arXiv subjects

Chandra Sekhar Seelamantula

Publications and source records attributed to Chandra Sekhar Seelamantula.

41 records · Page 3Linked to original sources

arXiv2015

Risk Estimation Without Using Stein's Lemma -- Application to Image Denoising

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly, optimal denoising techniques have been developed. One of the successful approaches for denoising relies on the notion of unbiased risk estimation, which enables one to obtain a useful substitute for the mean-square error. For the case of additive white Gaussian noise contamination, the risk estimation procedure relies on Stein's lemma. Sophisticated wavelet-based denoising techniques, which are essentially nonlinear, have been developed with the help of the lemma. We show that, for linear, shift-invariant denoisers, it is possible to obtain unbiased risk estimates of the mean-square error without using Stein's lemma. An interesting consequence of this development is that the unbiased risk estimator becomes agnostic to the statistical distribution of the noise. As a proof of principle, we show how the new methodology can be used to optimize the parameters of a simple Gaussian smoother. By locally adapting the parameters of the Gaussian smoother, we obtain a shift-variant smoother, which has a denoising performance (quantified by the improvement in peak signal-to-noise ratio (PSNR)) that is competitive to far more sophisticated methods reported in the literature. The proposed solution exhibits considerable parallelism, which we exploit in a Graphics Processing Unit (GPU) implementation.

cs.CV↗

arXiv2014

Directional Bilateral Filters

We propose a bilateral filter with a locally controlled domain kernel for directional edge-preserving smoothing. Traditional bilateral filters use a range kernel, which is responsible for edge preservation, and a fixed domain kernel that performs smoothing. Our intuition is that orientation and anisotropy of image structures should be incorporated into the domain kernel while smoothing. For this purpose, we employ an oriented Gaussian domain kernel locally controlled by a structure tensor. The oriented domain kernel combined with a range kernel forms the directional bilateral filter. The two kernels assist each other in effectively suppressing the influence of the outliers while smoothing. To find the optimal parameters of the directional bilateral filter, we propose the use of Stein's unbiased risk estimate (SURE). We test the capabilities of the kernels separately as well as together, first on synthetic images, and then on real endoscopic images. The directional bilateral filter has better denoising performance than the Gaussian bilateral filter at various noise levels in terms of peak signal-to-noise ratio (PSNR).

cs.CV↗

arXiv2014

A Risk Minimization Framework for Channel Estimation in OFDM Systems

We address the problem of channel estimation for cyclic-prefix (CP) Orthogonal Frequency Division Multiplexing (OFDM) systems. We model the channel as a vector of unknown deterministic constants and hence, do not require prior knowledge of the channel statistics. Since the mean-square error (MSE) is not computable in practice, in such a scenario, we propose a novel technique using Stein's lemma to obtain an unbiased estimate of the mean-square error, namely the Stein's unbiased risk estimate (SURE). We obtain an estimate of the channel from noisy observations using linear and nonlinear denoising functions, whose parameters are chosen to minimize SURE. Based on computer simulations, we show that using SURE-based channel estimate in equalization offers an improvement in signal-to-noise ratio of around 2.25 dB over the maximum-likelihood channel estimate, in practical channel scenarios, without assuming prior knowledge of channel statistics.

cs.IT↗

arXiv2014

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm for parallel dictionary learning. The fundamental idea behind the algorithm is to learn a sparse representation in two phases. In the first phase, the whole training dataset is partitioned into small non-overlapping subsets, and a dictionary is trained independently on each small database. In the second phase, the dictionaries are merged to form a global dictionary. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy operating on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques, that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

cs.LG↗

arXiv2013

Template-Based Active Contours

We develop a generalized active contour formalism for image segmentation based on shape templates. The shape template is subjected to a restricted affine transformation (RAT) in order to segment the object of interest. RAT allows for translation, rotation, and scaling, which give a total of five degrees of freedom. The proposed active contour comprises an inner and outer contour pair, which are closed and concentric. The active contour energy is a contrast function defined based on the intensities of pixels that lie inside the inner contour and those that lie in the annulus between the inner and outer contours. We show that the contrast energy functional is optimal under certain conditions. The optimal RAT parameters are computed by maximizing the contrast function using a gradient descent optimizer. We show that the calculations are made efficient through use of Green's theorem. The proposed formalism is capable of handling a variety of shapes because for a chosen template, optimization is carried with respect to the RAT parameters only. The proposed formalism is validated on multiple images to show robustness to Gaussian and Poisson noise, to initialization, and to partial loss of structure in the object to be segmented.

cs.CV↗