Camer-Rao Lower Bound Analysis Of 1H Magnetic Resonance Spectroscopic Imaging for Breast With Singular Value Decomposition Method And Linear Combination Method
W Feng1, A Chu2, Y Xuan3, J Hu4*, (1) New York Presbyterian Hospital, New York, NY, (2) Yale New Haven Hospital, New Haven, CT, (3, 4) Wayne State University, Detroit, MITU-G-217A-8 Tuesday 4:30:00 PM - 6:00:00 PM Room: 217A
To study the Singular Value Decomposition (SVD) and Linear Combination (LC) quantification with Camer-Rao Lower Bound (CRLB) analysis.
In-house Singular Value Decomposition (SVD) and LC program was developed with Matlab version 7.6 (Mathworks.com). Hankel SVD method (singular value decomposition of the acquired FID signal arranged in a Hankel matrix) is used to compute the signal poles and amplitude, and from them the signal frequencies and damping factors. In LC method, poles are generated from SVD analysis of averaged 10 FID, the amplitudes of the signal components were estimated by the least square method for individual FID signal. The estimated FID signals are constructed from the quantification parameters, residue error spectrum was calculated by FFT of the difference of original FID and estimated FID.
In order to study the CR lower bound, known simulated spectrum without noise was analyzed with SVD and LC method. Then introduce random noise, quantification residue was analyzed, and estimated parameters with CRLB were compared with results without noise.
CRLB estimation is verified with the standard deviation calculation, CRLB is larger than and comparable to standard deviation.
For small signal as low as 1.5% of maximum, SVD can detect at SNR 10, LC can handle SNR 5. For SNR 5, SVD can reliably detect signal like 12.5% of maximum.
Typical patient data from breast tumor data was analyzed with SVD and LC methods too, results are reliable and consistent.
CRLB estimation is verified with the standard deviation calculation. Both SVD and LC method can be used for human MRSI, the SVD method is sensitive to noise, since it has no prior knowledge to reduce noise; if noise is larger than signal, fake peak can be introduced. LC method combined with SVD generated poles can be exploited in MRSI with best results.