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HILBERT TRANSFORM RELATIONS IN FREQUENCY-DOMAIN OPTICAL-COHERENCE TOMOGRAPHIC IMAGING

Theo Lasser, Chandra Sekhar Seelamantula

Interferometric imaging techniques typically embed the object phase information in the magnitude during the measurement process. During reconstruction, the phase is recovered from the magnitude by certain approximations on the measured magnitude and underlying phase. In this paper, we review some of our recent contributions on exact recovery of phase from Fourier transform magnitude measurements. We show that, under certain conditions, which are easily ensured during acquisition, the phase can be reconstructed accurately from the magnitude. More specifi cally, we show that there exist Hilbert transform relations between the logarithm of the magnitude and the phase. The new set of results constitute a generalization of the minimum-phase property to a larger class of signals than previously known in the literature. The key results are generic and are applicable to one-dimensional as well as two-dimensional signals. We fi rst present the results in a generic fashion. The theoretical claims are validated using the specifi c example of frequency-domain optical-coherence tomographic imaging.

2013

A Savitzky-Golay Filtering Perspective of Dynamic Feature Computation

Mathew Magimai Doss, Chandra Sekhar Seelamantula

We address the classical problem of delta feature computation, and interpret the operation involved in terms of Savitzky-Golay (SG) filtering. Features such as the mel-frequency cepstral coefficients (MFCCs), obtained based on short-time spectra of the speech signal, are commonly used in speech recognition tasks. In order to incorporate the dynamics of speech, auxiliary delta and delta-delta features, which are computed as temporal derivatives of the original features, are used. Typically, the delta features are computed in a smooth fashion using local least-squares (LS) polynomial fitting on each feature vector component trajectory. In the light of the original work of Savitzky and Golay, and a recent article by Schafer in IEEE Signal Processing Magazine, we interpret the dynamic feature vector computation for arbitrary derivative orders as SG filtering with a fixed impulse response. This filtering equivalence brings in significantly lower latency with no loss in accuracy, as validated by results on a TIMIT phoneme recognition task. The SG filters involved in dynamic parameter computation can be viewed as modulation filters, proposed by Hermansky

2013

A Shape-Template Based Two-Stage Corpus Callosum Segmentation Technique for Sagittal Plane T1-Weighted Brain Magnetic Resonance Images

Michaël Unser, Chandra Sekhar Seelamantula

We propose a semi-automatic technique to segment corpus callosum (CC) using a two-stage snake formulation: A restricted affine transform (RAT) constrained snake followed by an unconstrained snake in an iterative fashion. A statistical model is developed to capture the shape variations of CC from a training set, which restrict the unconstrained snake to lie in the shape-space of CC. The geometry of the constrained snake is optimized using a local contrast-based energy over RAT space (which allows for five degrees of freedom). On the other hand, the unconstrained snake is optimized using a unified energy (region, gradient, and curvature energy) formulation. Joint optimization resulted in increased robustness to initialization as well as fast and accurate segmentation. The technique was validated on 243 images taken from the OASIS database and performance was quantified using Jaccard's distance, sensitivity, and specificity as the metrics.

IEEE2013