Osama A. Ahmed

New denoising scheme for magnetic resonance spectroscopy signals

A new scheme for denoising magnetic resonance spectroscopy (MRS) signals is presented. This scheme is based on projecting noisy MRS signals in different domains, consecutively, and performing noise filtering operations in these domains. The domains are chosen such that the noise portion, which is inseparable from the desired signal in one domain, is separable in the other. A set of stable, linear, time-frequency (SLTF) transforms with different resolutions was selected for these projections as an example. Scheme evaluation was performed using extensive MRS signals with various noise levels. Compared with one domain denoising, it was observed that the proposed scheme gives superior results that compensate for the excess computational requirements. The proposed scheme supersedes also the wavelet packet denoising schemes.

NMR signal enhancement via a new time-frequency transform

In this paper, a reliable method to reduce the noise from nuclear magnetic resonance (NMR) signals using a recently developed linear critically sampled time-frequency transform is proposed. In addition to its low computational requirements, this transform has many theoretical advantages that make it a good candidate for NMR signal enhancement. NMR signals in the transform domain are concentrated in a few coefficients while the noise is well distributed. Performing a thresholding technique in the transform domain, therefore, significantly enhances the signal. A comparison with other signal enhancement techniques shows that this technique has a superior performance, thus confirming the theoretical expectations.

Stable critically-sampled Gabor transform with localized biorthogonal function

In this paper, a new critically-sampled Gabor transform is presented. This transform, unlike all currently available critically-sampled Gabor transforms, leads to a stable transform. In addition, the resulting biorthogonal function, which is unique in the critical sampling case, is well localized in both time and frequency. It thus overcomes the main two problems of previous transforms.

Critically sampled Gabor transform with localized biorthogonal function

A new implementation of the critically sampled nonperiodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the propsed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biorthogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is the non-localization of the resultant biorthogonal function. A fast algorithm to compute the derived biorthogonal function is proposed.

Fast computation of discrete SLTF transform

A fast algorithm for SLTF analysis and SLTF synthesis computations is presented. The proposed algorithm exploits the special structure of the SLTF transformation matrix. The algorithm requires K (2 log/sub 2/ M-1/2) multiplications and K (4 log/sub 2/ M-3/2) additions for calculating the biorthogonal function and K (log/sub 2/ K-1/2 log/sub 2/ N) multiplications and K (2 log/sub 2/ K-log/sub 2/ N-3) additions for both the analysis and the synthesis transform computations where K is the signal length and M and N are arbitrary numbers such that MN=K.

Enhanced denoising scheme for NMR signals

A new scheme for denoising Nuclear Magnetic Resonance (NMR) signals using time-frequency (TF) transforms is presented. This scheme utilizes some inherent characteristics of NMR signals to discriminate them from the noise. More specifically, the envelop of the NMR signal decays exponentially in the TF domain along the time direction while the noise is not. This decay along with the difference in energy level was utilized to differentiate between NMR signals and noise in the TF domain. The evaluation of this scheme was performed using extensive simulation of NMR signals with different noise levels. It was observed that the proposed scheme gives superior results for all noise levels.

Orthogonal Gabor-DCT transform

A new implementation of the Gabor-DCT transform, is presented which leads to an orthogonal transform which is thus stable. In addition, this transform is computationally less demanding than other Gabor transforms. The conditions on the window function to be a candidate of an orthogonal Gabor-DCT are derived.