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Prabhu Babu

Bio: Prabhu Babu is an academic researcher from Indian Institute of Technology Delhi. The author has contributed to research in topics: Computer science & Iterative method. The author has an hindex of 23, co-authored 91 publications receiving 3013 citations. Previous affiliations of Prabhu Babu include Indian Institutes of Technology & Uppsala University.


Papers
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TL;DR: An overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost and is elaborated by a wide range of applications in signal processing, communications, and machine learning.
Abstract: This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.

1,073 citations

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TL;DR: This paper presents a novel SParse Iterative Covariance-based Estimation approach, abbreviated as SPICE, to array processing, obtained by the minimization of a covariance matrix fitting criterion and is particularly useful in many- snapshot cases but can be used even in single-snapshot situations.
Abstract: This paper presents a novel SParse Iterative Covariance-based Estimation approach, abbreviated as SPICE, to array processing. The proposed approach is obtained by the minimization of a covariance matrix fitting criterion and is particularly useful in many-snapshot cases but can be used even in single-snapshot situations. SPICE has several unique features not shared by other sparse estimation methods: it has a simple and sound statistical foundation, it takes account of the noise in the data in a natural manner, it does not require the user to make any difficult selection of hyperparameters, and yet it has global convergence properties.

473 citations

Journal ArticleDOI
TL;DR: A new semiparametric/sparse method is introduced, called SPICE, which is computationally quite efficient, enjoys global convergence properties, can be readily used in the case of replicated measurements and, unlike most other sparse estimation methods, does not require any subtle choices of user parameters.
Abstract: Separable models occur frequently in spectral analysis, array processing, radar imaging and astronomy applications Statistical inference methods for these models can be categorized in three large classes: parametric, nonparametric (also called “dense”) and semiparametric (also called “sparse”) We begin by discussing the advantages and disadvantages of each class Then we go on to introduce a new semiparametric/sparse method called SPICE (a semiparametric/sparse iterative covariance-based estimation method) SPICE is computationally quite efficient, enjoys global convergence properties, can be readily used in the case of replicated measurements and, unlike most other sparse estimation methods, does not require any subtle choices of user parameters We illustrate the statistical performance of SPICE by means of a line-spectrum estimation study for irregularly sampled data

228 citations

Journal ArticleDOI
TL;DR: Numerical experiments show that the proposed algorithms outperform existing ones in terms of both the merit factors of designed sequences and the computational complexity.
Abstract: Unimodular sequences with low autocorrelation are desired in many applications, especially in radar systems and code-division multiple access (CDMA) communication systems. In this paper, we propose a new algorithm to design unimodular sequences with low autocorrelation via directly minimizing the integrated sidelobe level (ISL) of the autocorrelation. The algorithm is derived based on the general framework of majorization-minimization (MM) algorithms and thus shares the monotonic property of such methods, and two acceleration schemes have been considered to accelerate the overall convergence. In addition, the proposed algorithm can be implemented via fast Fourier transform (FFT) operations and thus is computationally efficient. Furthermore, after some modifications the algorithm can be adapted to incorporate spectral constraints, which makes the design more flexible. Numerical experiments show that the proposed algorithms outperform existing ones in terms of both the merit factors of designed sequences and the computational complexity.

227 citations

Journal ArticleDOI
TL;DR: Two algorithms based on the general majorization-minimization method are developed to tackle the WISL minimization problem with guaranteed convergence to a stationary point and can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval.
Abstract: Sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems. In this paper, we first consider the problem of minimizing the weighted integrated sidelobe level (WISL), which can be used to design sequences with impulse-like autocorrelation and a zero (or low) correlation zone. Two algorithms based on the general majorization-minimization method are developed to tackle the WISL minimization problem with guaranteed convergence to a stationary point. The proposed methods are then extended to optimize the $\ell_{p}$-norm of the autocorrelation sidelobes, which leads to a way to minimize the peak sidelobe level (PSL) criterion. All the proposed algorithms can be implemented via the fast Fourier transform (FFT) and thus are computationally efficient. An acceleration scheme is considered to further accelerate the algorithms. Numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller PSL compared with some well known analytical sequences.

208 citations


Cited by
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[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Christopher M. Bishop1
01 Jan 2006
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements subject to individual link budget guarantees for the mobile users.
Abstract: The adoption of a reconfigurable intelligent surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to 300% higher energy efficiency in comparison with the use of regular multi-antenna amplify-and-forward relaying.

1,967 citations