Manu Ghulyani

Contact

manugATiiscDOTacDOTin

About

I am a PhD student at the Indian Institute of Science in the Department of Electrical Engineering. I am working under the supervision of Dr. Muthuvel Arigovindan in the broad area of imaging inverse problems. Here is my CV.

Education History

B.E: Electronics and Instrumentation

M.Sc (Engg.) : System Sciences and Signal Processing

Ph.D (Engg.) System Sciences and Signal Processing

Current Project

Inverse problems in imaging arise in various contexts in biological and astronomical imaging such as super-resolution microscopy, MRI reconstruction, CAT reconstruction, and deconvolution. These problems are generally solved by two approaches. In the first approach, the inverse problem is solved by using off-the-shelf regularization based methods, e.g., Wavelet regularization, Total Variation regularization, Tikhonov regularization, and many others. These regularizations correspond to certain ad-hoc beliefs on the image characteristics which often lead to artefacts in the reconstructions. For example, first-order Total Variation promotes piece-wise constant estimates. In the second approach, training data containing typical measured images and the corresponding ground-truth images are collected and desired mapping from the measured image to the required image is learned. The map is generally modelled as Deep Neutral Network (DNN) and the parameters of the network are learned by minimizing an error metric corresponding to the error between the recovered estimate and the ground truth. Among these two classes of methods, the deep learning methods are believed to give better results in terms of various comparison metrics in various inverse problems; however, their practical use by the biological and medical community in sensitive applications has been limited. This is mainly because of Black-box like behaviour of the DNN. Also, due to the large number of parameters in the network, a substantial amount of training data is required for training the DNN which is also not readily publicly available. In this project, we adopt a middle path between the above two approaches. The project aims to learn a prior for the regularization terms which does not require as many parameters as the deep learning-based methods but is sufficiently flexible to avoid artefacts in the reconstruction. Towards this goal, we first explore the Total Generalized Variation (TGV) regularization as a framework, which generalizes the Total Variation regularization.

Project status:

(1) Extended second order TGV to accommodate Hessian-Schatten norm regularization which is well known to have excellent structure preservation property.

(2) We verified that the above-mentioned method outperforms some state of the art DNN based methods that use thousands of images for training.

(3) We also have developed a minimization algorithm for image restoration using $n^th$ order TGV that works for any n. To the best of our knowledge, this is the first algorithm for image restoration using n th order TGV.

(4) We have proposed a new regularization based on eigenvalues of the hessian and a non-convex shrinkage penalty. We have showed that the proposed penalty is restricted proximal regular. This helps us to show the convergence of the ADMM applied on image restoration problem. Proof document.

ˆCourses:

Mathematical Analysis, Matrix Analysis, Online Prediction and Learning, Bio-medical Imaging Inverse Problems.

Publications

1) S. Viswanath, M. Ghulyani, S. De Beco, M. Dahan and M. Arigovindan, "Image Restoration by Combined Order Regularization With Optimal Spatial Adaptation," in IEEE Transactions on Image Processing, vol. 29, pp. 6315-6329, 2020, doi: 10.1109/TIP.2020.2988146.

2)Ghulyani M and Arigovindan M 2019 Fast roughness minimizing image restoration under mixed Poisson-Gaussian noise (Preprint 1902.11173)

(Accepted for publication IEEE TIP).arxiv.org/abs/1902.11173

Research Interests

Image Processing, Optimization, Inverse Problems, Compressive Sensing, Machine Learning