A convex formulation for hyperspectral image superresolution via subspace-based regularization (1411.4005v1)

Abstract: Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.

• The paper introduces a convex optimization framework using subspace-based regularization for effective hyperspectral image superresolution.
• It employs a variant of vector Total Variation with the SALSA algorithm to merge high-spectral and high-spatial resolution images efficiently.
• Experimental results demonstrate enhanced performance and robust blind estimation of spatial and spectral responses in remote sensing applications.

A Convex Formulation for Hyperspectral Image Superresolution via Subspace-Based Regularization

This paper presents a robust method for hyperspectral image superresolution, leveraging convex optimization through subspace-based regularization. The fusion of hyperspectral (HSI) and multispectral images (MSI) is prevalent in remote sensing, aiming to merge the high spectral resolution of HSIs with the higher spatial resolution of MSIs.

Problem Formulation

The problem is formulated as a convex optimization task involving quadratic data-fitting terms alongside an edge-preserving regularizer. The primary objective function includes two quadratic terms accounting for blurring, different spatial resolutions, and additive noise. The regularizer employed is a variant of vector Total Variation (VTV), which encourages piecewise-smooth solutions while allowing for discontinuities aligned across the hyperspectral bands.

Methodology

The proposed method employs dimensionality reduction by factoring HSIs into a lower-dimensional subspace, recognizing that hyperspectral data usually inhabit such spaces. The use of the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), a variant of the Alternating Direction Method of Multipliers (ADMM), is pivotal in efficiently addressing the non-quadratic and non-smooth optimization problem. Additionally, the spatial blur and spectral linear operators, intrinsic to HSI and MSI data acquisition, are concurrently estimated to optimize the data fusion process.

Experimental Validation

Experimental validation was conducted using both simulated and real-life datasets. The algorithm demonstrated superior performance over existing state-of-the-art methods, as evidenced by several quality indices such as ERGAS, SAM, and UIQI. Moreover, the paper provides insight into the estimation of unknown parameters such as the spatial and spectral responses, accommodating scenarios where full sensor specifications may not be available. This blind estimation capability is notably advantageous for practical applications where such information is incomplete or imprecise.

Implications and Future Directions

The implications of this research are substantial for remote sensing technologies, improving the quality and applicability of spectral data in various fields like agriculture, mineralogy, and environmental monitoring. The integration of vector Total Variation introduces robustness against misalignments and noise, potentially leading to advancements in other areas of image processing and computer vision.

The research hints at future developments in AI, particularly in enhancing the resolution and quality of data retrieved from spectral imaging. Further exploration could focus on real-time implementation and adaptations to accommodate different imaging modalities and sensor arrays.

The use of convex optimization in fusing diverse image types presents an avenue for cross-disciplinary enhancements, potentially applicable in areas such as bioinformatics and astrophysical imaging where high-dimensional and multi-resolution datasets are crucial. Overall, this work represents a meaningful contribution to hyperspectral imaging, providing a rigorous approach to addressing the ongoing challenges in data fusion.