Eric W. Tramel

Nearest Regularized Subspace for Hyperspectral Classification

A classifier that couples nearest-subspace classification with a distance-weighted Tikhonov regularization is proposed for hyperspectral imagery. The resulting nearest-regularized-subspace classifier seeks an approximation of each testing sample via a linear combination of training samples within each class. The class label is then derived according to the class which best approximates the test sample. The distance-weighted Tikhonov regularization is then modified by measuring distance within a locality-preserving lower-dimensional subspace. Furthermore, a competitive process among the classes is proposed to simplify parameter tuning. Classification results for several hyperspectral image data sets demonstrate superior performance of the proposed approach when compared to other, more traditional classification techniques.

Block-Based Compressed Sensing of Images and Video

A number of techniques for the compressed sensing of imagery are surveyed. Various imaging media are considered, including still images, motion video, as well as multiview image sets and multiview video. A particular emphasis is placed on block-based compressed sensing due to its advantages in terms of both lightweight reconstruction complexity as well as a reduced memory burden for the random-projection measurement operator. For multiple-image scenarios, including video and multiview imagery, motion and disparity compensation is employed to exploit frame-to-frame redundancies due to object motion and parallax, resulting in residual frames which are more compressible and thus more easily reconstructed from compressed-sensing measurements. Extensive experimental comparisons evaluate various prominent reconstruction algorithms for still-image, motion-video, and multiview scenarios in terms of both reconstruction quality as well as computational complexity.

Compressed-sensing recovery of images and video using multihypothesis predictions

Compressed-sensing reconstruction of still images and video sequences driven by multihypothesis predictions is considered. Specifically, for still images, multiple predictions drawn for an image block are made from spatially surrounding blocks within an initial non-predicted reconstruction. For video, multihypothesis predictions of the current frame are generated from one or more previously reconstructed reference frames. In each case, the predictions are used to generate a residual in the domain of the compressed-sensing random projections. This residual being typically more compressible than the original signal leads to improved reconstruction quality. To appropriately weight the hypothesis predictions, a Tikhonov regularization to an ill-posed least-squares optimization is proposed. Experimental results demonstrate that the proposed reconstructions outperform alternative strategies not employing multihypothesis predictions.

Spectral–Spatial Preprocessing Using Multihypothesis Prediction for Noise-Robust Hyperspectral Image Classification

Spectral-spatial preprocessing using multihypothesis prediction is proposed for improving accuracy of hyperspectral image classification. Specifically, multiple spatially collocated pixel vectors are used as a hypothesis set from which a prediction for each pixel vector of interest is generated. Additionally, a spectral-band-partitioning strategy based on inter-band correlation coefficients is proposed to improve the representational power of the hypothesis set. To calculate an optimal linear combination of the hypothesis predictions, a distance-weighted Tikhonov regularization to an ill-posed least-squares optimization is used. The resulting predictions effectively integrate spectral and spatial information and thus are used during classification in lieu of the original pixel vectors. This processed hyperspectral image dataset has less intraclass variability and more spatial regularity as compared to the original dataset. Classification results for two hyperspectral image datasets demonstrate that the proposed method can enhance the classification accuracy of both maximum-likelihood and support vector classifiers, especially under small sample size constraints and noise corruption.

Video Compressed Sensing with Multihypothesis

The compressed-sensing recovery of video sequences driven by multihypothesis predictions is considered. Specifically, multihypothesis predictions of the current frame are used to generate a residual in the domain of the compressed-sensing random projections. This residual being typically more compressible than the original frame leads to improved reconstruction quality. To appropriately weight the hypothesis predictions, a Tikhonov regularization to an ill-posed least-squares optimization is proposed. This method is shown to outperform both recovery of the frame independently of the others as well as recovery based on single-hypothesis prediction.

Variational free energies for compressed sensing

We consider a variational free energy approach for compressed sensing. We first show that the naïve mean field approach performs remarkably well when coupled with a noise learning procedure. We also notice that it leads to the same equations as those used for iterative thresholding.We then discuss the Bethe free energy and how it corresponds to the fixed points of the approximate message passing algorithm. In both cases, we test numerically the direct optimization of the free energies as a converging sparse-estimation algorithm. We further derive the Bethe free energy in the context of generalized approximate message passing.

Reconstruction of Hyperspectral Imagery From Random Projections Using Multihypothesis Prediction

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 reconstruction. 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.

Compressed sensing of multiview images using disparity compensation

Compressed sensing is applied to multiview image sets and inter-image disparity compensation is incorporated into image reconstruction in order to take advantage of the high degree of inter-image correlation common to multiview scenarios. Instead of recovering images in the set independently from one another, two neighboring images are used to calculate a prediction of a target image, and the difference between the original measurements and the compressed-sensing projection of the prediction is then reconstructed as a residual and added back to the prediction in an iterated fashion. The proposed method shows large gains in performance over straightforward, independent compressed-sensing recovery. Additionally, projection and recovery are block-based to significantly reduce computation time.

Compressed-sensing recovery of multiview image and video sequences using signal prediction

In the compressed sensing of multiview images and video sequences, signal prediction is incorporated into the reconstruction process in order to exploit the high degree of interview and temporal correlation common to multiview scenarios. Instead of recovering each individual frame independently, neighboring frames in both the view and temporal directions are used to calculate a prediction of a target frame, and the difference is used to drive a residual-based compressed-sensing reconstruction. The proposed approach demonstrates a significant gain in reconstruction quality relative to the straightforward compressed-sensing recovery of each frame independently of the others in the multiview set, as well as a significant performance advantage as compared to a pair of benchmark multiple-frame compressed-sensing reconstructions.

Multistage compressed-sensing reconstruction of multiview images

Compressed sensing is applied to multiview image sets and the high degree of correlation between views is exploited to enhance recovery performance over straightforward independent view recovery. This gain in performance is obtained by recovering the difference between a set of acquired measurements and the projection of a prediction of the signal they represent. The recovered difference is then added back to the prediction, and the prediction and recovery procedure is repeated in an iterated fashion for each of the views in the multiview image set. The recovered multiview image set is then used as an initialization to repeat the entire process again to form a multistage refinement. Experimental results reveal substantial performance gains from the multistage reconstruction.