In this dissertation, new digital image processing methods for hyperdimensional imagery are developed and experimentally tested on remotely sensed Earth observations and medical imagery. The high dimensionality of the imagery is either inherent due to the type of measurements forming the image, as with imagery obtained with hyperspectral sensors, or the result of preprocessing and feature extraction, as with synthetic aperture radar imagery and digital mammography. In the first study, two omni-directional adaptations of gray level co-occurrence matrix analysis are developed and experimentally evaluated. The adaptations are based on a previously developed rubber band straightening transform that has been used for analysis of segmented masses in digital mammograms. The new methods are beneficial because they can be applied to imagery where the region of interest is either poorly segmented or not segmented. The methods are based on the concept of extracting circular windows s around each pixel in the image which are radially resampled to derive rectangular images. The images derived from the resampling are then suitable for standard GLCM techniques. The methods were applied to both remotely sensed synthetic aperture radar imagery, for the purpose of automated detection of landslides on earthen levees, and to digital mammograms, for the purpose of automated classification of masses as either benign or malignant. Experimental results show the newly developed methods to be valuable for texture feature extraction and classification of un-segmented objects. In the second study, a new technique of using spatial information in spectral band grouping for remotely sensed hyperspectral imagery is developed and experimentally tested. The technique involves clustering the spectral bands based on similarity of spatial features extracted from each band. The newly developed technique is evaluated in automated classification systems that utilize a single classifier and systems that utilize multiple classifiers combined with decision fusion. The systems are experimentally tested on remotely sensed imagery for agricultural applications. The spatial-spectral band grouping approach is compared to uniform band windowing and spectral only band grouping. The results show that the spatial-spectral band grouping method significantly outperforms both of the comparison methods, particularly when using multiple classifiers with decision fusion.

To overcome the dimensionality curse of hyperspectral data, an investigation has been done on the use of grouping spectral bands, followed by feature level fusion and classifier decision fusion, to develop an automated target recognition (ATR) system for data reduction and enhanced classification. The entire span of spectral bands in the hyperspectral data is subdivided into groups based on performance metrics. Feature extraction is done using supervised methods as well as unsupervised methods. The effects of classification of the lower dimension data by parametric, as well as non-parametric, classifiers are studied. Further, multiclassifiers and decision level fusion using Qualified Majority Voting is applied to the features extracted from each group. The effectiveness of the ATR system is tested using the hyperspectral signatures of a target class, Cogongrass (Imperata Cylindrica), and a non-target class, Johnsongrass (Sorghum halepense). A comparison of target detection accuracies by before and after decision fusion illustrates the effect of the influence of each group on the final decision and the benefits of using decision fusion with multiclassifiers. Hence, the ATR system designed can be used to detect a target class while significantly reducing the dimensionality of the data.

Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification.