Using the boxcar representation in the spatial domain and a signal-space representation of its frequency-weighted

Phase errors in MRI can result from off resonance effects due to imperfections of the static magnetic field or significant changes in the susceptibility within the imaged field-of-view (FOV) [

For real data, phase errors are shown to arise from main field inhomogeneities which is caused by bone-air-tissue interface (also known as susceptibility effects). Apart from phase error, imposition of temporally constrained acquisition, or acquisition of incomplete set of phase-encodes can result in truncation effects [

In the first group of methods, a narrow strip of data having symmetric phase-encode coverage is selected to provide a low-resolution approximation of the spatial phase variation. With the acquired data consisting of the entire set of positive phase-encodes, the region of this symmetric phase-encode coverage includes the set of fractional lines in the negative phase-encode region. The phase of this low-resolution data is then used for phase correction. In the homodyne method [

One reason that partial Fourier reconstruction algorithms are not as successful in practice as in theory is associated with distortions introduced during the phase correction. Multiplying an image with a phase correction in the spatial domain is equivalent to circularly convolving the spatial frequency domain with FT of the correction factor. Many of the points in the corrected

The effect of phase correction using homodyne method is illustrated using magnitude and phase images of Susceptibility Weighted Image (SWI) shown in Figure

Structural distortion with homodyne phase correction applied to SWI data. (a) Magnitude and phase images reconstructed from full

In this paper, we address the problem of improving the efficiency of low-resolution phase correction by combining the same with a model-based approach. Using this model, signal samples in the unacquired higher phase-encode regions are predicted without introducing artifacts in the reconstructed image. Prior to introducing the details of the proposed method in Section

In model-based methods, extrapolation of missing

The following sections describe the mathematical background required for understanding the algorithms used for partial

Consider a tissue having proton density distribution

Using the boxcar representation [

Using the differentiation property of FT, the Transform of the spatial derivative

The prediction coefficients

Using the filter coefficients, the next sample in the higher phase-encode line is predicted using (

Partial

The next section describes how the Levinson algorithm applied to frequency-weighted

As the algorithm is iterated through a larger number of steps, the nonregular component of prediction error will introduce artifacts in both the magnitude and phase of the reconstructed image. Increase in the number of steps implies prediction in the higher frequency region of the

Phase error compensation using iterated prediction.

As discussed in the previous section, a low-resolution approximation of the predicted

The subspace projection approach is found to work well in sparse MR images. Sparsity means that there are only few significant pixels with nonzero values [

The dataset consisting of the positive phase-encode steps at a given location along frequency encode axis is first distributed into an

This section includes illustrations using

SWI provides a high resolution mapping of the brain’s venous vasculature. It combines the phase and magnitude data to generate an image whose contrast is sensitive to venous blood and iron content. When all data samples from full

Phase correction using iterated prediction applied to SWI data. (a) Top panel: magnitude image reconstructed using homodyne phase correction applied to 2D partial

Figures

Subspace projection applied to GE DQA phantom. (a1)–(a3) Sketch of 2D partial

Subspace projection applied to MR angiogram. (a1)–(a3) Sketch of 2D partial

This work presents FIR filters for reduction of artifacts and phase errors resulting from truncation of conjugate asymmetric

When the number of fractional lines acquired is less compared to the number of lines available in the energy-concentric regions, the resulting intensity distortion can smear intensity variations in areas with steep phase transitions. In this paper, we have developed a linear prediction based