S.D. Babacan

Bio: S.D. Babacan is an academic researcher from Northwestern University. The author has contributed to research in topics: Image restoration & Estimation theory. The author has an hindex of 7, co-authored 9 publications receiving 1175 citations.

Bayesian Compressive Sensing Using Laplace Priors

Abstract: In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

Variational Bayesian Blind Deconvolution Using a Total Variation Prior

Abstract: In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.

Parameter Estimation in TV Image Restoration Using Variational Distribution Approximation

Abstract: In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyperparameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyperparameters and clearly outperform existing methods when additional information is included.

Total variation super resolution using a variational approach

Abstract: In this paper we propose a novel algorithm for super resolution based on total variation prior and variational distribution approximations. We formulate the problem using a hierarchical Bayesian model where the reconstructed high resolution image and the model parameters are estimated simultaneously from the low resolution observations. The algorithm resulting from this formulation utilizes variational inference and provides approximations to the posterior distributions of the latent variables. Due to the simultaneous parameter estimation, the algorithm is fully automated so parameter tuning is not required. Experimental results show that the proposed approach outperforms some of the state-of-the-art super resolution algorithms.

Bayesian Blind Deconvolution From Differently Exposed Image Pairs

Abstract: Photographs acquired under low-lighting conditions require long exposure times and therefore exhibit significant blurring due to the shaking of the camera. Using shorter exposure times results in sharper images but with a very high level of noise. In this paper, we address the problem of utilizing two such images in order to obtain an estimate of the original scene and present a novel blind deconvolution algorithm for solving it. We formulate the problem in a hierarchical Bayesian framework by utilizing prior knowledge on the unknown image and blur, and also on the dependency between the two observed images. By incorporating a fully Bayesian analysis, the developed algorithm estimates all necessary model parameters along with the unknown image and blur, such that no user-intervention is needed. Moreover, we employ a variational Bayesian inference procedure, which allows for the statistical compensation of errors occurring at different stages of the restoration, and also provides uncertainties of the estimates. Experimental results with synthetic and real images demonstrate that the proposed method provides very high quality restoration results and compares favorably to existing methods even though no user supervision is needed.

Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

Abstract: As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of the l1-norm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a precollected dataset of example image patches, and then, for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image nonlocal self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.

The variational approximation for Bayesian inference

Abstract: The influence of this Thomas Bayes' work was immense. It was from here that "Bayesian" ideas first spread through the mathematical world, as Bayes's own article was ignored until 1780 and played no important role in scientific debate until the 20th century. It was also this article of Laplace's that introduced the mathematical techniques for the asymptotic analysis of posterior distributions that are still employed today. And it was here that the earliest example of optimum estimation can be found, the derivation and characterization of an estimator that minimized a particular measure of posterior expected loss. After more than two centuries, we mathematicians, statisticians cannot only recognize our roots in this masterpiece of our science, we can still learn from it.

Bayesian Compressive Sensing Using Laplace Priors

Abstract: In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

Image Analysis and Recognition

Abstract: In this paper, we investigate applying semi-supervised clustering to audio-visual emotion analysis, a complex problem that is traditionally solved using supervised methods. We propose an extension to the semi-supervised aligned cluster analysis algorithm (SSACA), a temporal clustering algorithm that incorporates pairwise constraints in the form of must-link and cannot-link. We incorporate an exhaustive constraint propagation mechanism to further improve the clustering process. To validate the proposed method, we apply it to emotion analysis on a multimodal naturalistic emotion database. Results show substantial improvements compared to the original aligned clustering analysis algorithm (ACA) and to our previously proposed semi-supervised approach.

Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference

Abstract: Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid.