important subtlety, we note that the almost sure convergence guarantees of MD and OMD with stochastic gradients for strictly coherent saddle point problems that are claimed in Mertikopoulos et al. are not fully justified by their proof. As such, we fill out the missing details in the proof and as a result have only been able to prove convergence with high probability. We would like to note that our analysis relies heavily on the core ideas and proof techniques introduced in Zhou et al. and Mertikopoulos et al., and we only aim to re-state and correct the results in light of what we were able to prove rigorously while filling in the much needed missing details in their proofs.

Jiawei Ma, Zheng Shou, Alireza Zareian et al.

Many real-world applications involve multivariate, geo-tagged time series data: at each location, multiple sensors record corresponding measurements. For example, air quality monitoring system records PM2.5, CO, etc. The resulting time-series data often has missing values due to device outages or communication errors. In order to impute the missing values, state-of-the-art methods are built on Recurrent Neural Networks (RNN), which process each time stamp sequentially, prohibiting the direct modeling of the relationship between distant time stamps. Recently, the self-attention mechanism has been proposed for sequence modeling tasks such as machine translation, significantly outperforming RNN because the relationship between each two time stamps can be modeled explicitly. In this paper, we are the first to adapt the self-attention mechanism for multivariate, geo-tagged time series data. In order to jointly capture the self-attention across multiple dimensions, including time, location and the sensor measurements, while maintain low computational complexity, we propose a novel approach called Cross-Dimensional Self-Attention (CDSA) to process each dimension sequentially, yet in an order-independent manner. Our extensive experiments on four real-world datasets, including three standard benchmarks and our newly collected NYC-traffic dataset, demonstrate that our approach outperforms the state-of-the-art imputation and forecasting methods. A detailed systematic analysis confirms the effectiveness of our design choices.

Hassan Mansour, Dehong Liu, Ulugbek S. Kamilov et al.

A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imaging, where mapping the position ambiguity to phase errors breaks down. In this paper, we propose an alternate formulation where the position error of each antenna is mapped to a spatial shift operator in the image-domain. Thus, the radar autofocus problem becomes a multichannel blind deconvolution problem, in which the radar measurements correspond to observations of a static radar image that is convolved with the spatial shift kernel associated with each antenna. To solve the reformulated problem, we also develop a block coordinate descent framework that leverages the sparsity and piece-wise smoothness of the radar scene, as well as the one-sparse property of the two dimensional shift kernels. We evaluate the performance of our approach using both simulated and experimental radar measurements, and demonstrate its superior performance compared to state-of-the-art methods.

Zheng Shou, Junting Pan, Jonathan Chan et al.

We aim to tackle a novel task in action detection - Online Detection of Action Start (ODAS) in untrimmed, streaming videos. The goal of ODAS is to detect the start of an action instance, with high categorization accuracy and low detection latency. ODAS is important in many applications such as early alert generation to allow timely security or emergency response. We propose three novel methods to specifically address the challenges in training ODAS models: (1) hard negative samples generation based on Generative Adversarial Network (GAN) to distinguish ambiguous background, (2) explicitly modeling the temporal consistency between data around action start and data succeeding action start, and (3) adaptive sampling strategy to handle the scarcity of training data. We conduct extensive experiments using THUMOS'14 and ActivityNet. We show that our proposed methods lead to significant performance gains and improve the state-of-the-art methods. An ablation study confirms the effectiveness of each proposed method.

Yanting Ma, Hassan Mansour, Dehong Liu et al.

The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship, there is an increased interest in considering nonlinear formulations that can account for multiple light scattering. In this paper, we propose an image reconstruction method, called CISOR, for nonlinear diffractive imaging, based on a nonconvex optimization formulation with total variation (TV) regularization. The nonconvex solver used in CISOR is our new variant of fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and memory-efficient implementation of the new FISTA variant and prove that it reliably converges for our nonconvex optimization problem. In addition, we systematically compare our method with other state-of-the-art methods on simulated as well as experimentally measured data in both 2D and 3D settings.

Hsiou-Yuan Liu, Dehong Liu, Hassan Mansour et al.

Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence even for strongly scattering objects. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). The proposed method is validated on both simulated and experimentally measured data.

Andrew Knyazev, Akshay Gadde, Hassan Mansour et al.

