Complex Wavelet transform for MRI

Full text: There is a perpetual compromise encountered in magnetic resonance (MRl) image reconstruction, between the traditional elements of image quality (noise, spatial resolution and contrast). Additional factors exacerbating this trade-off include various artifacts, computational (and hence time-dependent) overhead, and financial expense. This paper outlines a new approach to the problem of minimizing MRI image acquisition and reconstruction time without compromising resolution and noise reduction. The standard approaches for reconstructing magnetic resonance (MRI) images from raw data (which rely on relatively conventional signal processing) have matured but there are a number of challenges which limit their use. A major one is the 'intrinsic' signal-to-noise ratio (SNR) of the reconstructed image that depends on the strength of the main field. A typical clinical MRI almost invariably uses a super-cooled magnet in order to achieve a high field strength. The ongoing running cost of these super-cooled magnets prompts consideration of alternative magnet systems for use in MRIs for developing countries and in some remote regional installations. The decrease in image quality from using lower field strength magnets can be addressed by improvements in signal processing strategies. Conversely, improved signal processing will obviously benefit the current conventional field strength MRI machines. Moreover, the 'waiting time' experienced in many MR sequences (due to the relaxation time delays) can be exploited by more rigorous processing of the MR signals. Acquisition often needs to be repeated so that coherent averaging may partially redress the shortfall in SNR, at the expense of further delay. Wavelet transforms have been used in MRI as an alternative for encoding and denoising for over a decade. These have not supplanted the traditional Fourier transform methods that have long been the mainstay of MRI reconstruction, but have some inflexibility. The dual-tree complex wavelet transform (DTCWT) is an example of an over-complete or expansive wavelet transform. Compared with the Discrete Wavelet Transform it has the advantage of spatial invariance and directional selectivity though with greater computational burden. This processing load can be redressed by hardware approaches if necessary. It has recently been used for diffusion tensor imaging, but it has yet to be determined if it is optimal for the particular noise characteristics encountered in MRI (typically Rician-distributed amplitude distribution at low SNR, and with a 1/f, rather than exclusively white, spectral density suggested for some modalities). The complex wavelet transform offers a new possibility for MRI processing: the improved spatial invariance and directional selectivity promising both shorter overall acquisition time and improved image quality. Copyright (2004) Australasian College of Physical Scientists and Engineers in Medicine