Recently, compressive sensing (CS) has emerged as a powerful tool for solving a class of inverse/underdetermined problems in computer vision and image processing. In this paper, we investigate the application of CS paradigms on single image super-resolution (SR) problems that are considered to be the most challenging in this class. In light of recent promising results, we propose novel tools for analyzing sparse representation-based inverse problems using redundant dictionary basis. Further, we provide novel results establishing tighter correspondence between SR and CS. As such, we gain insights into questions concerning regularizing the solution to the underdetermined problem, such as follows. 1) Is sparsity prior alone sufficient? 2) What is a good dictionary? 3) What is the practical implication of noncompliance with theoretical CS hypothesis? Unlike in other underdetermined problems that assume random down-projections, the low-resolution image formation model employed in CS-based SR is a deterministic down-projection that may not necessarily satisfy some critical assumptions of CS. We further investigate the impact of such projections in concern to the above questions.

Recently, Computer Vision problems like Face Recognition and Super-Resolution solved using sparse representation based methods with large dictionaries have shown state-of-the-art results. However such methods are computationally prohibitive for typical CPUs, especially for a large dictionary size. We present fast implementation of these methods by exploiting the massively parallel processing capabilities of a GPU within a CUDA framework, owing to its easy off-the-shelf availability and programmer friendliness. We provide details of system level design, memory management and implementation strategies. Further, we integrate the solution to the preferred scientific computational platform - MATLAB.

We propose a novel technique based on compressive sensing for expression-invariant face recognition. We view the different images of the same subject as an ensemble of intercorrelated signals and assume that changes due to variation in expressions are sparse with respect to the whole image. We exploit this sparsity using distributed compressive sensing theory, which enables us to grossly represent the training images of a given subject by only two feature images: one that captures the holistic (common) features of the face, and the other that captures the different expressions in all training samples. We show that a new test image of a subject can be fairly well approximated using only the two feature images from the same subject. Hence we can drastically reduce the storage space and operational dimensionality by keeping only these two feature images or their random measurements. Based on this, we design an efficient expression-invariant classifier. Furthermore, we show that substantially low dimensional versions of the training features, such as (i) ones extracted from critically-downsampled training images, or (ii) low-dimensional random projection of original feature images, still have sufficient information for good classification. Extensive experiments with publically-available databases show that, on average, our approach performs better than the state-of-the-art despite using only such super-compact feature representation.

In this paper, we propose a novel compressive imaging framework for color images. We first introduce an imaging architecture based on combining the existing single-pixel Compressive Sensing (CS) camera with a Bayer color filter, thereby enabling acquisition of compressive color measurements. Then we propose a novel CS reconstruction algorithm that employs joint sparsity models in simultaneously recovering the R, G, B channels from the compressive measurements. Experiments simulating the imaging and reconstruction procedures demonstrate the feasibility of the proposed idea and the superior quality in reconstruction.