We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

Reconstructing complex brain source activity at a high spatiotemporal resolution from magnetoencephalography (MEG) or electroencephalography (EEG) remains a challenging problem. Adaptive beamformers are routinely deployed for this imaging domain using the sample data covariance. However adaptive beamformers have long been hindered by 1) high degree of correlation between multiple brain sources, and 2) interference and noise embedded in sensor measurements. This study develops a novel framework for minimum variance adaptive beamformers that uses a model data covariance learned from data using a sparse Bayesian learning algorithm (SBL-BF). The learned model data covariance effectively removes influence from correlated brain sources and is robust to noise and interference without the need for baseline measurements. A multiresolution framework for model data covariance computation and parallelization of the beamformer implementation enables efficient high-resolution reconstruction images. Results with both simulations and real datasets indicate that multiple highly correlated sources can be accurately reconstructed, and that interference and noise can be sufficiently suppressed. Reconstructions at 2-2.5mm resolution ( ∼ 150K voxels) are possible with efficient run times of 1-3 minutes. This novel adaptive beamforming algorithm significantly outperforms the state-of-the-art benchmarks. Therefore, SBL-BF provides an effective framework for efficiently reconstructing multiple correlated brain sources with high resolution and robustness to interference and noise.

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.

In the classical bilateral filter, a range kernel is used together with a spatial kernel for smoothing out fine details while simultaneously preserving edges. More recently, it has been demonstrated that even coarse textures can be smoothed using joint bilateral filtering. In this paper, we demonstrate that the superior texture filtering results can be obtained by adapting the spatial kernel at each pixel. To the best of our knowledge, spatial adaptation (of the bilateral filter) has not been explored for texture smoothing. The rationale behind adapting the spatial kernel is that one cannot smooth beyond a certain level using a fixed spatial kernel, no matter how we manipulate the range kernel. In fact, we should simply aggregate more pixels using a sufficiently wide spatial kernel to locally enhance the smoothing. Based on this reasoning, we propose to use the classical bilateral filter for texture smoothing, where we adapt the width of the spatial kernel at each pixel. We describe a simple and efficient gradient-based rule for the latter task. The attractive aspect is that we are able to develop a fast algorithm that can accelerate the computations by an order without visibly compromising the filtering quality. We demonstrate that our method outperforms classical bilateral filtering, joint bilateral filtering, and other filtering methods, and is competitive with the optimization methods. We also present some applications of texture smoothing using the proposed method.

We consider the problem of enhancing images captured under low-light conditions. Several variational and filtering based solutions have been proposed for this problem that are based on the retinex model. The idea in retinex is to first estimate the illumination and reflectance from the observed image, enhance the illumination, and then combine it with the reflectance to get the rectified image. A variant of bilateral filtering, called bright-pass bilateral filtering (BPBF), can be used for illumination estimation. However, BPBF is computation intensive and takes up a significant amount of the processing time. Motivated by recent work, we propose a Fourier approximation of BPBF that can accelerate the filtering (by an order) without loss in visual quality. Experimental results demonstrate that our algorithm is sufficiently fast and can effectively enhance low-light images. In particular, our proposal is competitive with recent algorithms in terms of visual perception and quality metrics.

Image filtering is a fundamental preprocessing task in computer vision and image processing. While the dominant applications of kernel filtering are enhancement and denoising, it can also be used as a powerful regularizer for image reconstruction. In general, the brute-force implementations of kernel filtering is prohibitively expensive. They are often too slow for real-time applications. In the first half of the thesis, we propose fast algorithms for bilateral filtering (BLF) and nonlocal means (NLM). In particular, we demonstrate that by using the Fourier approximation of the underlying kernel, we can obtain state-of-the-art fast algorithms for BLF of grayscale images. We next extend the idea for fast filtering of color images, which involves the approximation of a three-dimensional kernel. We next propose a fast separable formulation for NLM of grayscale images. In the second half of the dissertation, we turn to some applications of kernel filtering. We introduce a scale-adaptive variant of BLF that is used for suppressing fine textures in images. We develop a fast implementation of a symmetrized variant of NLM that is used for regularization (i.e., as a prior) within the plug-and-play framework for image restoration. The core idea can be extended to other forms of kernel filtering.

Guided image filter (GIF) is an efficient edge-preserving image filter which has numerous applications in image processing. The filtered output of GIF is locally a linear transform of a guide image, which can be the input image itself or a different image. The key feature of GIF is that it does not suffer from gradient reversal artifacts. In this article, we extend the concept of guided image filtering to the context of hyperspectral imaging. We consider a new (linear) model to perform the joint guided filtering of all the spectral components at a time at each pixel. Our proposed technique involves computation of matrix-inversion just once; regardless of the number of spectral bands of the image to be filtered. Thus, bypassing the redundant computations in the original proposal of GIF, we introduce a fast variant of guided filtering algorithm. The proposed algorithm produces exactly same filtered output as GIF. Experimental results demonstrate the effectiveness of the proposed variant of GIF. Finally, we extend our filter to a variety of hyperspectral imaging applications - edge preserving smoothing, detail enhancement and denoising.

We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic range of the input image. The error from such an approximation depends on the period, the number of sinusoids, and the coefficient of each sinusoid. For a fixed period, we recently proposed a model for optimizing the coefficients using least squares fitting. Following the compressive bilateral filter (CBF), we demonstrate that the approximation can be improved by taking the period into account during the optimization. The accuracy of the resulting filtering is found to be at least as good as the CBF, but significantly better for certain cases. The proposed approximation can also be used for non-Gaussian kernels, and it comes with guarantees on the filtering accuracy.

