Signal-to-Noise Ratios and Effective Repetition Times for Wavelet Encoding and Encoding with Wavelet Packet Bases

Abstract

Wavelet encoding is a method of localizing MR signal. Bands of spins of variable length and position are excited to encode position. Wavelet encoding is a compromise between phase encoding, which excites all the spins with each RF excitation, and line scanning, which excites only one pixel with each RF excitation. Expressions for the SNR are developed. Phase encoding produces optimum SNR, but it has relatively short effective repetition times. Line scanning has poor SNR but has long effective repetition times. Wavelet encoding is generalized to use wavelet packet bases. Wavelet packet bases include a wide class of bases. They include the bases used for Hadamard and phase encoding at one extreme and line scanning at the other. If the appropriate basis is chosen from among the wavelet packet bases, SNR can be freely traded for longer effective repetition times. Several other results are shown; e.g., wavelet encoding is very effective at edge detection in terms of SNR and number of excitations required. In addition, an alternative statistical formulation is introduced that quantifies the bias in the reconstruction. The bias quantifies the sensitivity of each basis to artifacts.