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Statistical image comparison and monitoring

• Formulating statistical methodologies for image comparison and monitoring in real-world applications across diverse scientific disciplines.
• Intending to address fundamental challenges in image monitoring by unifying state-of-the-art techniques from both domains: image processing and statistical process control.
• Aiming to lay the groundwork for more robust, scalable, and interpretable image-based monitoring systems and advancing the field towards broader practical impact.
• Selected publications:
  • Roy, A.^* and Mukherjee, P.S. "A Registration-free Approach for Image Monitoring", Statistics and Computing, 2026, 36(20), 1--20. [Link] [Computer Codes]
  • Roy, A.^* and Mukherjee, P.S. "Image Comparison Based On Local Pixel Clustering", Technometrics, 2024, 66(4), 495--506. [Link][Computer Codes]
  ^* doctoral student

Image registration using jump regression analysis

• Aiming to make the first stride towards widening the scope of rigid-body image registration to include zooming or scaling under the framework of jump regression analysis.
• The goal is to develop image registration methods that can perform well on a wide range of situations so that they can be useful in various downstream applications, such as image comparisons, image monitoring, and so forth.
• Intending to develop ideas which are adaptable and may serve as a foundation for developing a broader class of techniques in data science, including methods for nonlinear image registration.
• Selected publications:
  • Das, S.^* and Mukherjee, P.S. "Image Registration for Zooming Using Similarity Matching", Journal of Data Science, 2024, 22(4), 558--574. [Link] [Computer Codes]
  • Das, S.^*, Roy, A.^* and Mukherjee, P.S. "Image registration for zooming: A statistically consistent local feature mapping approach", Stat, 2024, 13(1), e664. [Link] [Computer Codes]
  ^* doctoral student

Jump regression analysis using regression trees

• Working on a regression tree–based framework based on Oblique-axis Regression Trees (ORT) for estimating discontinuous regression functions in finite-dimensional spaces, and demonstrates its potential through effective image denoising.
• Supervising a doctoral student who is rethinking the assumptions imposed on the underlying regression function, so that the resulting theoretical analysis attains a level of structural simplicity that departs from much of the existing regression tree literature.
• Extending the ORT framework beyond static estimation, and intending to develop a method for monitoring drift patterns in image sequences. Although gradual temporal variations, commonly referred to as drifts, are ubiquitous in sequential imaging data, principled statistical approaches for drift monitoring remain largely unexplored.
• Selected publications:
  • Basak, S.^*, Roy, A.^* and Mukherjee, P.S. "Estimation of Piecewise Continuous Regression Function in Finite Dimension using Oblique-axis Regression Tree with Applications in Image Denoising", Statistica Sinica, To appear. DOI: 10.5705/ss.202025.0120. [Link] [Supplementary] [Computer Codes]
  ^* doctoral student

Blind image deblurring under jump regression analysis

• Intending to develop methods for the well-known challenging problem of deblurring images in the presence of noise when the blurring mechanism is unknown.
• Selected publications:
  • Kang, Y., Roy, A.^* and Mukherjee, P.S. "Adaptive Blind Image Deblurring and Denoising", Scandinavian Journal of Statistics, 2026, 53(1), 413--441. [Link]
  • Kang, Y., Mukherjee, P.S. and Qiu, P. "Efficient Blind Image Deblurring Using Nonparametric Regression And Local Pixel Clustering", Technometrics, 2018, 60(4), 522--531. [Link] [Computer Codes]
  ^* doctoral student

Statistical image denoising

• Developing methods for removing various types of noise from images so that the details of the edge-structures are preserved well.
• Selected publications:
  • Basak, S.^* and Mukherjee, P.S. "An Efficient Image Denoising Method Integrating Multi-resolution Local Clustering and Adaptive Smoothing", Statistical Methods & Applications, 2025, 34(4), 767--785. [Link] [Computer Codes]
  • Mukherjee, P.S. "A multi-resolution and adaptive 3-D image denoising framework with applications in medical imaging," Signal, Image and Video Processing, 2017, 11(7), 1379--1387. [Link] [Computer Codes]
  • Mukherjee, P.S. and Qiu, P., "Image Denoising by a Local Clustering Framework," Journal of Computational and Graphical Statistics, 2015, 24(1), 254--273. [Link] [Computer Codes]
  • Mukherjee, P.S. and Qiu, P., "3-D Image Denoising By Local Smoothing And Nonparametric Regression," Technometrics, 2011, 53(2), 196--208. [Link] [Computer Codes]
  ^* doctoral student