This paper presents the results of a within-subject longitudinal evaluation on Inscript keyboard, which is the national standard layout for Indian scripts. We studied the practical upper bound speed and accuracy as well as the effect of practice. Through longitudinal transcription task of 400 repeated attempts, we observed typing speeds for highly experienced users consistently peak close to 120 cpm i.e. 2.5 times that of fastest speeds reported in literature. Our analysis compared the lower bound times for Tap, Tap+LongPress and Shift+Tap, the three text input mechanisms in this keyboard. Among the two alternative methods, our findings established Tap+LongPress method to be faster than Shift+Tap method and almost equally accurate. Also, we derived a model which explains the influence of corrected errors and number of practice attempts on the typing speed.

We consider the task of removing the effect of camera shake during a long exposure. Technically, this is a blind deconvolution problem in which both the image and the motion blur have to be jointly inferred. Several algorithms have been proposed till date for removing camera shake that work with one or more images. However, most of these algorithms are computationally expensive and hence cannot be used in real-time. In this work, we propose a simple and cheap algorithm that can effectively recover the original sharp image from multiple burst images (captured using the burst modality of modern cameras). In summary, we pick selected images from the burst (using ideas from lucky imaging), which are then aggregated using the discrete cosine transform (similar to the idea of Fourier burst accumulation). We present some preliminary results and comparisons to demonstrate the effectiveness of the proposal.

Gesture based interaction and its recognition has been an area of active research with the growing popularity of wearables. We here propose an approach to detect fine-grained finger and palm motions using inertial sensors in a commercial smartwatch. A user specific SVM based classifier is developed for 7 microgestures with a classification accuracy of 94.4%. We extend this to a user adaptive model by including a few representative instances of a new user and achieve a classification accuracy of 91.7%. Further, we are able to differentiate between variations of a microgesture using three fundamental building blocks - distance, speed and orientation. A novel regression based approach is presented to predict the distance parameter. The idea is demonstrated on a swipe gesture with an error of 14%.

This paper describes our experience in customizing the software design of an existing smartphone product for a localized market. This was targeted as a low-cost smartphone for the masses in the rapidly emerging market of India, and the sub-continent region. The earlier commercial version of the product was already designed with enough user research and R&D efforts for few other markets. The challenge was to improve the existing features to make the next product version more appealing to the users. Due to the pressing business demand for short release time, we adopted the 'Localization' strategy based on user-centered design process, wherein user research was conducted alongside the design activities. This paper shares our experiences and learnings from the challenges we encountered. We share several instances of how user stories were inferred, converted into localization concepts and finally refined into commercially viable solutions.

In non‐local means (NLM), each pixel is denoised by performing a weighted averaging of its neighbouring pixels, where the weights are computed using image patches. The authors demonstrate that the denoising performance of NLM can be improved by pruning the neighbouring pixels, namely, by rejecting neighbouring pixels whose weights are below a certain threshold . While pruning can potentially reduce pixel averaging in uniform‐intensity regions, they demonstrate that there is generally an overall improvement in the denoising performance. In particular, the improvement comes from pixels situated close to edges and corners. The success of the proposed method strongly depends on the choice of the global threshold , which in turn depends on the noise level and the image characteristics. They show how Stein's unbiased estimator of the mean‐squared error can be used to optimally tune , at a marginal computational overhead. They present some representative denoising results to demonstrate the superior performance of the proposed method over NLM and its variants.

In this paper, we consider a natural extension of the edge-preserving bilateral filter for vector-valued images. The direct computation of this non-linear filter is slow in practice. We demonstrate how a fast algorithm can be obtained by first approximating the Gaussian kernel of the bilateral filter using raised-cosines, and then using Monte Carlo sampling. We present simulation results on color images to demonstrate the accuracy of the algorithm and the speedup over the direct implementation.

As part of an ongoing standardization effort, we were asked to evaluate Marathi text input mechanisms on smartphones. We undertook a between-subject longitudinal evaluation of four existing keyboards with 153 novice users who participated for 31 sessions each, spread over 3--4 weeks. In this paper, we present the empirical results of the performance of these keyboards and discuss them with respect to their designs. We found that keyboards with logical layouts performed marginally better than keyboards with partially frequency-based layouts. Results also showed that users performed poorly on keyboards that have word prediction features in comparison with keyboards that don't have prediction features while typing Marathi. We speculate that this difference in performance is related to a "cognitive toll" that the users pay to use word prediction. We identify several directions for future research.

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

Our experiences with industrial software development projects have often revealed that requirements change even after their formal approvals. Although the requirements are never stable, proactive identification of potentially changeable or deferrable requirements, and estimation of their impacts early in a project can be useful in minimizing the risks and cost overruns. In practice, the decisions to change or defer certain requirements are based on experience, and are mostly driven by business needs and product release timelines. There are no techniques available which could foresee such changes early in the project. In this work, we perform exploratory analysis of the requirement artifacts from thirty three industrial software development projects and shared our observations on different requirement change attributes. Through empirical analysis, we evolve the relative weights of each of these attributes in terms of their impacts on the project schedule and effort. Based on the analysis, a model is developed to predict the impact due to requirement changes and it is validated. This model can be used to develop a requirement change decision support tool to assist decision makers.