arXiv subjects

Ali Pezeshki

Publications and source records attributed to Ali Pezeshki.

At least 19 recordsLinked to original sources

arXiv2026

A Performance Bound for the Greedy Algorithm in a Generalized Class of String Optimization Problems

We present a simple performance bound for the greedy scheme in string optimization problems that obtains strong results. Our approach vastly generalizes the group of previously established greedy curvature bounds by Conforti and Cornuéjols (1984). We consider three constants, $α_G$, $α_G'$, and $α_G''$ introduced by Conforti and Cornuéjols (1984), that are used in performance bounds of greedy schemes in submodular set optimization. We first generalize both of the $α_G$ and $α_G''$ bounds to string optimization problems in a manner that includes maximizing submodular set functions over matroids as a special case. We then derive a much simpler and computable bound that allows for applications to a far more general class of functions with string domains. We prove that our bound is superior to both the $α_G$ and $α_G''$ bounds and provide a counterexample to show that the $α_G'$ bound is incorrect under the assumptions in Conforti and Cornuéjols (1984). We conclude with two applications. The first is an application of our result to sensor coverage problems. We demonstrate our performance bound in cases where the objective function is set submodular and string submodular. The second is an application to a social welfare maximization problem with black-box utility functions.

eess.SY↗

arXiv2026

Performance Guarantees for Data-Driven Sequential Decision-Making

The solutions to many sequential decision-making problems are characterized by dynamic programming and Bellman's principle of optimality. However, due to the inherent complexity of solving Bellman's equation exactly, there has been significant interest in developing various approximate dynamic programming (ADP) schemes to obtain near-optimal solutions. A fundamental question that arises is: how close are the objective values produced by ADP schemes relative to the true optimal objective values? In this paper, we develop a general framework that provides performance guarantees for ADP schemes in the form of ratio bounds. Specifically, we show that the objective value under an ADP scheme is at least a computable fraction of the optimal value. We further demonstrate the applicability of our theoretical framework through several applications: data-driven robot path planning, pendulum stabilization, and multi-agent sensor coverage.

eess.SY↗

arXiv2025

RASPNet: A Benchmark Dataset for Radar Adaptive Signal Processing Applications

We present a large-scale dataset called RASPNet for radar adaptive signal processing (RASP) applications to support the development of data-driven models within the adaptive radar community. RASPNet exceeds 16 TB in size and comprises 100 realistic scenarios compiled over a variety of topographies and land types across the contiguous United States. For each scenario, RASPNet comprises 10,000 clutter realizations from an airborne radar setting, which can be used to benchmark radar and complex-valued learning algorithms. RASPNet intends to fill a prominent gap in the availability of a large-scale, realistic dataset that standardizes the evaluation of RASP techniques and complex-valued neural networks. We outline its construction, organization, and several applications, including a transfer learning example to demonstrate how RASPNet can be used for real-world adaptive radar scenarios.

cs.LG↗

arXiv2025

Dual-Function Radar-Communication Beamforming with Outage Probability Metric

The integrated design of communication and sensing may offer a potential solution to address spectrum congestion. In this work, we develop a beamforming method for a dual-function radar-communication system, where the transmit signal is used for both radar surveillance and communication with multiple downlink users, despite imperfect channel state information (CSI). We focus on two scenarios of interest: radar-centric and communication-centric. In the radar-centric scenario, the primary goal is to optimize radar performance while attaining acceptable communication performance. To this end, we minimize a weighted sum of the mean-squared error in achieving a desired beampattern and a mean-squared cross correlation of the radar returns from directions of interest (DOI). We also seek to ensure that the probability of outage for the communication users remains below a desired threshold. In the communication-centric scenario, our main objective is to minimize the maximum probability of outage among the communication users while keeping the aforementioned radar metrics below a desired threshold. Both optimization problems are stochastic and untractable. We first take advantage of central limit theorem to obtain deterministic non-convex problems and then consider relaxations of these problems in the form of semidefinite programs with rank-1 constraints. We provide numerical experiments demonstrating the effectiveness of the proposed designs.

eess.SP↗

arXiv2025

Steinmetz Neural Networks for Complex-Valued Data

We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.

cs.LG↗

arXiv2024

Offline Stochastic Optimization of Black-Box Objective Functions

Many challenges in science and engineering, such as drug discovery and communication network design, involve optimizing complex and expensive black-box functions across vast search spaces. Thus, it is essential to leverage existing data to avoid costly active queries of these black-box functions. To this end, while Offline Black-Box Optimization (BBO) is effective for deterministic problems, it may fall short in capturing the stochasticity of real-world scenarios. To address this, we introduce Stochastic Offline BBO (SOBBO), which tackles both black-box objectives and uncontrolled uncertainties. We propose two solutions: for large-data regimes, a differentiable surrogate allows for gradient-based optimization, while for scarce-data regimes, we directly estimate gradients under conservative field constraints, improving robustness, convergence, and data efficiency. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world tasks.

