Recently, unfolding techniques have been widely utilized to solve the inverse problems in various applications. In this paper, we study optimization guarantees for two popular unfolded networks, i.e., unfolded network...
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ISBN:
(纸本)9781665405409
Recently, unfolding techniques have been widely utilized to solve the inverse problems in various applications. In this paper, we study optimization guarantees for two popular unfolded networks, i.e., unfolded networks derived from iterative soft thresholding algorithms (ISTA) and derived from Alternating Direction Method of Multipliers (ADMM). Our guarantees - leveraging the Polyak-Lojasiewicz* (PL*) condition - state that the training (empirical) loss decreases to zero with the increase in the number of gradient descent epochs provided that the number of training samples is less than some threshold that depends on various quantities underlying the desired information processing task. Our guarantees also show that this threshold is larger for unfolded ISTA in comparison to unfolded ADMM, suggesting that there are certain regimes of number of training samples where the training error of unfolded ADMM does not converge to zero whereas the training error of unfolded ISTA does. A number of numerical results are provided backing up our theoretical findings.
We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key mo...
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We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key modeling elements in conjunction with data-driven components. More precisely, we put forth a neural network architecture inspired by the algorithmic unfolding of the iterative weighted minimum mean squared error (WMMSE) method, that we denote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are parameterized using graph neural networks (GNNs), where the time-varying underlying graphs are given by the fading interference coefficients in the wireless network. These GNNs are trained through a gradient descent approach based on multiple instances of the power allocation problem. We show that the proposed architecture is permutation equivariant, thus facilitating generalizability across network topologies. Comprehensive numerical experiments illustrate the performance attained by UWMMSE along with its robustness to hyper-parameter selection and generalizability to unseen scenarios such as different network densities and network sizes.
We address the detection of material defects, which are inside a layered material structure using compressive sensing-based multiple-input and multiple-output (MIMO) wireless radar. Hem strong clutter due to the refle...
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We address the detection of material defects, which are inside a layered material structure using compressive sensing-based multiple-input and multiple-output (MIMO) wireless radar. Hem strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited, and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose joint rank and sparsity minimization for defect detection. In particular, we propose a non-convex approach based on the iteratively reweighted nuclear and l(1)-norm (a double-reweighted approach) to obtain a higher accuracy compared to the conventional nuclear norm and l(1)-norm minimization. To this end, an iterative algorithm is designed to estimate the low-rank and sparse contributions. Further, we propose deep learning-based parameter tuning of the algorithm (i.e., algorithm unfolding) to improve the accuracy and the speed of convergence of the algorithm. Our numerical results show that the proposed approach outperforms the conventional approaches in terms of mean squared errors of the recovered low-rank and sparse components and the speed of convergence.
We study the problem of optimal power allocation in single-hop multi-antenna ad-hoc wireless networks. A standard technique to solve this problem involves optimizing a tri-convex function under power constraints using...
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ISBN:
(纸本)9781665439565
We study the problem of optimal power allocation in single-hop multi-antenna ad-hoc wireless networks. A standard technique to solve this problem involves optimizing a tri-convex function under power constraints using a block-coordinate-descent based iterative algorithm. This approach, termed WMMSE, tends to be computationally complex and time consuming. Several learning-based approaches have been proposed to speed up the power allocation process. A recent work, UWMMSE, learns an affine transformation of a WMMSE parameter in an unfolded structure to accelerate convergence. In spite of achieving promising results, its application is limited to single-antenna wireless networks. In this work, we present a UWMMSE framework for power allocation in (multiple-input multiple-output) MIMO interference networks. A major advantage of this method lies in its use of low-complexity learnable systems in which the number of parameters scales linearly with respect to the hidden layer size of embedded neural architectures and the product of the number of transmitter and receiver antennas only, fully independent of the number of transceivers in the network. We illustrate the superiority of our method through an empirical study of our approach in comparison to WMMSE and also analyze its robustness to changes in channel conditions and network size.
In this paper, we use algorithm unrolling approaches in order to design a new neural network structure applicable to hyperspectral unmixing challenges. In particular, building upon a constrained sparse regression form...
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ISBN:
(纸本)9781728176055
In this paper, we use algorithm unrolling approaches in order to design a new neural network structure applicable to hyperspectral unmixing challenges. In particular, building upon a constrained sparse regression formulation of the underlying unmixing problem, we unroll an ADMM solver onto a neural network architecture that can be used to deliver the abundances of different (known) endmembers given a reflectance spectrum. Our proposed network - which can be readily trained using standard supervised learning procedures - is shown to possess a richer structure consisting of various skip connections and shortcuts than other competing architectures. Moreover, our proposed network also delivers state-of-the-art unmixing performance compared to competing methods.
Multi-spectral (MS) image super-resolution aims to reconstruct super-resolved multi-channel images from their low-resolution images by regularizing the image to be reconstructed. Recently data-driven regularization te...
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ISBN:
(纸本)9781538646588
Multi-spectral (MS) image super-resolution aims to reconstruct super-resolved multi-channel images from their low-resolution images by regularizing the image to be reconstructed. Recently data-driven regularization techniques based on sparse modeling and deep learning have achieved substantial improvements in single image reconstruction problems. Inspired by these data-driven methods, we develop a novel coupled analysis and synthesis dictionary (CASD) model for MS image super-resolution, by exploiting a regularizer that operates within, as well as across, multiple spectral channels using convolutional dictionaries. To learn the CASD model parameters, we propose a deep dictionary learning framework, named DeepCASD, by unfolding and training an end-to-end CASD based reconstruction network over an image data set. Experimental results show that the DeepCASD framework exhibits improved performance on multi-spectral image super-resolution compared to state-of-the-art learning based super-resolution algorithms.
Multi-spectral (MS) image super-resolution aims to reconstruct super-resolved multi-channel images from their low-resolution images by regularizing the image to be reconstructed. Recently data-driven regularization te...
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ISBN:
(纸本)9781538646595
Multi-spectral (MS) image super-resolution aims to reconstruct super-resolved multi-channel images from their low-resolution images by regularizing the image to be reconstructed. Recently data-driven regularization techniques based on sparse modeling and deep learning have achieved substantial improvements in single image reconstruction problems. Inspired by these data-driven methods, we develop a novel coupled analysis and synthesis dictionary (CASD) model for MS image super-resolution, by exploiting a regularizer that operates within, as well as across, multiple spectral channels using convolutional dictionaries. To learn the CASD model parameters, we propose a deep dictionary learning framework, named DeepCASD, by unfolding and training an end-to-end CASD based reconstruction network over an image data set. Experimental results show that the DeepCASD framework exhibits improved performance on multi-spectral image super-resolution compared to state-of-the-art learning based super-resolution algorithms.
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