I am doing my PhD studies under the supervision of Matthias Bethge. I am working on statistical modeling of natural images and unsupervised representation learning. One goal is to develop new image models and to compare their coding performance to that of existing models. Another goal is to develop new unsupervised learning methods for time-dependent and invariant image representations.
In this project we are trying to provide good bounds on redundancy of natural images. We use conditional likelihood for providing meaningful bounds on redundancy of natural images.
Elliptically contoured distributions are generalization of the Gaussian distribution that recently successfully applied for statistical modeling of natural images. In this project I am trying to derive Maximum likelihood estimation for Elliptically Gamma distribution , etc.
In this project we applied Hierarchical ICA (a variation of projection pursuit) and mixture of elliptically contoured distributions for modeling natural image patches (Note that it outperformed the state-of-the-art methods for density modeling of natural image patches)
Our Scientific Advisory Report:
Mixture Models and Hierarchical Models of Natural Images
A talk that I gave about it:
Statistical modeling of natural images
Bernstein Conference Abstract :
Hierachical Models of Natural Images
This is the prize-winning method for shear estimation in weak gravitational lensing
Spectral Stacking: Unbiased Shear Estimation for Weak Gravitational Lensing
Implemented algorithm in Matlab
We derived an effective lossy image compression algorithm. A patent is pending about our proposed algorithm.
Method and Device for Image Compression
This is the work that I did during my Master studies. In my Master thesis, I successfully applied this wavelet for activity detection of fMRI images.
Almost Perfect Reconstruction Filter Bank for Non-redundant, Approximately Shift-Invariant, Complex Wavelet Transforms
A code for applying wavelet transform and inverse wavelet transform for 1D, 2D or 3D signals
A 45 minute talk about the proposed method
I have become interested in causal inference, especially since it is related to the quantitative aspect of time and its relation to action and causality. I think, I will focus on this question for my next career, provided that I continue working on modern science questions.
I will use projection pursuit statistical models (An example would be deep networks) for quantitative modeling of natural images. In mathematical science, natural images are considered as two-dimensional array of numbers measured by a device exp. sensor of a ccd camera.
I think, I will be able to extend the result of my paper to fractional and steerable wavelets.
A meaningful definition for fast directional discrete cosine transform.
The image model can be used for different applications like denoising, segmentation, etc.
Extension of patent for video compression
How to use natural image models for lossless compression and how to have a scalable lossless compression
Designing meaningful combination of quantized coefficients as letters for entropy coding of image compression algorithm.
It is a second part of my Master thesis that I did not have time to publish it.
It is my Bachelor work that I did not have time to publish an improved version of it
I have some ideas to extend proposed shear estimation method for weak lensing power spectrum estimation.
, , and (September-2016) Inference and mixture modeling with the Elliptical Gamma Distribution
Computational Statistics & Data Analysis 101 29–43.
, , and (October-2014) Statistical inference with the Elliptical Gamma Distribution
Machine Learning . submitted
, and (July-2012) Mixtures of Conditional Gaussian Scale Mixtures Applied to Multiscale Image Representations
PLoS ONE 7(7) 1-8.
, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , and (September-2011) Gravitational Lensing Accuracy Testing 2010 (GREAT10) Challenge Handbook
Annals of Applied Statistics 5(3) 2231-2263.
, , ,
, and (October-2010) Lower bounds on the redundancy of natural images
Vision Research 50(22) 2213-2222.
, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , and (July-2010) Results of the GREAT08 Challenge: An image analysis competition for cosmological lensing
Monthly Notices of the Royal Astronomical Society 405(3) 2044-2061.
and (November-2008) Almost Perfect Reconstruction Filter Bank for Non-redundant, Approximately Shift-Invariant, Complex Wavelet Transforms
Journal of Wavelet Theory and Applications 2(1) 1-14.
Conference papers (2):
, , and (May-2015) Data modeling with the elliptical gamma distribution, 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015), International Machine Learning Society, Madison, WI, USA, 903–911, Series: JMLR Workshop and Conference Proceedings ; 38.
and (2014) Geometric optimisation on positive definite matrices with
application to elliptically contoured distributions In: Advances in Neural Information Processing Systems 26, , Twenty-Seventh Annual Conference on Neural Information Processing Systems (NIPS 2013), Curran, Red Hook, NY, USA, 2564-2572.
Technical reports (1):
and : Spectral Stacking: Unbiased Shear Estimation for Weak Gravitational Lensing, 186, Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, (October-2009).
, and (September-14-2012): Mixtures of conditional Gaussian scale mixtures: the best
model for natural images, Bernstein Conference 2012, München, Germany, Frontiers in Computational Neuroscience, Conference Abstract: Bernstein Conference 2012 247.
, and (October-2011): A multiscale model of natural images, 12th Conference of Junior Neuroscientists of Tübingen (NeNA 2011), Heiligkreuztal, Germany.
, and (October-2010): New Estimate for the Redundancy of Natural Images, Bernstein Conference on Computational Neuroscience (BCCN 2010), Berlin, Germany, Frontiers in Computational Neuroscience, 2010(Conference Abstract: Bernstein Conference on Computational Neuroscience).
and (September-30-2009): Hierarchical models of natural images, Bernstein Conference on Computational Neuroscience (BCCN 2009), Frankfurt a.M., Germany, Frontiers in Computational Neuroscience, 2009(Conference Abstract: Bernstein Conference on Computational Neuroscience) 112.
and : Method and Device for Image Compression, WO/2009/146933, (December-2009).