Goodness-of-Fit Analysis of Radial Velocity Surveys.

Using eigenmode expansion of the Mark III and SFI surveys of cosmological radial velocities, a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements the Bayesian maximum likelihood analysis that finds the most probable model given the data. Analyzing the surveys with their corresponding most likely models from the CMB-like family of models, as well as with the currently popular LambdaCDM model, reveals a systematic inconsistency of the data with these "best" models. There is a systematic trend of the cumulative chi(2) to increase with the mode number (where the modes are sorted by decreasing order of the eigenvalues). This corresponds to a decrease of the chi(2) with the variance associated with a mode and hence with its effective scale. It follows that the differential analysis finds that on small (large) scales the global analysis of all the modes "puts" less (more) power than actually required by the data. This observed trend might indicate one of the following: (1) the theoretical model (i.e., power spectrum) or the error model (or both) have an excess of power on large scales, (2) velocity bias, or (3) the velocity data suffers from systematic errors that have not yet been corrected.

Complex denoising of MR data via wavelet analysis: application for functional MRI.

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.