Reconstruction of Hyperspectral Imagery from Random Projections
Using Multihypothesis Prediction

Chen Chen, Wei Li, Eric W. Tramel, and James E. Fowler


Reconstruction of hyperspectral imagery from spectral random projections is considered. Specifically, multiple predictions drawn for a pixel vector of interest are made from spatially neighboring pixel vectors within an initial non-predicted re-construction. A two-phase hypothesis-generation procedure based on partitioning and merging of spectral bands according to the correlation coefficients between bands is proposed to fine-tune the hypotheses. The resulting prediction is used to generate a residual in the projection domain. This residual being typically more compressible than the original pixel vector leads to improved reconstruction quality. To appropriately weight the hypothesis predictions, a distance-weighted Tikhonov regularization to an ill-posed least-squares optimization is proposed. Experimental results demonstrate that the proposed reconstruction significantly outperforms alternative strategies not employing multihypothesis prediction.



Reconstruction Framework

Fig. 1 MH prediction and residual reconstruction as post-processing for HSI reconstruction

For more information about Compressive-Projection Principle Component Analysis (CPPCA), please visit

Experiment Results

1. To measure the quality of the reconstructed image, we use both signal-to-noise ratio (SNR) and spectral-angle distortion. The results are reported in Table 1 and 2 at various sampling subrates (K/N).

Table 1. Average SNR in dB

Table 2. Average spectral-angle distortion

2. In many applications, the users are generally interested in assigning each pixel-vector of a hyperspectral image to one of a number of given classes.To measure how well hyperspectral datasets which are reconstructed from random projections preserve such class information, we further perform classification tasks on the reconstructed datasets. We take the Indian Pines dataset for example. The original dataset and the reconstructed datasets using seven different algorithms are used. Two classification algorithms are used in the experiments: 1) a maximum-likelihood estimation (MLE) classifier applied after a dimensionality reduction using Fisher's linear discriminant analysis (LDA), and 2) the popular support-vector-machine (SVM) classifier with the radial-basis-function (RBF) kernel. More classification results can be found in my master's thesis here.

Moreover, we apply this technique (MH prediction) as a preprocessing procedure to effectively integrate spectral and spatial information for improving accuracy of hyperspectral image classification. Experimental results on two real hyperspectral image datasets demonstrate that MH prediction is a simple but effective preprocessing algorithm for noise-robust hyperspectral image classification! For more details, please refer to our JSTARS paper.
Fig. 2 Classification accuracy (%) using FLDA-MLE

Fig. 3 Classification accuracy (%) using SVM