Simultaneous Super-Resolution and Denoising of Images

Most super-resolution algorithms are sensitive to the presence of noise, since SR algorithms try to preserve the high frequency content of the image. Using a denoising algorithm as a preprocessing step is also not advantageous since denoising algorithms tend to remove the useful high frequency textural content of the image, which restricts the performance of the subsequent SR algorithm.

Since super-resolved images are typically starved of high frequency content, and since denoising algorithms typically discard excess high frequency content, we propose here an algorithm that attempts to utilize the high frequency content discarded by denoising algorithms, for the benefit of super-resolution.

Abhishek Singh, Fatih Porikli and Narendra Ahuja. Super-Resolving Noisy ImagesIEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014)

Abhishek Singh, Fatih Porikli and Narendra Ahuja. On Simultaneous Denoising and Super-Resolution of Natural Images. IEEE Transactions on Pattern Analysis and Machine Intelligence. (submitted)

Transform Domain Methods for Single Image Super-Resolution

Super-resolution of a single image is a highly ill-posed problem since the number of high resolution pixels to be be estimated far exceeds the number of low resolution pixels available. Therefore, appropriate regularization or priors play an important role in the quality of results. 

In this line of work, we propose a family of methods for learning transform domain priors for the single-image super-resolution problem. Our algorithms are able to better synthesize high frequency textural details as compared to the state-of-the-art.

Abhishek Singh and Narendra Ahuja. Super-Resolution Using Sub-Band Self-Similarity. In Asian Conference on Computer Vision (ACCV 2014). 

Abhishek Singh and Narendra Ahuja. Sub-Band Energy Constraints for Self-Similarity Based Super-Resolution. In International Conference on Pattern Recognition (ICPR 2014). 

Structure Based Super-Resolution

A popular choice of priors for the super-resolution problem are edge based priors that impose additional constraints on the gradient field of the image.

In this line of work, we propose an edge based prior that overcomes some of the drawbacks of classical gradient domain methods. Instead of using arbitrarily chosen gradient filters for edge extraction, we propose to extract structural information using the 'Ramp Transform' of the image, that quantifies structure in a bottom-up, parameter free manner. Conventional gradient filters on the other hand entail strict assumptions on the scale and orientation of the structures to be detected.

We show that our ramp based structural prior generally yields results that are sharper, and have significantly less ringing artifacts as compared to related algorithms.

Abhishek Singh and Narendra Ahuja. Structure Based Super Resolution. Computer Vision and Image Understanding. (submitted)

Abhishek Singh and Narendra Ahuja. Single Image Super-Resolution Using Adaptive Domain Transformation. In IEEE International Conference on Image Processing (ICIP 2013).

Robust, Large Scale Registration and Alignment Using Quadratic Mutual Information*

Mutual Information is the preferred cost function for applications like multimodal image registration, due to its ability to handle non-linear relationships between intensities of the images. However, computation of the classical measure of mutual information is difficult. We propose to overcome these computational challenges in multimodal image registration by using quadratic mutual information (QMI) in place of classical mutual information. We show that the sample estimator for QMI has a lower variance as compared to that of the classical measure, and yields smoother optimization cost functions. Faster optimization machinery like stochastic gradient descent are much more effective over this new cost function. The use of QMI also increases the domain of convergence of misaligned images. 

Abhishek Singh and Narendra Ahuja. On Stochastic Gradient Descent and Quadratic Mutual Information for Image Registration. In IEEE International Conference on Image Processing (ICIP 2013).

Abhishek Singh, Ying Zhu and Christophe Chefd'hotel. A Variational Approach for Optimizing Quadratic Mutual Information for Medical Image Registration. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2012).

*This work was awarded the Computational Science and Engineering Fellowship for interdisciplinary and computation-oriented research at the University of Illinois, 2012.

Exploiting Image Structure For Optical Flow Estimation

Classical optical flow objective functions consist of a data term that enforces brightness constancy, and a spatial smoothing term that encourages smooth flow fields. The use of structural information from images has been conventionally used for designing more robust regularizers, to prevent oversmoothing motion discontinuities. 

In this line of work, we are looking at exploiting image structure in a more detailed manner. We go beyond conventionally used derivative filters and use the 'ramp transform' of images to obtain structural information. We not only propose better regularization terms using this structural information, but also show incorporate it in the data term to improve results.

Abhishek Singh and Narendra Ahuja. Exploiting Ramp Structures for Improving Optical Flow Estimation. In International Conference on Pattern Recognition (ICPR 2012).

