Project abstracts

Expansion-compression Variance-component Based Sparse-signal Reconstruction from Noisy Measurements
Kun Qiu
Abstract:
In this project, we propose an expansion-compression variance-component based method (ExCoV) for reconstructing sparse or compressible signals from noisy measurements. The measurements follow an underdetermined linear model, with noise covariance matrix known up to a constant. Compressible or sparse signal structure is imposed by defining high- and low-signal coefficients, where  each high-signal coefficient is assigned its own variance, all low-signal coefficients are assigned a common variance, and all the variance components are unknown. We apply the proposed method to reconstruct signals from compressive samples, compare it with existing well known approaches such as CoSaMP, GPSR, l1-magic, etc. and demonstrate the performance via numerical simulations.


Estimating Sparse Contour Deformations using Compressed Sensing : Applications to Deformable Contour Tracking
Samarjit Das
Abstract:
In this project, we attempt to explore the possibility of using compressed sensing in order to estimate temporal contour deformations. Thus, starting with the initial contour, our ultimate goal is to develop a compressed sensing based deformable contour tracking algorithm. We assume that the associated deformation signals are sparse in frequency  domain and hence we can recover them from a very small number (relative to the full contour length) of random measurements. Our algorithm takes the initial contour information and reconstructs the contours corresponding to the successive time  instants from random observations. The observations are considered to be randomly sub-sampled version of the true deformation signal. We have used a nearest edge-based search method for the observation extraction. We demonstrate the working of the algorithm for multiple examples, both simulated and real-life sequences; including how the system could possibly work as a deformable contour tracking algorithm. The methodology developed in this work has potential applications in many areas including deformable contour tracking over biomedical image sequences which are often corrupted with noise  and occlusion/clutter scattered randomly all over the contour. In that scenario, we can extract observations using the points which are not corrupted (also assumed to be randomly scattered over the contour) and 'robustly' reconstruct the entire contour using our technique.

COSAMP and Sequential COSAMP
Fardad Raisali
Abstract: This project investigate the performance of the OMP(Orthognal  Matching Pursuit) and Cosamp(Compressive sampling) in the reconstructioin of
the sparse signals. We use MR images here as our signal.Also we would like to  test the sequential MR image reconstruction which the main aidea is using
previous estimate to improve current one.By this approach we expect an  increase in the speed of the algorithm.