Research summary

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Statistical learning

A variety of real-world tasks involve classifying sensed imagery into pre-determined categories. Detection-theoretic approaches formulate such classification tasks as hypothesis testing problems, under the idealized assumption of knowledge of the true class conditional densities, or abundant training when true densities are not known. Often, the available image data is assumed to be noise-free. In many real-world problems however, such methods need to be equipped with a notion of robustness to various types of modeling uncertainty - insufficient training, noisy acquisition, inadequate modeling of all physical effects, etc. In addition, the computational cost of inference scales with the dimension of data, rendering sophisticated robust tests intractable for real-world application. My research has explored tractable algorithms for robust image classification problems using discriminative graphical models for feature fusion.

Structured sparsity for image classification

Sparse representation-based classification has emerged as one of the most significant recent innovations in signal processing and machine learning. Its remarkable success in practical applications can be attributed to the innate discriminative power of sparse representations (corresponding to dictionaries designed using training from all classes) and the robustness offered by such representations to real-world distortions. Sparsity merely conveys first-order information about signal structure. Developments in model-based compressive sensing have revealed that sparse signals often exhibit more elaborate structure in the locations of their non-zero entries. This observation is being exploited in classification tasks in the form of group/joint/collaborative sparsity-based classification algorithms that incorporate contextual information. My research seeks interpretations for these various notions of structured sparsity from a Bayesian viewpoint.

Interesting connections are also emerging between sparse representations and graphical models. My recent work on learning discriminative graphical models on sparse coefficients offers encouraging signs for a more detailed study of such inter-connections and its ramifications for classification tasks.

Computational color and imaging

The problem of resolution enhancement in images from multiple low-resolution captures, popularly known as image super-resolution, has garnered significant attention over the last two decades. Despite advances in techniques to jointly estimate registration parameters and the high-resolution image, a key computational challenge remains - algorithmic tractability of the resulting optimization problem. We have developed a novel constrained optimization framework to address this issue, with the following highlights:

• The choice of constraints is guided by real-world imaging physics, leading to meaningful image reconstruction.

• Several existing formulations reduce to special cases of our framework, making the algorithm broadly applicable.

• Inspired by related work in color image demosaicing, we have also successfully extended our algorithm for color images via an image-adaptive framework.