Objectives Diffusion weighted MRI measures molecular displacements by tagging spins phase according to their posthon, consequently, incoherent displacements cause dephasing, which results in a measurable signal attenuation. Usually, in clinical and biological applications, this incoherent motion is attributed to molecular diffusion (i.e., Brownian motion) within hindered and restricted domains....

In this thesis, a new approach is studied for inverse modeling of ill-posed problems with spatially continuous parameters that exhibit sparseness in an incoherent basis (e.g. a Fourier basis). The solution is constrained to be sparse in the transform domain and the dimension of the search space is effectively reduced to a low frequency subspace to improve estimation efficiency. The solution sub...

The Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is a subspace-based analysis method used in source localization or frequency estimation, originally designed in a block signal processing context. In other respects, the Projection Approximation Subspace Tracker (PAST) is a fast and robust subspace tracking method. This paper introduces a new frequency e...

The period estimation and periodic decomposition of a signal are the long-standing problems in the field of signal processing and biomolecular sequence analysis. To address such problems, we introduce the Ramanujan subspace pursuit (RSP) based on the Ramanujan subspace. As a greedy iterative algorithm, the RSP can uniquely decompose any signal into a sum of exactly periodic components, by selec...

A signal eigenvalue sensitivity analysis for subspace-based methods that exploit the shift-invariance property present in the signal subspace is considered. It is proved that signal eigenvalues are rather insensitive to small perturbations in the data provided the dimension of the problem is large enough and the eigenvalues themselves are not extremely close to each other. In addition, bounds o...

In our earlier work [1, 2], we developed a robust detector for multipath constrained environments when the transmitted signal is known. In this paper, we extend these results to the case where the transmitted signal is a random process. The approach in [1, 2] is to replace the orthogonal projection on the multipath signal subspace S by the orthogonal projection on a representation subspace G, s...

Introduction: It is shown in [1] that the weighted subspace fitting (WSF) method, a minimising technique, always outperforms the deterministic maximum likelihood (DML) estimator for the problem of the direction-of-arrival (DOA) estimation. However, the WSF estimator is still subject to high computational cost, partially attributable to the estimation of the signal subspace. In this Letter, the ...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

This paper presents a blind adaptive detector for asynchronous DS-CDMA in multipath channels. The receiver exploits the underlying subspace structure for recursive estimation of the desired signal vector, and eliminates the need of explicit channel or delay estimation. The detector is constrained to the signal subspace (hence reduced rank), leading to computational efficiency while also benefit...