Gradient and Laplacian-Based Hyperspectral Anisotropic Diffusion

Abstract

To improve accuracy and efficiency of object detection and classification with hyperspectral imagery (HSI), we propose a novel smoothing algorithm by coupling of a Laplacianbased reaction term to a classical divergence-based anisotropic diffusion partial differential equation (PDE). In addition, an adaptive parameter is introduced to regularize this nonlinear reactiondiffusion PDE by explicitly integrating the interband correlations with the noise level of each band in HSI. It is also well-known that the interband correlations can be implicitly embedded into the diffusion coefficient of the divergence-based PDE, to allow a selective smoothing that reduces the local homogeneous area variability while preventing smoothing across edges. Therefore, the interband correlations in HSI are exploited in the proposed method in both explicit and implicit ways. As a result, our algorithm is more effective at controlling the behavior of the diffusion evolution when compared to previous multi/hyperspectral diffusion algorithms. The simulations based on both synthetic data and real hyperspectral remote sensing data show that our algorithm can improve the hyperspectral data quality in terms of both visual inspection and image quality indices.Index Terms-Anisotropic diffusion, hyperspectral, image smoothing, interband correlations, partial differential equation (PDE), remote sensing.

A Review on Performance Analysis of PDE based Anisotropic Diffusion Approaches for Image Enhancement

“…Anisotropic diffusion has also been used in the detection and removal of cracks in digital paintings [20] because the appearance of cracks on paintings deteriorates the quality perceived. Mineralogy, surveillance, agriculture, and astronomical area mostly use hyper spectral images [21] where anisotropic smoothing helps to restore the image features. Remote sensing image [22] helps in detecting vehicles, buildings, road-linked objects and acquisition of transportation data.…”

“…𝐼 𝑃 (𝑞) = { 1 𝑤ℎ𝑒𝑛𝑑(𝑝, 𝑞) ≤ 𝑇 0 𝑤ℎ𝑒𝑛𝑑(𝑝, 𝑞) > 𝑇 (21) where 𝑁 = ((2𝑤 + 1) 2 − 1) denotes the number of pixels in a squared size window w. The value of 𝑔 𝑛 is minimum at edge, maximum at interior pixels and intermediate at noise. The value of 𝜆 𝑛 is minimum at noise, maximum at interior pixels and intermediate at edges.…”

“…However, it is not suitable for noisy images. Wang et al [21] suggested gradient and laplacian based hyperspectral anisotropic diffusion (GLHAD) algorithm by introducing the Laplacian function into classical PMD [3] for HSI improvement. The operational utility of GLHAD method needs to be improved further by proper parameter selection and optimization.…”