arXiv subjects

Jonathan Monsalve

Publications and source records attributed to Jonathan Monsalve.

4 recordsLinked to original sources

arXiv2025

Diffusion model for gradient preconditioning in hyperspectral imaging inverse problems

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints. A common workaround is to partition measurements and estimate local statistics-such as the covariance matrix-using only partial observations. However, this strategy introduces noise in the optimization gradients, especially when each partition contains few samples. In this work, we reinterpret this accumulation of gradient noise as a diffusion process, where successive partitions inject increasing uncertainty into the learning signal. Building on this insight, we propose a novel framework that leverages denoising diffusion models to learn a reverse process in gradient space. The model is trained to map noisy gradient estimates toward clean, well-conditioned updates, effectively preconditioning the optimization. Our approach bridges generative modeling and inverse problem solving, improving convergence and reconstruction quality under aggressive sampling regimes. We validate our method on hyperspectral recovery tasks, demonstrating significant gains in accuracy and stability over traditional optimization pipelines.

eess.IV↗

arXiv2025

CLuP-Based Dual-Deconvolution in Automotive ISAC Scenarios

Accurate target parameter estimation of range, velocity, and angle is essential for vehicle safety in advanced driver assistance systems (ADAS) and autonomous vehicles. To enable spectrum sharing, ADAS may employ integrated sensing and communications (ISAC). This paper examines a dual-deconvolution automotive ISAC scenario where the radar waveform is known but the propagation channel is not, while in the communications domain, the channel is known but the transmitted message is not. Conventional maximum likelihood (ML) estimation for automotive target parameters is computationally demanding. To address this, we propose a low-complexity approach using the controlled loosening-up (CLuP) algorithm, which employs iterative refinement for efficient separation and estimation of radar targets. We achieve this through a nuclear norm restriction that stabilizes the problem. Numerical experiments demonstrate the robustness of this approach under high-mobility and noisy automotive environments, highlighting CLuP's potential as a scalable, real-time solution for ISAC in future vehicular networks.

eess.SP↗

arXiv2022

Beurling-Selberg Extremization for Dual-Blind Deconvolution Recovery in Joint Radar-Communications

Recent interest in integrated sensing and communications has led to the design of novel signal processing techniques to recover information from an overlaid radar-communications signal. Here, we focus on a spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown to the common receiver. In this dual-blind deconvolution (DBD) problem, the receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-times or delays corresponding to multiple transmission paths and targets, respectively. Prior works addressed recovery of unknown channels and signals in this ill-posed DBD problem through atomic norm minimization but contingent on individual minimum separation conditions for radar and communications channels. In this paper, we provide an optimal joint separation condition using extremal functions from the Beurling-Selberg interpolation theory. Thereafter, we formulate DBD as a low-rank modified Hankel matrix retrieval and solve it via nuclear norm minimization. We estimate the unknown target and communications parameters from the recovered low-rank matrix using multiple signal classification (MUSIC) method. We show that the joint separation condition also guarantees that the underlying Vandermonde matrix for MUSIC is well-conditioned. Numerical experiments validate our theoretical findings.

cs.IT↗

arXiv2021

Covariance Estimation from Compressive Data Partitions using a Projected Gradient-based Algorithm

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 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 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 (8-15% approx). 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.

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