In accordance with the present invention, there is provided a method of determining whether a particular high fidelity vibratory seismic survey phase encoding is likely to be a good one based on an analysis of the eigenvalue structure (i.e., eigenvalues, eigenvalue separation, condition number, and model resolution matrix) of a matrix formed from the Fourier transforms of the sweep signals. Preferably, a singular valuedecomposition will be used to calculate the eigenvalues. Using this same approach, the condition number and eigenvalues of matrices that are associated with multiple proposed designs can be compared with each other to determine which is likely to be yield the best seismic data. This approach is preferably used either as a component of the advanced planning for a survey or in the field during pre-survey testing. The use of the instant approach to determine an optimal phase encoding scheme is also taught.
An authenticationsystem using a correlator that correlates an input with a reference wherein at least one of the input and reference comprises a phase volumemask having structures, preferably points, that are each less than about six microns in size and can have an aspect ratio (AR) greater than 1:1 so as to produce a phase encoded random pattern having millions of combinations in a mask that is as small as one square millimeter. The random pattern can be convolved with a second pattern, such as a biometric pattern, to produce a phase convolved mask. The correlator preferably is a nonlinear joint transform correlator that can use “chirp” encoding to permit the input to be located in a different plane than the reference. The correlator optically Fourier transforms images of the reference and input that are thereafter nonlinearly transformed and inverse Fourier transformed by a processor to determine the presence or absence of a correlation spike indicative of authenticity. A spatial light modulator (SLM) can be used as an input or reference and preferably is a liquid crystal panel having pixels or elements whose phase or grey scale intensity can be selectively controlled by a processor. The SLM can be used to display a biometric pattern, preferably scanned in real time from a person, that is correlated against an input or reference that can comprise a label on a card, a tag, or another object.
A system and method for reducing the scan time of an MR imagingsystem using a data acquisition technique that combines partial Fourier acquisition and compressed sensing includes a computer programmed to acquire a partial MR data set in k-space along a phase encoding direction, the data set having missing data in the phase encoding direction due to the omission of phase encoding steps. The computer is further programmed to generate an estimate of a reconstructed image, compensate the partial MR data set for the missing data, and reconstruct an MR image by iteratively minimizing the total squared difference between the k-space data of the estimate of the reconstructed image and the measured k-space data of the compensated partial MR data set.