Gelvez Tatiana, Rueda Hoover, Arguello Henry
Appl Opt. 2017 Aug 20;56(24):6785-6795. doi: 10.1364/AO.56.006785.
Compressive spectral imaging techniques encode and disperse a hyperspectral image (HSI) to sense its spatial and spectral information with few bidimensional (2D) multiplexed projections. Recovering the original HSI from the 2D projections is carried by traditional compressive sensing-based techniques that exploit the sparsity property of natural HSI as they are represented in a proper orthonormal basis. Nevertheless, HSIs also exhibit a low rank property inasmuch only a few numbers of spectral signatures are present in the images. Specifically, when an HSI is rearranged as a matrix whose columns represent vectorized 2D spatial images in a different wavelength, this matrix is said to be low rank. Therefore, this paper proposes an HSI recovering algorithm from compressed measurements involving a joint sparse and low rank optimization problem, which seeks to jointly minimize the ℓ-, ℓ-, and ℓ-norm, leading the solution to fit the given projections, and be simultaneously sparse and low rank. Several simulations, along different data sets and optical sensing architectures, show that when the low rank property is included in the inverse problem formulation, the reconstruction quality increases up to four (dB) in terms of peak signal to noise ratio.
压缩光谱成像技术对高光谱图像（HSI）进行编码和色散，以通过少量二维（2D）多路复用投影来感知其空间和光谱信息。从二维投影中恢复原始高光谱图像是由基于传统压缩感知的技术来完成的，这些技术利用自然高光谱图像在适当的正交基中表示时的稀疏特性。然而，高光谱图像也表现出低秩特性，因为图像中仅存在少量的光谱特征。具体而言，当将高光谱图像重新排列为一个矩阵，其列表示不同波长下的矢量化二维空间图像时，该矩阵被称为低秩矩阵。因此，本文提出了一种从压缩测量中恢复高光谱图像的算法，该算法涉及联合稀疏和低秩优化问题，旨在联合最小化ℓ -、ℓ - 和ℓ - 范数，使解符合给定的投影，并且同时具有稀疏性和低秩性。沿着不同数据集和光学传感架构进行的多次模拟表明，当在反问题公式中纳入低秩特性时，在峰值信噪比方面，重建质量提高了多达4（dB）。
