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This paper investigates the hybrid source localization problem using the four radio measurements - time of arrival (TOA), time difference of arrival (TDOA), received signal strength (RSS) and angle of arrival (AOA). First, after invoking tractable approximations in the RSS and AOA models, the maximum likelihood estimation (MLE) problem for the hybrid TOA-TDOA-RSS-AOA data model is derived. Then, in the MLE, which has the least-squares objective, weights determined using the range-based characteristics of the four heterogeneous measurements, are introduced. The resultant weighted least-squares problem obtained, which is non-smooth and non-convex, is solved using the principle of the majorization-minimization (MM), leading to an iterative algorithm that has a guaranteed convergence. The key feature of the proposed method is that it provides a unified framework where localization using any possible merger out of these four measurements can be implemented as per the requirement/application. Extensive numerical simulations are conducted to study the estimation efficiency of the proposed method. The proposed method employing all four measurements is compared against a conventionally used method and also against the proposed method employing only limited combinations of the four measurements. The results obtained indicate that the hybrid localization model improves the localization accuracy compared to the heterogeneous measurements. The integration of different measurements also yields good accuracy in the presence of non-line of sight (NLOS) errors.

In this paper, we consider the problem of $\ell_{p}$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. The problem, even though convex, does not enjoy a closed-form solution. The state-of-the-art algorithms are iterative but suffer from convergence issues, i.e., they either diverge for p>3 or the convergence to the optimal solution is sensitive to the initialization of the algorithm. Also, these algorithms are not generalizable to every possible value of $p$. In this paper, we propose an iterative algorithm : Parallel IteRative AlgOrithM for $\ell_{P}$ norm regression via MajorizaTion Minimization (PROMPT) based on the principle of Majorization Minimization and prove that the proposed algorithm is monotonic and converges to the optimal solution of the problem for any value of $p$. The proposed algorithm can also parallelly update each element of the regression variable, which helps to handle large scale data efficiently, a common scenario in this era of data explosion. Subsequently, we show that the proposed algorithm can also be applied for the graph based semi-supervised learning problem. We show through numerical simulations that the proposed algorithm converges to the optimal solution for any random initialization and also performs better than the state-of-the-art algorithms in terms of speed of convergence. We also evaluate the performance of the proposed algorithm using simulated and real data for the graph based semi-supervised learning problem.

An Equiangular tight frame (ETF) - also known as the Welch-bound-equality sequences - consists of a sequence of unit norm vectors whose absolute inner product is identical and minimal. Due to this unique property, these frames are preferred in different applications such as in constructing sensing matrices for compressed sensing systems, robust transmission, and quantum computing. Construction of ETFs involves solving a challenging non-convex minimax optimization problem, and only a few methods were successful in constructing them, albeit only for smaller dimensions. In this paper, we propose an iterative algorithm named TEchnique to devise Large dimensional Equiangular Tight-frames (TELET-frames) based on the majorization minimization (MM) procedure - in which we design and minimize a tight upper bound for the ETF cost function at every iteration. Since TELET is designed using the MM approach, it inherits useful properties of MM such as monotonicity and guaranteed convergence to a stationary point. Subsequently, we use the derived frames to construct optimized sensing matrix for compressed sensing systems. In the numerical simulations, we show that the proposed algorithm can generate complex and real frames (in the order of hundreds) with very low mutual coherence value when compared to the state-of-the-art algorithm, with a slight increase in computational cost. Experiments using synthetic data and real images reveal that the optimized sensing matrix obtained through the frames constructed by TELET performs better, in terms of image reconstruction accuracy, than the sensing matrix constructed using state-of-the-art methods.

Constant modulus sequence set with low peak side-lobe level is a necessity for enhancing the performance of modern active sensing systems like Multiple Input Multiple Output (MIMO) RADARs. In this paper, we consider the problem of designing a constant modulus sequence set by minimizing the peak side-lobe level, which can be cast as a non-convex minimax problem, and propose a Majorization-Minimization technique based iterative monotonic algorithm. The iterative steps of our algorithm are computationally not very demanding and they can be efficiently implemented via Fast Fourier Transform (FFT) operations. We also establish the convergence of our proposed algorithm and discuss the computational and space complexities of the algorithm. Finally, through numerical simulations, we illustrate the performance of our method with the state-of-the-art methods. To highlight the potential of our approach, we evaluate the performance of the sequence set designed via our approach in the context of probing sequence set design for MIMO RADAR angle-range imaging application and show results exhibiting good performance of our method when compared with other commonly used sequence set design approaches.

Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any two classes by optimizing over the likelihood objective. With the advent of big data, the inundation of data has resulted in large dimensional weight vector and has also given rise to a huge number of classes, which makes the classical methods applicable for model estimation not computationally viable. To handle this issue, we here propose a parallel iterative algorithm: Parallel Iterative Algorithm for MultiNomial LOgistic Regression (PIANO) which is based on the Majorization Minimization procedure, and can parallely update each element of the weight vectors. Further, we also show that PIANO can be easily extended to solve the Sparse Multinomial Logistic Regression problem - an extensively studied problem because of its attractive feature selection property. In particular, we work out the extension of PIANO to solve the Sparse Multinomial Logistic Regression problem with l1 and l0 regularizations. We also prove that PIANO converges to a stationary point of the Multinomial and the Sparse Multinomial Logistic Regression problems. Simulations were conducted to compare PIANO with the existing methods, and it was found that the proposed algorithm performs better than the existing methods in terms of speed of convergence.

Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful interpretation of the data. Thus, nonnegative matrix factorization has an edge over the other decomposition techniques. In this paper, we propose two novel iterative algorithms based on Majorization Minimization (MM)-in which we formulate a novel upper bound and minimize it to get a closed form solution at every iteration. Since the algorithms are based on MM, it is ensured that the proposed methods will be monotonic. The proposed algorithms differ in the updating approach of the two nonnegative matrices. The first algorithm-Iterative Nonnegative Matrix Factorization (INOM) sequentially updates the two nonnegative matrices while the second algorithm-Parallel Iterative Nonnegative Matrix Factorization (PARINOM) parallely updates them. We also prove that the proposed algorithms converge to the stationary point of the problem. Simulations were conducted to compare the proposed methods with the existing ones and was found that the proposed algorithms performs better than the existing ones in terms of computational speed and convergence. KeyWords: Nonnegative matrix factorization, Majorization Minimization, Big Data, Parallel, Multiplicative Update

We consider the problem of localizing the source using range and range-difference measurements. Both the problems are non-convex and non-smooth and are challenging to solve. In this paper, we develop an iterative algorithm - Source Localization Via an Iterative technique (SOLVIT) to localize the source using all the distinct range-difference measurements, i.e., without choosing a reference sensor. SOLVIT is based on the Majorization Minimization approach - in which a novel upper bound is formulated and minimized to get a closed-form solution at every iteration. We also solve the source localization problem based on range measurements and rederive the Standard Fixed Point algorithm using the Majorization Minimization approach. By doing so, we show a less intricate way to prove the convergence of the Standard Fixed Point algorithm. Numerical simulations and experiments in an anechoic chamber confirm that SOLVIT performs better than existing reference-based and reference-free methods in terms of source positioning accuracy.