Abstract: The discrete inverse scattering (DIST) approach is used to design selective RF pulses. As in SLR, a hard pulse approximation is used to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. The reflection coefficient is approximated in order to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, direct control on the phase of the magnetization profile is retained throughout the design process. Explicit recursive algorithms are provided for computing the hard pulse from the inverse scattering data. These algorithms are essentially discretizations of the Marchenko equations. When bound states are present, both the left and right Marchenko equations are used in order to improve the numerical stability of the algorithm.

Abstract: Methods for providing practical magnetic resonance imaging systems that utilize non-homogeneous background fields, B0, as well as, possibly non-linear, gradient fields G1, G2 to make non-invasive measurements to determine, among other things, a spin density function. Two types of non-homogeneous background fields are considered: background fields B0 in which the function |B0| does not have a critical point within the field of view, and background fields B0 such that the function |B0| has a single critical point within the field of view. In the first case, an MR-imaging device may be constructed by using the permanent gradient in the background field, B0, as a slice select gradient, so long as particular criteria are met. In the second case, magnets may be constructed so that |B0| has an isolated non-zero local minimum. Using selective excitation, one can excite only the spins lying in a small neighborhood of this local minimum.

Abstract: A method of obtaining an arbitrary, admissible transverse magnetization profile as the summed response of two, self refocused selective “half pulse” excitations for use in, e.g., magnetic resonance imaging pulse generation. The problem of finding the pair of half pulses is rephrased in the inverse scattering formalism and a simple closed form algorithm for the solution is given, provided the target transverse profile has constant phase (modulo 180°). The problem has a unique low energy solution for sufficiently small, complex valued data, and an algorithm for finding the solution is provided. This solution is used to generate pairs of half pulses for given target transverse profiles.

Abstract: Methods for providing practical magnetic resonance imaging systems that utilize non-homogeneous background fields, B0, as well as, possibly non-linear, gradient fields G1, G2 to make non-invasive measurements to determine, among other things, a spin density function. These methods are time and SAR efficient, using one or two refocusing pulses for each line measured in k-space. Two types of non-homogeneous background fields are considered: background fields B0 in which the function |B0| does not have a critical point within the field of view, and background fields B0 such that the function |B0| has a single critical point within the field of view. In the first case, an MR-imaging device may be constructed by using the permanent gradient in the background field, B0, as a slice select gradient, so long as particular criteria are met. The methods demonstrate that there are many practical circumstances where these criteria can all be met.

Abstract: The discrete inverse scattering (DIST) approach is used to design selective RF pulses. As in SLR, a hard pulse approximation is used to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. The reflection coefficient is approximated in order to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, direct control on the phase of the magnetization profile is retained throughout the design process. Explicit recursive algorithms are provided for computing the hard pulse from the inverse scattering data. These algorithms are essentially discretizations of the Marchenko equations. When bound states are present, both the left and right Marchenko equations are used in order to improve the numerical stability of the algorithm.

Abstract: The discrete inverse scattering (DIST) approach is used to design selective RF-pulses. As in SLR, a hard pulse approximation is used to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. The reflection coefficient is approximated in order to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, direct control on the phase of the magnetization profile is retained throughout the design process. Explicit recursive algorithms are provided for computing the hard pulse from the inverse scattering data. These algorithms are essentially discretizations of the Marchenko equations. When bound states are present, both the left and right Marchenko equations are used in order to improve the numerical stability of the algorithm.

Abstract: A method of obtaining an arbitrary, admissible transverse magnetization profile as the summed response of two, self refocused selective “half pulse” excitations for use in, e.g., magnetic resonance imaging pulse generation. The problem of finding the pair of half pulses is rephrased in the inverse scattering formalism and a simple closed form algorithm for the solution is given, provided the target transverse profile has constant phase (modulo 180°). The problem has a unique low energy solution for sufficiently small, complex valued data, and an algorithm for finding the solution is provided. This solution is used to generate pairs of half pulses for given target transverse profiles.

Abstract: The discrete inverse scattering (DIST) approach is used to design selective RF-pulses. As in SLR, a hard pulse approximation is used to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. The reflection coefficient is approximated in order to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, direct control on the phase of the magnetization profile is retained throughout the design process. Explicit recursive algorithms are provided for computing the hard pulse from the inverse scattering data. These algorithms are essentially discretizations of the Marchenko equations. When bound states are present, both the left and right Marchenko equations are used in order to improve the numerical stability of the algorithm.