An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a reconstruction set, defined as a shortest pathway between the sample consistent set and the guiding set. Existence and uniqueness of the reconstruction set are investigated in a Hilbert space, where the guiding set is a closed subspace and the sample consistent set is a closed plane, formed by a sampling subspace. Connections to earlier known consistent, generalized, and regularized reconstructions are clarified. New stability and reconstruction error bounds are derived, using the largest nontrivial angle between the sampling and guiding subspaces. Conjugate gradient iterative reconstruction algorithms are proposed and illustrated numerically for image magnification.

Hsiou-Yuan Liu, Ulugbek S. Kamilov, Dehong Liu et al.

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon, which makes the method preferable in applications where linear measurement models are inaccurate. We construct the measurement model by expanding the scattered wave-field with an accelerated-gradient method, which is guaranteed to converge and is suitable for large-scale problems. We provide explicit formulas for computing the gradient of our measurement model with respect to the unknown image, which enables image formation with a sparsity- driven numerical optimization algorithm. We validate the method both analytically and with numerical simulations.

Ulugbek S. Kamilov, Dehong Liu, Hassan Mansour et al.

The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.

Petros T Boufounos, Shantanu Rane, Hassan Mansour

Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear approximations, sparse representations, and rate-distortion theory. Very often, however, the goal of processing is to extract specific information from the signal, and the distortion should be measured on the extracted information. The corresponding representation should, therefore, represent that information as parsimoniously as possible, without necessarily accurately representing the signal itself. In this paper, we examine the problem of encoding signals such that sufficient information is preserved about their pairwise distances and their inner products. For that goal, we consider randomized embeddings as an encoding mechanism and provide a framework to analyze their performance. We also demonstrate that it is possible to design the embedding such that it represents different ranges of distances with different precision. These embeddings also allow the computation of kernel inner products with control on their inner product-preserving properties. Our results provide a broad framework to design and analyze embeddins, and generalize existing results in this area, such as random Fourier kernels and universal embeddings.

Ulugbek S. Kamilov, Hassan Mansour

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.

Dong Tian, Hassan Mansour, Andrew Knyazev et al.

In 3D image/video acquisition, different views are often captured with varying noise levels across the views. In this paper, we propose a graph-based image enhancement technique that uses a higher quality view to enhance a degraded view. A depth map is utilized as auxiliary information to match the perspectives of the two views. Our method performs graph-based filtering of the noisy image by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian. We discuss two graph spectral denoising methods: first using Chebyshev polynomials, and second using iterations of the conjugate gradient algorithm. Our framework generalizes previously known polynomial graph filters, and we demonstrate through numerical simulations that our proposed technique produces subjectively cleaner images with about 1-3 dB improvement in PSNR over existing polynomial graph filters.

Aleksandr Y. Aravkin, Rajiv Kumar, Hassan Mansour et al.

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem. Since practitioners typically have strong prior knowledge about target error level, this innovation makes it easy to apply the algorithm in practice, leaving only the factor rank to be determined. Within the established framework, we propose two extensions that are highly relevant to solving practical challenges of data interpolation. First, we propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation. Second, we propose matrix completion formulations that are robust to large measurement errors in the available data. We illustrate the advantages of LR-BPDN on the collaborative filtering problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use the new method, along with its robust and subspace re-weighted extensions, to obtain high-quality reconstructions for large scale seismic interpolation problems with real data, even in the presence of data contamination.

Hassan Mansour

Sparse signal recovery has been dominated by the basis pursuit denoise (BPDN) problem formulation for over a decade. In this paper, we propose an algorithm that outperforms BPDN in finding sparse solutions to underdetermined linear systems of equations at no additional computational cost. Our algorithm, called WSPGL1, is a modification of the spectral projected gradient for $\ell_1$ minimization (SPGL1) algorithm in which the sequence of LASSO subproblems are replaced by a sequence of weighted LASSO subproblems with constant weights applied to a support estimate. The support estimate is derived from the data and is updated at every iteration. The algorithm also modifies the Pareto curve at every iteration to reflect the new weighted $\ell_1$ minimization problem that is being solved. We demonstrate through extensive simulations that the sparse recovery performance of our algorithm is superior to that of $\ell_1$ minimization and approaches the recovery performance of iterative re-weighted $\ell_1$ (IRWL1) minimization of Cand{è}s, Wakin, and Boyd, although it does not match it in general. Moreover, our algorithm has the computational cost of a single BPDN problem.