Abstract
Convolutional dictionary learning (CDL) is an unsupervised learning method to seek a translation-invariant sparse representation for signals, and has gained a lot of interest in various image processing and computer vision applications. However, 3D hyperspectral images pose unique challenges due to their high dimensionality and complex structures, making optimization of the dictionary and its application to inverse problems difficult. This paper proposes an efficient CDL algorithm that neither explicit evaluation of the Hessians nor their inversion is required in the optimization process, which leads to substantial acceleration and memory savings. Furthermore, we exploit the learned kernels as the convolutional sparse coding (CSC) image prior for the compressive chromo-tomographic (CCT) reconstruction problem, and examine the usability and performances of the proposed method for CCT reconstruction. Numerical experiments show that, for CCT, 1) the proposed CSC can provide an efficient representation for HSI by using several tens of 3D filters; 2) the learned convolutional dictionary has reliable generalization capability; and 3) the proposed CSC-based method outperforms the classical reconstruction method using an analytic sparsifying basis.
Highlights
Hyperspectral imagery (HSI) measures the radiation intensity of every pixel in the scene over many wavelength bands
This paper introduces the Preconditioned alternating direction method of multipliers (ADMM) (PADMM) framework [26], [27] into CDL for HSI and compressive chromo-tomography (CCT) [28], and further proposes two efficient diagonal preconditioner design methods that allow for Hessian free solutions, resulting in substantial algorithm acceleration and memory savings
Two efficient construction methods of diagonal preconditioners have been proposed, which contributes to a Hessian free CDL algorithm for HSI with substantial algorithm acceleration and memory savings
Summary
Hyperspectral imagery (HSI) measures the radiation intensity of every pixel in the scene over many wavelength bands These spatially registered spectral images exhibit three important attributes: local spatial smoothness, high spectral correlation and nonlocal spatial similarity, which make dictionary learning (DL) a well-suited approach to seeking for a sparse and redundant representation model for various HSI analysis and processing tasks, including hyperspectral classification [1]–[3], hyperspectral image denoising [4], anomaly detection [5], hyperspectral image super-resolution [6]–[8], and hyperspectral compressive sensing [9], [10], among others. The flexibility and adaptability of DL has made it a rather appealing sparse representation approach and its evolution has displayed three important stages that are worthy of mention: i) Patched-based dictionary learning, extracts the so-called dictionary atoms from overlapped image patches, forming the columns of the dictionary D, and approximates every image patch with a linear combination x ≈ Dz, where z is
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