Partial Fourier reconstruction algorithms exploit the redundancy in magnetic resonance data sets so that half of the data is calculated during image reconstruction rather than acquired. The conjugate synthesis, Margosian, homodyne detection, Cuppen and POCS algorithms are evaluated using spatial frequency domain analysis to show their characteristics and where limitations may occur. The phase correction used in partial Fourier reconstruction is equivalent to a convolution in the frequency domain and the importance of accurately implementing this convolution is demonstrated. New reconstruction approaches, based on passing the partial data through a phase correcting, finite impulse response (FIR), digital filter are suggested. These FIR and MoFIR algorithms have a speed near that of the Margosian and homodyne detection reconstructions, but with a lower error; close to that of the Cuppen/POCS iterative approaches. Quantitative analysis of the partial Fourier algorithms, tested with three phase estimation techniques, are provided by comparing artificial and clinical data reconstructed using full and partial Fourier techniques.
Estimating the true signal-to-noise ratio (SNR) of magnetic resonance (MR) images with low signal is confounded by the magnitude presentation of the data. This paper suggests a simple solution to this problem. A common method of measuring SNR compares the mean signal to the standard deviation of the noise. This SNR measure was found to be satisfactory for high but not low signal-to-noise image regions because of noise bias. These inconsistencies are removed by introducing unbiased definitions of the signal and noise levels in terms of their root-mean-square values. The approaches are compared by evaluating the SNR values for MR medical images.
In this paper we propose an architecture for the implementation of fault-tolerant computation within a high throughput multirate equalizer for an asymmetrical wireless LAN. The area overhead is minimized by exploiting the algebraic structure of the Modulus Replication Residue Number System (MRRNS). We demonstrate that for our system the area cost to correct a fault in a single computational channel is 82.7%. Generalized results for single error correction showing significant area savings are also presented.
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