Arindama Singh

Bio: Arindama Singh is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Image restoration & Singular perturbation. The author has an hindex of 8, co-authored 37 publications receiving 202 citations. Previous affiliations of Arindama Singh include University UCINF & Indian Institute of Technology Kanpur.

Ringing Artifact Reduction in Blind Image Deblurring and Denoising Problems by Regularization Methods

Abstract: Image deblurring and denoising are the main steps in early vision problems. A common problem in deblurring is the ringing artifacts created by trying to restore the unknown point spread function (PSF). The random noise present makes this task even harder. Variational blind deconvolution methods add a smoothness term for the PSF as well as for the unknown image. These methods can amplify the outliers correspond to noisy pixels. To remedy these problems we propose the addition of a first order reaction term which penalizes the deviation in gradients. This reduces the ringing artifact in blind image deconvolution. Numerical results show the effectiveness of this additional term in various blind and semi-blind image deblurring and denoising problems.

Edge Detectors Based Anisotropic Diffusion for Enhancement of Digital Images

Abstract: Using the edge detection techniques we propose a new enhancement scheme for noisy digital images. This uses inhomogeneous anisotropic diffusion scheme via the edge indicator provided by well known edge detection methods. Addition of a fidelity term facilitates the proposed scheme to remove the noise while preserving edges. This method is general in the sense that it can be incorporated into any of the nonlinear anisotropic diffusion methods. Numerical results show the promise of this hybrid technique on real and noisy images.

Prime implicants of first order formulas via transversal clauses

Abstract: Knowledge compilation techniques are usually applied for propositional knowledge bases. In this article, an extension of the notion of prime implicants of a knowledge base using first order formulas in Skolem conjunctive normal form is suggested. The method of transversal clauses used earlier for computing prime implicants of a propositional formula in conjuctive normal form is adopted to the first order case via substitutions. Partial correctness of the algorithm is proved. The algorithm is adopted heuristically for computing approximate prime implicants.

Theory of Functions

Abstract: THE criticism on the passage quoted from p. 3 of the book by Profs. Harkness and Morley (NATURE, February 23, p. 347) turns on the fact that, in dealing with number divorced from measurement, the authors have used the phrase “an infinity of objects” without an explicit statement of its meaning. I am not sure that I understand the passage in their letter which refers to this point; but it seems to me to imply that the distinction between “finite” and “infinite” is one which does not require definition. This is not the only accepted view. It is not, for instance, the view taken in Herr Dedekind's book, “Was sind und was sollen die Zahlen.” As regards the opening sentences of Chapter xv., the authors have apparently misunderstood the point of my objection. With the usually received definition of convergence of an infinite product, Π(1-αn), if convergent, is different from zero. So far as the passage quoted goes, Π(1-αn) might be zero; and it is therefore not shown to be convergent, if the usual definition of convergence be assumed. As to the passage quoted from p. 232, I must express to the authors my regret for having overlooked the fact that the particular rearrangement, there made use of, has been fully justified in Chapter viii. Whether Log x is or is not, at the beginning of Chapter iv., defined by means of a string and a cone, will be obvious to any one who will read the whole passage (p. 46, line 16, to p. 47, line 9) leading up to the definition.

A Basis for a Mathematical Theory of Computation

Abstract: Publisher Summary This chapter discusses the mathematical theory of computation. Computation essentially explores how machines can be made to carry out intellectual processes. Any intellectual process that can be carried out mechanically can be performed by a general purpose digital computer. There are three established directions of mathematical research that are relevant to the science of computation—namely, numerical analysis, theory of computability, and theory of finite automata. The chapter explores what practical results can be expected from a suitable mathematical theory. Further, the chapter presents several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms. A few mathematical results about the properties of the formalisms are also presented.

Singular perturbations and time scales in control theory and applications: An overview

Abstract: This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 (the last such overviews were provided by [231, 371]). Due to the limitations on space, this is in way intended to be an exhaustive survey on the topic.