AZHAR Y. TANTARY
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Hi! Welcome to my website. I am a native of the picturesque Jammu and Kashmir, India. I have a PhD in Applied Mathematics with specialization in Wavelets and Signal Processing.
I have served as a Postdoctoral Fellow at the Department of Computer Science and Engineering (CSE), Indian Institute of Technology (IIT) Bombay, from May 2023 to May 2025. Presently, I am working as a Sr. Project Engineer at CSE, IIT Bombay.
Primary Discipline: Mathematics
Secondary Discipline: Computer Science (Signal and Image Processing)
You can contact me at: aytku92@gmail.com or azharyousuf@iitb.ac.in
Office Address: Room No. 121, Computing Complex (CC) Building, Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai-400076, Mumbai, Maharashtra, India
Research Interests
Research Interests
My research interests broadly lie within Applied Harmonic Analysis, specifically the theory of Wavelets, and I am particularly interested in Signal Processing. My mathematical background offers me a very transpiring and enriching experience while diving into different research problems within the realm of signal and image processing.
Nevertheless, my long-term research interests broadly encompass the intertwined fields of AI/ML and signal processing. Very recently, neural networks have proved to be extremely useful in a multitude of signal and image processing tasks, however, most of such methods lack explainability and work like a black-box. My goal is to work on the proper theoretical performance analysis of neural networks for the inverse problems such as image reconstruction from noisy, compressive measurements to ultimately develop mathematically grounded learning frameworks that are reliable in high-dimensional and data-limited regimes.
What's New
What's New
I will be joining as a Research Staff Member with Transnational AI for Networked Universal Healthcare (TANUH) at the Indian Institute of Science (IISc), Bengaluru.
Our work "Hyper-Pyramid-Adapted Shearlet Transform with Application to Compressive Level Set estimation" is published in the journal Inverse Problems.
The paper "Shearlets: A Good Sparsifying System for Compressive Reconstruction," is accepted for the 10-th International Conference on Computer Vision and Image Processing (CVIP) to be held at IIT Ropar, Punjab, India from December 10-13, 2025.
Our latest work concerning "Analytical Expressions for KL Transforms of Some Random Processes in 1D and 2D" is in preparation for journal submission.
Selected Journal Articles (Best 5)
Selected Journal Articles (Best 5)
Azhar Yousuf, Agnipratim Nag, Vineet Ghule and Ajit Rajwade, Hyper-Pyramid-Adapted Shearlet Transform with Application to Compressive Level Set Estimation, Inverse Problems, 41(10), Article ID 105012 (2025). (IOP Publishing, IF 2.1)
Azhar Y. Tantary, Firdous A. Shah and Ahmed I. Zayed, Papoulis’ Sampling Theorem: Revisited, Applied and Computational Harmonic Analysis, 64(May 2023), 118-142 (2023). (ScienceDirect, IF 3.055)
Firdous A. Shah and Azhar Y. Tantary, Multi-Dimensional Linear Canonical Transform with Applications to Sampling and Multiplicative Filtering, Multi-Dimensional Systems and Signal Processing, 33(January 2022), 621-650 (2022). (Springer Nature, IF 2.030)
Firdous A. Shah and Azhar Y. Tantary, Lattice-Based Multi-Channel Sampling Theorem for Linear Canonical Transform, Digital Signal Processing, 117(October 2021), Article ID 103168 (2021). (ScienceDirect, IF 3.381)
Firdous A. Shah and Azhar Y. Tantary, Linear Canonical Stockwell Transform, Mathematical Analysis and Applications, 484(1), Article ID 123673 (2020). (ScienceDirect, IF 1.583)
Invited Talks
Invited Talks
Delivered an online talk on the theme "Compressive Level Set Estimation" at the Department of Electrical Engineering, Indian Institute of Science (IISc) Bengaluru on February 11, 2026.
Delivered an online talk on the theme "Stockwell Transform: Phase-Corrected Wavelet Transform" to the BIOSTATS research group of the King Abdullah University of Science and Technology (KAUST) Saudi Arabia on January 06, 2025.
Delivered a talk on the theme Time-Frequency Analysis Beyond the Fourier Domain at the Department of Electrical Engineering, Indian Institute of Technology Jammu on September 17, 2022.
Delivered a series of lectures on the topic "Non-Separable Wavelet Approaches for Multi-Scale Analysis of Multivariate Data" to the students of the courses EE 678-2023-1 and EE 678-2024-1 on Wavelets offered by Professor Vikram M. Gadre at the Department of Electrical Engineering, Indian Institute of Technology Bombay.
Concise Description of PhD Work
Concise Description of PhD Work
Research Topic: An Analysis of the Stockwell Transforms in Different Time-Frequency Domains
The research carried out during my PhD is mainly related to wavelet transforms as multi-scale tools for time-frequency analysis of non-transient signals. In the thesis work, we have accomplished two major objectives: First, we investigated the Stockwell transform (also known as phase-corrected wavelet transform) beyond the conventional Fourier domain by introducing the notions of the fractional Stockwell transform and the linear canonical Stockwell transform; these novel Stockwell transforms are demonstrated to have optimized concentrations in the time-frequency plane. Second, we extended the Stockwell transform to the higher-dimensional domains via two fundamental approaches; one relying upon the higher-dimensional analyzing functions and the other based on the concept of projections by invoking the well-known Radon transform. The thesis also embodies applications of the proposed work in obtaining high-resolution spectrograms for chirp-like signals, which reveal their characteristics beyond the conventional Fourier domain.
Concise Description of Postdoctoral Work
Concise Description of Postdoctoral Work
Research Topic: Topics in Compressed Sensing and Signal Representation
Compressed Sensing: We proposed a novel algorithm for estimating the level-set in the compressive regime, that is, when the function is not directly accessible but is acquired through indirect measurements, which may additionally be corrupted by additive noise. Note that the level-set of a function is a region in its domain over which the function exceeds a certain critical value. Accurate and efficient level-set estimation plays a pivotal role in many scientific and engineering pursuits. For example, in medical imaging, determining the level-set might correspond to the localization of tumours, whereas in remote sensing, the level-set extraction could correspond to finding the key topographic features in the field of digital terrain elevation. Estimation of the level-set in the compressive regime is a problem of significant interest with widespread applications in science and engineering. Our algorithm for compressive level-set estimation is basically a greedy technique that involves minimizing a cost function consisting of a properly designed risk function (data fidelity term) and a sparsity-promoting regularization term based on our newly proposed hyper-pyramid-adapted shearlet transform (HPAST). The HPAST-based complexity regularization has the prime advantage of being effective only on the boundary of the level-set, because the decay of HPAST coefficients is rapid both within and outside the boundary. This is of great significance, since the goal in level-set estimation is to localize the set boundary rather than perform signal estimation or regression.
Signal Representation: We have obtained analytical expressions for the KL Transforms of some random processes in both 1D and 2D. In the 1D case we have explicitly derived, from first principles, the analytical expressions for a family of sinusoidal transforms including the well-known DCT. Such a derivation is expected to be of great pedagogical value. In the 2D case we have obtained a family of new 2D transforms (non-separable) that are expected to improve the coding gain when compared to the 2D separable DCT. Nevertheless, our approach can also be extended to N dimensions, in general.
Strengths
Strengths
Optimistic
Conscientious
Hardworking
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