Dictionary Learning for Noisy and Incomplete Hyperspectral Images

Abstract

We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength-dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous three-dimensional (3D) spatio-spectral blocks, of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly ("collaboratively") to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelength-dependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the more-conventional approach of using an i.i.d. Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.

Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation

“…DL has also been investigated to restore HS images [34]. More precisely, a Bayesian scheme was introduced in [34] to learn a dictionary from an HS image, which imposes a self-consistency of the dictionary by using Beta-Bernoulli processes. This Monte Carlo-based method provided interesting results at the price of a high computational complexity.…”

Coded Hyperspectral Imaging and Blind Compressive Sensing

“…However, here we are considering diverse spectral patterns over several wavelengths, and devising a similarly appropriate scheme is beyond the scope of this paper. In fact, in previous work on denoising and inpainting of hyperspectral images [32], it has been observed that BPFA outperformed KSVD significantly. Furthermore, there is a lot of difference in the manner in which sparse codes are updated in KSVD and BPFA.…”

“…Beta process factor analysis (BPFA) is a non-parametric Bayesian dictionary learning technique that has been applied for denoising and inpainting of grayscale and RGB images [27], and it has also been utilized for inpainting hyperspectral images [32] with substantial missing data. The beta process is coupled with a Bernoulli process, to impose explicit sparseness on the coefficients {c i } i=1,N .…”

“…We develop a new inversion framework based on Bayesian dictionary learning, in which (i) a dictionary is learned to compactly represent patches in the form of small spatio-spectral cubes, and (ii) a Gaussian process is employed to explicitly account for correlation with wavelength. Related research was considered in [32], but each row of Σ i was composed of all zeros and a single one. In this paper we demonstrate how these methods may be applied to the CASSI camera, with more sophisticated Σ i .…”

Compressive Sensing in Microscopy: a Tutorial

“…CS approaches have been shown to reduce dose by as much as 90% in electron microscopy [2,3,4]. Optical imaging and microscopy have also seen substantial benefits [5,6,7,8,9,10,11,12,13]. This tutorial will briefly introduce the principles of CS.…”