Connections Between Deep Equilibrium and Sparse Representation Models With Application to Hyperspectral Image Denoising

Abstract

In this paper, we propose a novel methodology for addressing the hyperspectral image deconvolution problem. This problem is highly ill-posed, and thus, requires proper priors (regularizers) to model the inherent spectral-spatial correlations of the HSI signals. To this end, a new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. To tackle this problem, an effective solver is proposed using the half quadratic splitting methodology. The derived iterative solver is then expressed as a fixedpoint calculation problem within the Deep Equilibrium (DEQ) framework, resulting in an interpretable architecture, with clear explainability to its parameters and convergence properties with practical benefits. The proposed model is a first attempt to handle the classical HSI degradation problem with different blurring kernels and noise levels via a single deep equilibrium model with significant computational efficiency. Extensive numerical experiments validate the superiority of the proposed methodology over other state-of-the-art methods. This superior restoration performance is achieved while requiring 99.85% less computation time as compared to existing methods.

Deep Learning-Based Cooperative LiDAR Sensing for Improved Vehicle Positioning

“…This should be expected since a lower resolution makes the detection process more difficult, leading to fewer objects detected and a consequent increase of the CEP95 value. To improve the object detection performances, super-resolution methods could be adopted [83]. We remark that CLS-MPNN still outperforms GNSS-KF even when using low-resolution LiDAR sensors.…”

A Federated Deep Unrolling Method for Lidar Super-Resolution: Benefits in SLAM

“…The deep unrolling framework in an emerging research field with significant potential to numerous real-world inverse problems [22], [24], [25], [27], [29]- [31]. More formally, the deep unrolling approach transform effective optimizationbased algorithms into computationally efficient and interpretable deep learning networks, where each iteration of the solver corresponds to one layer of the network [32].…”

“…Specifically, our proposed method operates on range images directly derived from the lidar point clouds which are collected by different AVs that have the capability to communicate. Considering the unique local and non-local dependencies exhibited by 2D range images, our approach expands on recent studies that use learnable regularization terms in the form of suitable neural networks [19]- [22]. These regularizers, derived from the training data of each AV, are adept at encapsulating more complex and unique characteristics of the data under consideration.…”

“…Upon deriving an efficient iterative solver (e.g., based on the HQS ) for the lidar super resolution problem, a model-based deep learning architecture is generated, via the utilization of the deep unrolling (DU) framework [22], [24]- [27]. To elaborate, the derived solver is unrolled for a specific number of iterations, hence creating a structured neural network.…”

Federated Learning for Lidar Super Resolution on Automotive Scenes

“…where S ∈ R c×C denotes the downsampling operator that selects only the c channels from the high resolution range image and N is a zero-mean Gaussian noise term. Thus, it belongs to the category of the highly ill-posed inverse imaging problems [16]. The objective is to estimate the high-resolution range image X given the low-resolution range image Y , so that…”