On the zeros of the linear prediction-error filter for deterministic signals

Kumaresan, R.

doi:10.1109/tassp.1983.1164021

Cited by 133 publications

(75 citation statements)

References 9 publications

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“…Equivalently, representation of the low-resolution image as a series of boxcar functions [17], leads to the Fourier Transform (FT) of the spatial derivatives modeled as a summation of complex sinusoids in noise. This framework entails the application of linear prediction for extrapolation of partial -space samples weighted using the appropriate frequency terms [18,19], referred to as the frequency-weighted -space. A possible solution for increasing the efficiency of phase correction is to use a predictor in the frequencyweighted -space along phase-encode direction, followed by low-resolution phase correction.…”

Section: Model-based Methods For Partial -Space Fillingmentioning

confidence: 99%

“…Using the boxcar representation [17], the spatial derivative of the image in the -directioñ( , ) = ( , )/ can be represented using the weighted summation of discrete impulses as a function of . Hence, the 2D-FT of the spatial derivative can be modelled as a summation of finite number of sinusoids, which is linear-predictable to a certain order [18,19]. From (2), the FT of the spatial derivative can be expressed as…”

Section: Formulation Of -Space As a Signal-space Modelmentioning

confidence: 99%

“…Partial -space filling is accomplished by scaling each row of the predicted -space by 1/ 2 ΔV. At each prediction step, the unbiased autocorrelation of the filtered -space is computed and input to the Levinson algorithm [19] for estimating the filter coefficients. In the equivalent signal space model, (4) takes the form…”

Section: Formulation Of -Space As a Signal-space Modelmentioning

confidence: 99%

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Application of Linear Prediction for Phase and Magnitude Correction in Partially Acquired MRI

Paul

Pillai

2013

ISRN Biomedical Imaging

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Using the boxcar representation in the spatial domain and a signal-space representation of its frequency-weighted -space, an iterative prediction method is developed to derive an improved low-resolution phase approximation for phase correction. Compared to the homodyne filter, the proposed predictor is found to be more efficient due to its capability of exhibiting an equivalent degree of performance using a lower number of fractional lines. The phase correction performance is illustrated using partially acquired susceptibility weighted images (SWI). An extension of the predictor into higher frequency regions of phaseencodes in conjunction with a signal-space projection in the frequency-weighted partial k-space is shown to provide restoration of fine structural details of sparse magnitude images. The application of subspace projection filtering is demonstrated using magnetic resonance angiogram (MRA).

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Section: Model-based Methods For Partial -Space Fillingmentioning

confidence: 99%

Section: Formulation Of -Space As a Signal-space Modelmentioning

confidence: 99%

Section: Formulation Of -Space As a Signal-space Modelmentioning

confidence: 99%

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Application of Linear Prediction for Phase and Magnitude Correction in Partially Acquired MRI

Paul

Pillai

2013

ISRN Biomedical Imaging

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“…The resulting polynomial will have 2d pole-related roots and N -2d extraneous roots. The extraneous roots will lie symmetrically about the interior of the unit circle (see [11], [12], and [14] for proof of this statement). The algorithm calculates d using results presented in [5] and then constructs a polynomial of the form…”

Section: Transient Response Analysismentioning

confidence: 96%

“…We assume that stationary random narrow-band signals with center frequency co o are present and that these signals emanate from point sources in the far field. Although we are confining our development to the narrow-band case, the method can be easily extended to wide-band signals following the techniques of [14]. For simplicity, we will also restrict our consideration here to signals which are not coherent so that the signal covariance matrix A will have full rank.…”

Section: A Bearing Estimationmentioning

confidence: 99%

A transform-based covariance differencing approach for some classes of parameter estimation problems

Prasad

Williams

Mahalanabis

et al. 1988

IEEE Trans. Acoust., Speech, Signal Processing

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Abstract-In this paper, we present a method of parameter estimation for a class of problems where the desired signal is embedded in colored noise with unknown covariance. The new algorithm is a variation of the covariance differencing scheme proposed by Paulraj and Kailath. Unlike the previous method, however, the proposed algorithm does not require multiple estimates of the signal covariance matrix. Instead, it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while transforming the signal component in some appropriate manner. We can then eliminate the noise component by forming the difference of the original and transformed covariance matrices. This unique feature of the proposed method allows covariance differencing methods to be applied to a wider class of problems than was previously possible. To illustrate this, we apply the new covariance differencing algorithm to the problems of bearing estimation, resolution of overlapping echos, and transient response analysis. Simulation results are presented for each problem, and the new method's performance is compared to that of conventional methods for solving each respective problem. It is interesting to note that our algorithm eliminates the need for array rotation or translation which is often required for the conventional covariance differencing technique.

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Fourier Transform and Linear Prediction Methods

Led

Gesmar

2007

Encyclopedia of Magnetic Resonance

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On the zeros of the linear prediction-error filter for deterministic signals

Cited by 133 publications

References 9 publications

Application of Linear Prediction for Phase and Magnitude Correction in Partially Acquired MRI

Application of Linear Prediction for Phase and Magnitude Correction in Partially Acquired MRI

A transform-based covariance differencing approach for some classes of parameter estimation problems

Fourier Transform and Linear Prediction Methods

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