Statistical process control

• Aiming to use and adapt various statistical process control charts for various applications, including image monitoring.
• Selected publications:
  • Roy, A.^* and Mukherjee, P.S. "Upper quantile-based CUSUM-type control chart for detecting small changes in image data", Journal of Applied Statistics, 2025, 52(11), 2156--2171. [Link] [Computer Codes]
  • Mukherjee, P.S., "On phase II monitoring of the probability distributions of univariate continuous processes," Statistical Papers, 2016, 57(2), 539--562. [Link]
  ^* doctoral student

Applications of statistics and machine learning techniques in civil engineering

• Selected publications:
  • Gajurel, A., Chittoori, B., Mukherjee, P.S., and Sadegh, M. "Machine learning methods to map stabilizer effectiveness based on common soil properties", Transportation Geotechnics, 2021, 27, Article 100506. [Link]

Applications of statistical tools in immusciences research

• Selected publications:
  • Vojdani, A., Mukherjee, P.S., Berookhim, J. and Kharrazian, D. "Detection of antibodies against human and plant aquaporins in patients with multiple sclerosis," Autoimmune Diseases, 2015, Article ID 905208. [Link]
  • Vojdani, A., Kharrazian, D. and Mukherjee, P.S., "Elevated levels of antibodies against xenobiotics in a subgroup of healthy subjects," Journal of Applied Toxicology, 2015, 35(4), 383--397. [Link]
  • Vojdani, A., Kharrazian, D. and Mukherjee, P.S., "The Prevalence of Antibodies against Wheat and Milk Proteins in Blood Donors and their Contribution to Neuroimmune Reactivities," Nutrients, 2014, 6(1), 15--36. [Link]

Applications of statistical tools in the research on the effects of air pollution on human health

• Selected publications:
  • Calderon-Garciduenas, L., Ayala, A., and Mukherjee, P.S., "2024 United States Elections: Air Pollution, Neurodegeneration, Neuropsychiatric, and Neurodevelopmental Disorders. Who Cares?," Journal of Alzheimer's Disease, 2024, 98(4), 1277--1282. [Link]
  • Calderon-Garciduenas, L., Gonzalez-Maciel, A., Mukherjee, P.S., Reynoso-Robles, R., Perez-Guille, B., Gayosso-Chavez, C., Torres-Jardon, R., Cross, J.V., Ahmed, I.A., Karloukovski, V.V., and Maher, B.A. "Combustion- and friction-derived magnetic air pollution nanoparticles in human hearts," Environmental Research, 2019, 176, Article 108567. [Link]
  • Gonzalez-Maciel, A., Reynoso-Robles, R., Torres-Jardon, R., Mukherjee, P.S. and Calderon-Garciduenas, L. "Combustion-Derived Nanoparticles in Key Brain Target Cells and Organelles in Young Urbanites: Culprit Hidden in Plain Sight in Alzheimer's Disease Development," Journal of Alzheimer's Disease, 2017, 59(1), 189--208. [Link]
  • Calderon-Garciduenas, L., Reynoso-Robles, R., Vargas- Martinez, J., Gomez-Maqueo-Chew, A., Perez-Guille, B., Mukherjee, P.S., Torres-Jardon, R., Perry, G. and Gonzalez-Maciel, A. "Prefrontal white matter pathology in air pollution exposed Mexico City young urbanites and their potential impact on neurovascular unit dysfunction and the development of Alzheimer's disease," Environmental Research, 2016, 146, 404--417. [Link]
  • Calderon-Garciduenas, L., Vojdani, A., Busch, E.B., Busch, Y., Friedle, A., Franco-Lira, M., Mukherjee, P.S., Park, S.B., Torres-Jardon, R. and D'Angiulli, A., "Air pollution and children: Neural and tight junction antibodies and combustion metals, the role of barrier breakdown and brain immunity in neurodegeneration," Journal of Alzheimer's Disease, 2015, 43(3), 1039--1058. [Link]

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