Hossein Sedarat

On the optimality of the gridding reconstruction algorithm

Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.

Partial-FOV reconstruction in dynamic spiral imaging.

In many applications of dynamic MR imaging, only a portion of the field‐of‐view (FOV) exhibits considerable variations in time. In such cases, a prior knowledge of the static part of the image allows a partial‐FOV reconstruction of the dynamic section using only a fraction of the raw data. This method of reconstruction generally results in higher temporal resolution, because the scan time for partial‐FOV data is shorter. The fidelity of this reconstruction technique depends, among other factors, on the accuracy of the prior information of the static section. This information is usually derived from the reconstructed images at previous time frames. This data, however, is normally corrupted by the motion artifact. Because the temporal frequency contents of the motion artifact is very similar to that of the dynamic section, a temporal low‐pass filter can efficiently remove this artifact from the static data. The bandwidth of the filter can be obtained from the rate of variations inside and outside the dynamic area. In general, when the temporal bandwidth is not spatially uniform, a bank of low‐pass filters can provide a proper suppression of the motion artifact outside the dynamic section. This reconstruction technique is adapted for spiral acquisition and is successfully applied to cardiac fluoroscopy, doubling the temporal resolution. Magn Reson Med 43:429–439, 2000.

Multicarrier communication in presence of biased-Gaussian noise sources

Certain types of non-Gaussian noise sources in multicarrier communication systems behave effectively as modulating signals that control the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian and non-Gaussian noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. Impulsive interferers, timing phase error and radio frequency interference are examples of such non-Gaussian noise sources. The BER-equivalent power of a composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the scaled version of the underlying Gaussian noise source. The scale factor is derived from the characteristics of the non-Gaussian noise source. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.

Impulse noise protection for multicarrier communication systems

Impulse noise in multicarrier communication systems behaves effectively as a modulating signal that controls the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian noise and impulse noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. The BER-equivalent power of the composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the amplified version of the underlying Gaussian noise source. The amplification factor is derived from the characteristics of the impulse interference. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.

Generalized gridding reconstruction from nonuniformly sampled data

Gridding reconstruction is a method to derive data on a Cartesian grid from a set of non-uniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction, on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise; hence it is rarely used in practice. Despite the seemingly different approaches of reconstruction, the gridding and least squares reconstruction methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as ones yielding the least approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This method is used to find the optimal density compensation factors which minimize the weighted approximation error. An iterative method is also proposed for joint optimization of the interpolating kernel and the deapodization function. Some applications in magnetic resonance imaging are presented.

Simplified neural network architectures for a hybrid speech recognition system with small vocabulary size

Previous studies suggest that a hybrid speech recognition system based on a hidden Markov model (HMM) with a neural network (NN) subsystem as the estimator of the state conditional observation probability may have some advantages over the conventional HMMs with Gaussian mixture models for the observation probabilities. The HMM and NN modules are typically treated as separate entities in a hybrid system. This paper, however, suggests that the a priori knowledge of the HMM structure can be beneficial in the design of the NN subsystem. A case of isolated word recognition is studied to demonstrate that a substantially simplified NN can be achieved in a structured HMM by applying a Bayesian factorization and pre-classification. The results indicate a similar performance to that obtained with the classical approach with much less complexity in the NN structure.