Clustering of Data with Missing Entries

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a clustering algorithm, that will provide good clustering even in the presence of missing data. The proposed technique solves an $\ell_0$ fusion penalty based optimization problem to recover the clusters. We theoretically analyze the conditions needed for the successful recovery of the clusters. We also propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. The method is demonstrated on simulated and real datasets, and is observed to perform well in the presence of large fractions of missing entries.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0187

Super-resolution MRI Using Finite Rate of Innovation Curves

We propose a two-stage algorithm for the super-resolution of MR images from their low-frequency k-space samples. In the first stage we estimate a resolution-independent mask whose zeros represent the edges of the image. This builds off recent work extending the theory of sampling signals of finite rate of innovation (FRI) to two-dimensional curves. We enable its application to MRI by proposing extensions of the signal models allowed by FRI theory, and by developing a more robust and efficient means to determine the edge mask. In the second stage of the scheme, we recover the super-resolved MR image using the discretized edge mask as an image prior. We evaluate our scheme on simulated single-coil MR data obtained from analytical phantoms, and compare against total variation reconstructions. Our experiments show improved performance in both noiseless and noisy settings.Comment: Conference paper accepted to ISBI 2015. 4 pages, 2 figure

Novel Structured Low-rank algorithm to recover spatially smooth exponential image time series

We propose a structured low rank matrix completion algorithm to recover a time series of images consisting of linear combination of exponential parameters at every pixel, from under-sampled Fourier measurements. The spatial smoothness of these parameters is exploited along with the exponential structure of the time series at every pixel, to derive an annihilation relation in the $k-t$ domain. This annihilation relation translates into a structured low rank matrix formed from the $k-t$ samples. We demonstrate the algorithm in the parameter mapping setting and show significant improvement over state of the art methods.Comment: 4 pages, 3 figures, accepted at ISBI 2017, Melbourne, Australi