cs.LG↗

arXiv2024

On Bounds for Greedy Schemes in String Optimization based on Greedy Curvatures

We consider the celebrated bound introduced by Conforti and Cornuéjols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy curvature. We show that the bound holds for a very general class of string problems that includes maximizing submodular functions over set matroids as a special case. We also derive a bound that is computable in the sense that they depend only on quantities along the greedy trajectory. We prove that our bound is superior to the greedy curvature bound of Conforti and Cornuéjols. In addition, our bound holds under a condition that is weaker than submodularity.

eess.SY↗

arXiv2024

Data-Driven Target Localization Using Adaptive Radar Processing and Convolutional Neural Networks

Leveraging the advanced functionalities of modern radio frequency (RF) modeling and simulation tools, specifically designed for adaptive radar processing applications, this paper presents a data-driven approach to improve accuracy in radar target localization post adaptive radar detection. To this end, we generate a large number of radar returns by randomly placing targets of variable strengths in a predefined area, using RFView, a high-fidelity, site-specific, RF modeling & simulation tool. We produce heatmap tensors from the radar returns, in range, azimuth [and Doppler], of the normalized adaptive matched filter (NAMF) test statistic. We then train a regression convolutional neural network (CNN) to estimate target locations from these heatmap tensors, and we compare the target localization accuracy of this approach with that of peak-finding and local search methods. This empirical study shows that our regression CNN achieves a considerable improvement in target location estimation accuracy. The regression CNN offers significant gains and reasonable accuracy even at signal-to-clutter-plus-noise ratio (SCNR) regimes that are close to the breakdown threshold SCNR of the NAMF. We also study the robustness of our trained CNN to mismatches in the radar data, where the CNN is tested on heatmap tensors collected from areas that it was not trained on. We show that our CNN can be made robust to mismatches in the radar data through few-shot learning, using a relatively small number of new training samples.

cs.CV↗

arXiv2024

Statistical estimation theory detection limits for label-free imaging

The emergence of label-free microscopy techniques has significantly improved our ability to precisely characterize biochemical targets, enabling non-invasive visualization of cellular organelles and tissue organization. Each label-free method has specific benefits, drawbacks, and varied varied sensitivity under measurement conditions across different types of specimens. To link all these disparate label-free optical interactions together and to compare detection sensitivity of these modalities, we investigate their sensitivity within the framework of statistical estimation theory. This paper introduces a comprehensive unified framework for evaluating the bounds for signal detection with label-free microscopy methods, including second harmonic generation (SHG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), coherent Stokes Raman scattering (CSRS), stimulated Raman loss (SRL), stimulated Raman gain (SRG), stimulated emission (SE), impulsive stimulated Raman scattering (ISRS), transient absorption (TA), and photothermal effect (PTE). A general model for signal generation induced by optical scattering is developed. Based on this model, the information obtained is quantitatively analyzed using Fisher information, and the fundamental constraints on estimation precision are evaluated through the Cramér-Rao Lower Bound (CRLB).

physics.optics↗

arXiv2023

An Improved Greedy Curvature Bound in Finite-Horizon String Optimization with Application to a Sensor Coverage Problem

We study the optimization problem of choosing strings of finite length to maximize string submodular functions on string matroids, which is a broader class of problems than maximizing set submodular functions on set matroids. We provide a lower bound for the performance of the greedy algorithm in our problem, and then prove that our bound is superior to the greedy curvature bound of Conforti and Cornuejols. Our bound has lower computational complexity than most previously proposed curvature bounds. Finally, we demonstrate the strength of our result on a sensor coverage problem.

cs.DS↗

arXiv2023

Super resolution computational saturated absorption microscopy

Imaging beyond the diffraction limit barrier has attracted wide attention due to the ability to resolve image features that were previously hidden. Of the various super-resolution microscopy techniques available, a particularly simple method called saturated excitation microscopy (SAX) requires only a simple modification of a laser scanning microscope where the illumination beam power is sinusoidally modulated and driven into saturation. SAX images are extracted from harmonics of the modulation frequency and exhibit improved spatial resolution. Unfortunately, this elegant strategy is hindered by the incursion of shot noise that prevents high resolution imaging in many realistic scenarios. Here, we demonstrate a new technique for super resolution imaging that we call computational saturated absorption (CSA) in which a joint deconvolution is applied to a set of images with diversity in spatial frequency support among the point spread functions used in the image formation with saturated laser scanning fluorescence microscope. CSA microscopy allows access to the high spatial frequency diversity in a set of saturated effective point spread functions, while avoiding image degradation from shot noise.

physics.optics↗

arXiv2023

Minimax Concave Penalty Regularized Adaptive System Identification

We develop a recursive least square (RLS) type algorithm with a minimax concave penalty (MCP) for adaptive identification of a sparse tap-weight vector that represents a communication channel. The proposed algorithm recursively yields its estimate of the tap-vector, from noisy streaming observations of a received signal, using expectation-maximization (EM) update. We prove the convergence of our algorithm to a local optimum and provide bounds for the steady state error. Using simulation studies of Rayleigh fading channel, Volterra system and multivariate time series model, we demonstrate that our algorithm outperforms, in the mean-squared error (MSE) sense, the standard RLS and the $\ell_1$-regularized RLS.

