Signal recovery via compressive sensing
Bangalore Ramesh Jayanth
Date of Issue2014
School of Electrical and Electronic Engineering
Compressed Sensing (CS) has applications in many areas of signal processing such as data compression, data acquisition and dimensionality reduction. CS ensures faithful recovery of certain signals or images using a small number of samples or observations than traditional methods use. Many natural signals have sparse representations when expressed in a proper basis. Sparse signal can be recovered from the observation vector using convex optimization teclmiques like !!-minimization (Basis Pursuit). For a faster recovery, greedy algorithms such as Orthogonal Matching Pursuit (OMP), Regularized Orthogonal Matching Pursuit (ROMP), Stagewise Orthogonal Matching Pursuit (St- OMP), Backtracking-based Adaptive Orthogonal Matching Pursuit (BAOMP), etc. can be used . In my experiments OMP algoritlun is used to recover the original signal as it less complex and computationally inexpensive. The initial part of the project deals with understanding the recovery of sum of sine/cosine waves via compressive sensing using OMP algorithm by applying proper basis functions so that signal is represented with good sparsity. The second and third part of the project is aimed at recovering sine wave using different basis functions like DCT , DFT and WARPED DFT. This was challenging because there were multiple peaks and spectral leakages in the frequency spectrum which imposed difficulty while recovering the data with few measurements. The last part of the project involved recovering twin sine wave which was also challenging because of less frequency separation between two sine waves. This imposed problems while picking the location of the peak from the projection matrix ofOMP. This report shows the different plots of Mean Squared Error versus Number of Measurements for different basis functions which helps in determining the best basis function that can be applied to given signal so that the signal becomes nearly sparse or exactly sparse and can be recovered with less number of measurements.
DRNTU::Engineering::Electrical and electronic engineering