HDL Implementation of DFT Architectures Using Winograd Fast Fourier Transform Algorithm

The low spatial resolution of hyperspectral images means that existing mixed pixels rely heavily on spectral information, making it difficult to differentiate between the target of interest and the background. The endmember extraction method is powerful in enhancing spatial structure information for hyperspectral anomaly detection, whereas most approaches are based on matrix representation, which inevitably destroys the spatial or spectral information. In this paper, we treated the hyperspectral image as a third-order tensor and proposed a novel anomaly detection method based on a low-rank linear mixing model of the scene background. The obtained abundance maps possessed more distinctive features than the raw data, which was beneficial for identifying anomalies in the background. Specifically, the low-rank tensor background was approximated as the mode-3 product of an abundance tensor and endmember matrix. Due to the distinctive features of the background’s abundance maps, we characterized them by tensor regularization and imposed low rankness through CP decomposition, smoothness, and sparsity. In addition, we utilized the ℓ1,1,2-norm to characterize the tube-wise sparsity of the anomaly, since it accounted for a small portion of the scene. The experimental results obtained using five real datasets demonstrated the outstanding performance of our proposed method.

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“…where f f t and i f f t denote the fast Fourier transform [55] and its inverse, respectively. Update V 2 and V 3 :…”

Section: Optimization Proceduresmentioning

confidence: 99%

Hyperspectral Anomaly Detection Based on Regularized Background Abundance Tensor Decomposition

Shang

Jouni

et al. 2023

Remote Sensing

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“…D is a convolution, operating only in the spatial domain. The solution to G 3 in (30) can be acquired by a fast Fourier transform [72]:…”

Section: B Proposed Model and Optimizationmentioning

confidence: 99%

Weighted Nonlocal Low-Rank Tensor Decomposition Method for Sparse Unmixing of Hyperspectral Images

Sun

Zhan

et al. 2020

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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The low spatial resolution of hyperspectral images leads to the coexistence of multiple ground objects in a single pixel (called mixed pixels). A large number of mixed pixels in a hyperspectral image hinders the subsequent analysis and application of the image. In order to solve this problem, a novel sparse unmixing method, which considers highly similar patches in nonlocal regions of a hyperspectral image, is proposed in this article. This method exploits spectral correlation by using collaborative sparsity regularization and spatial information by employing total variation and weighted nonlocal low-rank tensor regularization. To effectively utilize the tensor decomposition, nonlocal similar patches are first grouped together. Then, these nonlocal patches are stacked to form a patch group tensor. Finally, weighted low-rank tensor regularization is enforced to constrain the patch group to obtain an estimated low-rank abundance image. Experiments on simulated and real hyperspectral datasets validated the superiority of the proposed method in better maintaining fine details and obtaining better unmixing results.

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“…where H represents a convolution. H can be applied independently in a band-by-band manner and calculated by discrete Fourier transform diagonalization [63]. The optimization problem of V 4 is:…”

mentioning

confidence: 99%

Sparse Unmixing for Hyperspectral Image with Nonlocal Low-Rank Prior

Zheng

Shim

et al. 2019

Remote Sensing

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Hyperspectral unmixing is a key preprocessing technique for hyperspectral image analysis. To further improve the unmixing performance, in this paper, a nonlocal low-rank prior associated with spatial smoothness and spectral collaborative sparsity are integrated together for unmixing the hyperspectral data. The proposed method is based on a fact that hyperspectral images have self-similarity in nonlocal sense and smoothness in local sense. To explore the spatial self-similarity, nonlocal cubic patches are grouped together to compose a low-rank matrix. Then, based on the linear mixed model framework, the nuclear norm is constrained to the abundance matrix of these similar patches to enforce low-rank property. In addition, the local spatial information and spectral characteristic are also taken into account by introducing TV regularization and collaborative sparse terms, respectively. Finally, the results of the experiments on two simulated data sets and two real data sets show that the proposed algorithm produces better performance than other state-of-the-art algorithms.

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HDL Implementation of DFT Architectures Using Winograd Fast Fourier Transform Algorithm

Cited by 7 publications

References 7 publications

Hyperspectral Anomaly Detection Based on Regularized Background Abundance Tensor Decomposition

Hyperspectral Anomaly Detection Based on Regularized Background Abundance Tensor Decomposition

Weighted Nonlocal Low-Rank Tensor Decomposition Method for Sparse Unmixing of Hyperspectral Images

Sparse Unmixing for Hyperspectral Image with Nonlocal Low-Rank Prior

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