Том 49, № 5 (2018)

Compressed-sensing magnetic resonance imaging (CSMRI) aims to reconstruct the magnetic resonance (MR) image from highly undersampled K-space data. In order to improve the reconstruction quality of the MR image, this paper proposes a new gradient-based tight frame (TFG) learning algorithm (TFG-MRI) for CSMRI. TFG-MRI effectively integrates the tight frame learning technique and total variation into the same framework. In TFG-MRI, the inherent gradient sparsity of the MR image in gradient domain is utilized to represent the sparse prior knowledge, and the sparse priors in the horizontal and vertical gradient directions are exploited to learn adaptive tight frames for reconstructing the desired images. Particularly, we employ the l₀-norm to promote the sparsity of the gradient image. The sparse representations of TFG are adapted for the horizontal and vertical gradient information of MR images. TFG-MRI can effectively help to capture edge contour structures in the gradient images, and to preserve more detail information of MR images. The experimental results demonstrate that the proposed TFG-MRI can reconstruct MR images more clearly in various sampling schemes. Compared with the existing MR image reconstruction algorithms, TFG-MRI can achieve higher accurate image reconstruction quality and better robustness to noises.

The concentration dependences of self-diffusion coefficient for intrinsically disordered milk protein α_S-casein were studied by pulsed field gradient nuclear magnetic resonance. The experimental data were analyzed in a view of phenomenological approach based on the frictional formalism of non-equilibrium thermodynamics by Vink. The results of α_S-CN hydrodynamic study showed that at low- and high-protein concentrations, α_S-CN exists in the different structural forms. At low concentrations in the rather broad concentration range, protein remains monomeric but with greater hydrodynamic size than have rigid globular proteins of the equal mass. At high concentrations beyond the definite protein content, α_S-CN tends to form associates. The application of the Vink’s approach to α_S-CN testifies that the role of flexible domains in the process of self-diffusion is mainly in increasing the friction of between α_S-CN molecules due to their inter-entanglement. The latter physically means that when α_S-CN molecules cling each other by their flexible domains, this phenomenon provides much more efficient friction than their interaction with solvent molecules.

The article describes experiments on the simultaneous recording nuclear magnetic resonance signals from two nuclei with different gyromagnetic ratios—¹H and ¹⁹F, ¹³C and ²³Na. It is shown that large frequency detunings or/and low sampling rates are not an obstacle to their realization even in a relatively weak (0.5 T) field. We use undersampling technique when registering the response of the spin system. In this case, the sampling frequency is much less than the distance between the Larmor frequencies for the indicated nuclear pairs. It gives the effect of multiple aliasing. Fourier processing of the response produces a spectrum consisting of two subspectra, each of which corresponds to specific nucleus of the investigated pair. The subordination of the spectral peaks in each subspectrum is the same as the spectrum obtained by the usual way. Two variants of the radio-frequency excitation of the spin system (single and double pulse) are considered. A formula for calculating the excitation frequency and sampling rate, which ensures a rational distribution of the lines in the hybrid spectrum, is proposed.

Nuclear magnetic resonance relaxometry measurements are frequently used to quantify sample constituents. The standard approach for quantification involves converting the time-domain data to a distribution of characteristic times, either by fitting a fixed number of exponentials or performing an inverse Laplace transform, and then integrating the area under the peaks. We evaluated an alternative method to quantify relaxometry data. Partial least squares (PLS) analysis was applied directly to a variety of simulated time-domain relaxation data under diverse conditions to predict constituent content and results were compared to the standard analysis methods. For many situations, PLS analysis displayed superior performance for quantification than the standard analyses. The technique consistently produced better predictions at lower signal to noise. This robustness to noise makes it an appealing alternative for analysing data from applications that typically have low SNR, such as one-sided sensors, surface measurements, or well-logging. The method also enabled quantification of relaxation rates too close to be separated by an inverse Laplace transform. This capability may allow quantification to be performed using only one-dimensional relaxation data where multi-dimensional measurements were previously necessary to provide constituent separation. The method also enabled quantification of relaxometry data without the need for human interpretation or prior knowledge of what relaxation time is associated with a given constituent. These advantages make PLS analysis an appealing alternative for quantification of relaxometry data in many situations.