Vineetha K V (41718015) <br/><br/>
Applications of Matrix completion theory to image processing 

 - MPhil CS 2018-2019 
<br/><br/> Matrix completion is the problem of recovering a low rank matrix from partially observed entries. It has<br/>been widely used in collaborative filtering and recommender systems, dimension reduction and multiclass<br/>learning. This area is a recently emerged field of study following the track of what has been explored in<br/>fields related to compressed sensing. Like in compressed sensing, matrix completion algorithms, therefore,<br/>involve reconstruction of the data matrix from a small subset of its noise corrupted entries. The missing<br/>entries can be recovered under certain conditions when the data matrix has a low rank. The conditions<br/>mainly stipulate that the number of available entries fall below a certain limit; and that some of the rows<br/>and columns of the matrix are completely unknown. There has been extensive work on designing efficient<br/>algorithms for matrix completion with guarantees. Earlier works on matrix completion were based on<br/>convex relaxations. These algorithms achieve strong statistical guarantees, but are quite computationally<br/>expensive in practice. More recently, there has been growing interest in analyzing non-convex algorithms<br/>for matrix completion. These algorithms are much faster than the convex relaxation algorithms, which is<br/>crucial for their empirical success in large-scale collaborative filtering applications. We compare both<br/>convex and non convex approaches for Matrix Completion. The results are generalized to the setting when<br/>the observed entries contain noise. 
<br/><br/>
<br/><br/><label>Subjects--Topical Terms: </label><br/>Matrix Completion  <br/>Data Matrix<br/> Low Rank Matrix<br/> Image Processing