Subspace Swap Improvement Techniques for Finite Rate of Innovation Signal Reconstruction

Abstract

Finite rate of innovation (FRI) framework has been developed for sampling and reconstruction of a class of continuous non-bandlimited signals known as signals with FRI. This is achieved utilizing suitable sampling kernels and reconstruction techniques. The FRI framework has been extended to discrete-time sparse signals for reconstruction. However, some reconstruction algorithms tend to breakdown at certain signal-to-noise ratios (SNR) due to subspace swap. In this thesis, we propose novel strategies to improve reconstruction performance in the breakdown region. First, we propose a universal FRI scheme based on the error decrease detector criterion which enables reconstructing sparse signals with an unknown number of nonzero coefficients. The scheme accomplishes perfect reconstruction in the noiseless scenario. An extension of the scheme is presented for the noisy case. When compared to the conventional scheme, the proposed scheme exhibits improvements in performance in the breakdown SNR. In addition, an application of the proposed FRI scheme for reconstructing magnetic resonance imaging (MRI) and electrocardiogram (ECG) is demonstrated. Next, we propose a sparse-Prony method which avoids polynomial rootfinding for reconstructing streams of Diracs. The method produces perfect reconstruction in a noise-free environment. Extensive simulations are carried out to compare the performance of sparse-Prony with that of Prony’s and matrix pencil methods for noisy cases, and the results demonstrate superior performance of the sparse-Prony method. We also provide a residual neural network approach which iteratively works on the training data for reconstructing streams of Diracs. The simulation results on synthetic noisy data have shown better reconstruction performance in the breakdown region when compared with the Prony’s and matrix pencil methods. Finally, we introduce a novel technique to estimate seismic reflectivity signals using the FRI theory which helps determine the subsurface structure. The seismic data is modelled as a convolution between the Ricker wavelet and the FRI signal-a Dirac impulse train. The experimental results have demonstrated comparable reflectivity estimation performance with lesser data in the noiseless and medium to high SNR regimes.