Linear Descriptors for Region Based Matching

Matching images based on regions/segments has several advantages over sparse keypoint and interest point based matching, due to the higher descriptive power of regions. We are developing linear descriptors for image segments that enable the region based matching problem to be formulated as a simple convex optimization problem. The proposed framework provides a way of overcoming problems caused by poor repeatability of segmentation algorithms, in the matching procedure. Robustness to occlusions is also achieved by adding a simple sparsity constraint in the optimization objective. We propose to apply the framework for joint segmentation and tracking of objects under clutter and occlusions in video sequences. We also propose to extend the framework to shape based matching for category level recognition tasks.

The C-Loss Function for Pattern Classification

This work presents a margin based loss function for classification inspired by a newly proposed similarity measure called Correntropy. The C-Loss function essentially behaves like square loss function for samples that are correctly classified and are well within the decision boundary, and becomes insensitive to outliers and 'confusers' that are difficult to classifiy. The resulting discriminant function obtained by optimizing the C-Loss function using a neural network is more robust to overfitting and to outliers, and is less sensitive to system parameters as compared to conventional loss function(s), even on prolonged training. 

Abhishek Singh and Jose Principe. The C-Loss Function for Pattern Classification. Pattern Recognition, 2014.

Abhishek Singh and Jose Principe. A Loss Function for Classification Based on a Robust Similarity Metric. In IEEE World Congress on Computational Intelligence (WCCI 2010): International Joint Conference on Neural Networks (IJCNN 2010).

Supervised Learning by minimizing error entropy

Minimizing the entropy of the error has been shown to be an effective principle for supervised learning. Training algorithms which optimize entropy involve choosing a kernel size for their sample estimators. In this work we present an algorithm for learning this kernel width parameter online, from data.  The kernel size essentially dictates the nature of the cost function over which the system parameters adapt. Our simulations show that having an adaptive kernel width results in faster convergence of parameters, while training linear and non-linear mappers using the minimum error entropy principle. 

Abhishek Singh and Jose Principe. Information Theoretic Learning with Adaptive Kernels. Signal Processing (Elsevier), vol. 91, issue 2, pp. 203-213, Feb 2011. 
Listed among Top 25 Hottest Articles in Signal Processing

Abhishek Singh and Jose Principe. Kernel Width Adaptation in Information Theoretic Cost Functions. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010).

Robust Regression and Adaptive Filtering Using a Novel Similarity Metric

Correntropy has been recently defined as a localized similarity measure between two random variables, exploiting higher order moments of the data. This work presents the use of Correntropy as a cost function for minimizing the error between the desired signal and the output of an adaptive filter, in order to train the filter weights. We have shown that this cost function has the computational simplicity of the popular LMS algorithm, along with the robustness that is obtained by using higher order moments for error minimization. We apply this technique for system identification and noise cancellation for speech signals.

Abhishek Singh and Jose C. Principe. Using Correntropy as a Cost Function in Linear Adaptive Filters. In IEEE  International Joint Conference on Neural Networks (IJCNN 2009).

Abhishek Singh and Jose C. Principe. A Closed Form Recursive Solution for Maximum Correntropy Training. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010).

Background Subtraction in Videos Using Resampling Based Bayesian Learning

This work proposes the use of a sampling-resampling based Bayesian learning technique for learning background and foreground processes in a still camera video. The proposed method is advantageous in the sense that it does not require elaborate numerical integration methods for performing Bayesian learning, and the posteriors are learnt via a resampling based approach. The background subtraction application achieves higher sensitivity and lower false alarm rates as compared to popular existing techniques.

Padmini Jaikumar, Abhishek Singh and Suman K. Mitra. Background Subtraction in Videos Using Bayesian Learning with Motion Information. In British Machine Vision Conference (BMVC 2008)

Abhishek Singh, Padmini Jaikumar and Suman K. Mitra. A Sampling-Resampling Based Bayesian Learning Approach for Object Tracking. In Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP 2008)
Best Paper Award in IEEE Region 10 (Asia-Pacific) Student Paper Contest 2008

Resampling based Bayesian Learning for segmenting satellite images

This work presents a technique for segmentation of satellite images using a `sampling-resampling' based Bayesian learning method. The multi-band pixel values of the satellite image are grouped into clusters that are learnt using the resampling based Bayesian approach. Bayesian estimates of model parameters are better regularized, since Bayesian learning yields a complete posterior distribution of model parameters, and not just singleton estimates that are otherwise obtained using frequentist techniques like Maximum Likelihood.

Abhishek Singh, Padmini Jaikumar and Suman K. Mitra. Segmentation of Remotely Sensed Images Using Resampling Based Bayesian Learning. In Journal of Pattern Recognition Research, vol. 5, no. 1, pp. 119-130, 2010.  

Abhishek Singh, Padmini Jaikumar and Suman K. Mitra. A Bayesian Learning Approach for Clustering of Satellite Images. In Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP 2008).