eess.SP↗

arXiv2023

Subspace Perturbation Analysis for Data-Driven Radar Target Localization

Recent works exploring data-driven approaches to classical problems in adaptive radar have demonstrated promising results pertaining to the task of radar target localization. Via the use of space-time adaptive processing (STAP) techniques and convolutional neural networks, these data-driven approaches to target localization have helped benchmark the performance of neural networks for matched scenarios. However, the thorough bridging of these topics across mismatched scenarios still remains an open problem. As such, in this work, we augment our data-driven approach to radar target localization by performing a subspace perturbation analysis, which allows us to benchmark the localization accuracy of our proposed deep learning framework across mismatched scenarios. To evaluate this framework, we generate comprehensive datasets by randomly placing targets of variable strengths in mismatched constrained areas via RFView, a high-fidelity, site-specific modeling and simulation tool. For the radar returns from these constrained areas, we generate heatmap tensors in range, azimuth, and elevation using the normalized adaptive matched filter (NAMF) test statistic. We estimate target locations from these heatmap tensors using a convolutional neural network, and demonstrate that the predictive performance of our framework in the presence of mismatches can be predetermined.

cs.CV↗

arXiv2022

Group-Theoretic Wideband Radar Waveform Design

We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and delayed replicas. We consider the WAF definition as a coefficient function of the unitary representation of the group $a\cdot x + b$. This is essentially an algebraic problem applied to the radar waveform design. Prior works on this subject largely analyzed narrow-band ambiguity functions. Here, we show that when the underlying wideband signal of interest is a pulse or pulse train, a tight frame can be built to design that waveform. Specifically, we design the radar signals by minimizing the ratio of bounding constants of the frame in order to obtain lower sidelobes in the WAF. This minimization is performed by building a codebook based on difference sets in order to achieve the Welch bound. We show that the tight frame so obtained is connected with the wavelet transform that defines the WAF.

cs.IT↗

arXiv2022

Toward Data-Driven STAP Radar

Using an amalgamation of techniques from classical radar, computer vision, and deep learning, we characterize our ongoing data-driven approach to space-time adaptive processing (STAP) radar. We generate a rich example dataset of received radar signals by randomly placing targets of variable strengths in a predetermined region using RFView, a site-specific radio frequency modeling and simulation tool developed by ISL Inc. For each data sample within this region, we generate heatmap tensors in range, azimuth, and elevation of the output power of a minimum variance distortionless response (MVDR) beamformer, which can be replaced with a desired test statistic. These heatmap tensors can be thought of as stacked images, and in an airborne scenario, the moving radar creates a sequence of these time-indexed image stacks, resembling a video. Our goal is to use these images and videos to detect targets and estimate their locations, a procedure reminiscent of computer vision algorithms for object detection$-$namely, the Faster Region-Based Convolutional Neural Network (Faster R-CNN). The Faster R-CNN consists of a proposal generating network for determining regions of interest (ROI), a regression network for positioning anchor boxes around targets, and an object classification algorithm; it is developed and optimized for natural images. Our ongoing research will develop analogous tools for heatmap images of radar data. In this regard, we will generate a large, representative adaptive radar signal processing database for training and testing, analogous in spirit to the COCO dataset for natural images. As a preliminary example, we present a regression network in this paper for estimating target locations to demonstrate the feasibility of and significant improvements provided by our data-driven approach.

cs.CV↗

arXiv2020

Single-Pixel Fluorescent Diffraction Tomography

Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial phase information is required to solve the inverse scattering problem. We introduce a method that extends optical diffraction tomography to imaging spatially incoherent contrast mechanisms such as fluorescent emission. Our strategy mimics the coherent scattering process with two spatially coherent illumination beams. The interferometric illumination pattern encodes spatial phase in temporal variations of the fluorescent emission, thereby allowing incoherent fluorescent emission to mimic the behavior of coherent illumination. The temporal variations permit recovery of the propagation phase, and thus the spatial distribution of incoherent fluorescent emission can be recovered with an inverse scattering model.

physics.optics↗

arXiv2020

Bayesian Learning of Occupancy Grids

Occupancy grids encode for hot spots on a map that is represented by a two dimensional grid of disjoint cells. The problem is to recursively update the probability that each cell in the grid is occupied, based on a sequence of sensor measurements from a moving platform. In this paper, we provide a new Bayesian framework for generating these probabilities that does not assume statistical independence between the occupancy state of grid cells. This approach is made analytically tractable through the use of binary asymmetric channel models that capture the errors associated with observing the occupancy state of a grid cell. Binary-valued measurement vectors are the thresholded output of a sensor in a radar, sonar, or other sensory system. We compare the performance of the proposed framework to that of the classical formulation for occupancy grids. The results show that the proposed framework identifies occupancy grids with lower false alarm and miss detection rates, and requires fewer observations of the surrounding area, to generate an accurate estimate of occupancy probabilities when compared to conventional formulations.

eess.SP↗

arXiv2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman's principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say $β$, of optimal. This paper introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value $β$ of the bound. The surrogate objective and its curvatures depend on the specific ADP.

math.OC↗