Research Projects

Deep convolutional neural networks have paved way for successful results in several practical machine learning applications in signal processing. One of the main objectives of machine learning is feature extraction. Deep convolutional neural networks (DCNN) comprise of multiple layers. Each layer performs convolutional transforms pursued by nonlinear and pooling operators. These DCNNs can be treated as classifiers based on the output of the last layer. They can also act as stand-alone feature extractors. These features can be fed to a classifier. When images/signals are dealt with, it is very much desired that the feature extractors be invariant to the spatial location and robust with respect to nonlinear deformations. The mathematical study of such feature extractors has been receiving a lot of attention. Such a study is one of the goals of this project. The mathematical aspects of deep convolutional neural networks for feature extraction was introduced by Mallat in 2012. He proposed a tree-structured convolutional neural network, also called scattering network, based on wavelets transform followed by modulus operator as a nonlinear operator. It is shown that the scattering network has properties like translation invariance and deformation stability subject to the condition that the underline wavelets satisfy certain admissibility conditions. Furthermore, Mallat's scattering network gives rise to state-of-the-art results in many classification functions. In order to relax the admissibility conditions of Mallat, a slightly different settings was considered by Wiatowski etl., which makes use of semi-discrete frames. In the proposed study involves, study the stability of existing networks and proposing new feature extractors. DCNN based analysis can also be extended certain inverse problems related signal analysis . Significant improvement in performance of reconstruction have been attained by using deep learning methods. Image denoising: Deep CNN can be used for achieving high performance in image denoising. Neural network based algorithms can be developed for perform better for denoising. Sparse-View CT reconstruction: One of the primary objectives in X-ray CT is to reduce the radiation dose as the risk due to exposure to radiation is high. In sparse-view CT, the number of projection views is reduced and this in turn reduces the radiation dose. As there are insufficient number of projection views, the standard reconstruction methods show serious streaking artifacts. Image inpainting: The main goal in image inpainting is estimating the mixing pixels. CNN based image inpainting algorithms may be developed for better performance.