Subsampling Approaches for Compressed Sensing with Ultrasound Arrays in Non-Destructive Testing.

Full Matrix Capture is a multi-channel data acquisition method which enables flexible, high resolution imaging using ultrasound arrays. However, the measurement time and data volume are increased considerably. Both of these costs can be circumvented via compressed sensing, which exploits prior knowledge of the underlying model and its sparsity to reduce the amount of data needed to produce a high resolution image. In order to design compression matrices that are physically realizable without sophisticated hardware constraints, structured subsampling patterns are designed and evaluated in this work. The design is based on the analysis of the Cramér-Rao Bound of a single scatterer in a homogeneous, isotropic medium. A numerical comparison of the point spread functions obtained with different compression matrices and the Fast Iterative Shrinkage/Thresholding Algorithm shows that the best performance is achieved when each transmit event can use a different subset of receiving elements and each receiving element uses a different section of the echo signal spectrum. Such a design has the advantage of outperforming other structured patterns to the extent that suboptimal selection matrices provide a good performance and can be efficiently computed with greedy approaches.

Self-assembly of smallest magnetic particles.

The assembly of tiny magnetic particles in external magnetic fields is important for many applications ranging from data storage to medical technologies. The development of ever smaller magnetic structures is restricted by a size limit, where the particles are just barely magnetic. For such particles we report the discovery of a kind of solution assembly hitherto unobserved, to our knowledge. The fact that the assembly occurs in solution is very relevant for applications, where magnetic nanoparticles are either solution-processed or are used in liquid biological environments. Induced by an external magnetic field, nanocubes spontaneously assemble into 1D chains, 2D monolayer sheets, and large 3D cuboids with almost perfect internal ordering. The self-assembly of the nanocubes can be elucidated considering the dipole-dipole interaction of small superparamagnetic particles. Complex 3D geometrical arrangements of the nanodipoles are obtained under the assumption that the orientation of magnetization is freely adjustable within the superlattice and tends to minimize the binding energy. On that basis the magnetic moment of the cuboids can be explained.

Element-specific magnetic hysteresis of individual 18 nm Fe nanocubes.

Correlating the electronic structure and magnetic response with the morphology and crystal structure of the same single ferromagnetic nanoparticle has been up to now an unresolved challenge. Here, we present measurements of the element-specific electronic structure and magnetic response as a function of magnetic field amplitude and orientation for chemically synthesized single Fe nanocubes with 18 nm edge length. Magnetic states and interactions of monomers, dimers, and trimers are analyzed by X-ray photoemission electron microscopy for different particle arrangements. The element-specific electronic structure can be probed and correlated with the changes of magnetic properties. This approach opens new possibilities for a deeper understanding of the collective response of magnetic nanohybrids in multifunctional materials and in nanomagnetic colloidal suspensions used in biomedical and engineering technologies.

Frequency Subsampling of Ultrasound Nondestructive Measurements: Acquisition, Reconstruction, and Performance.

In ultrasound nondestructive testing (NDT), a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using the synthetic aperture focusing technique (SAFT). However, SAFT is suboptimal in terms of resolution and requires oversampling in the time domain to obtain a fine grid for the delay-and-sum (DAS). On the other hand, parametric reconstruction algorithms give better resolution, but their usage for imaging becomes computationally expensive due to the size of the parameter space and a large amount of measurement data in realistic 3-D scenarios when using oversampling. In the literature, the remedies to this are twofold. First, the amount of measurement data can be reduced using state-of-the-art sub-Nyquist sampling approaches to measure Fourier coefficients instead of time-domain samples. Second, parametric reconstruction algorithms mostly rely on matrix-vector operations that can be implemented efficiently by exploiting the underlying structure of the model. In this article, we propose and compare different strategies to choose the Fourier coefficients to be measured. Their asymptotic performance is compared by numerically evaluating the Cramér-Rao bound (CRB) for the localizability of the defect coordinates. These subsampling strategies are then combined with an l1 -minimization scheme to compute 3-D reconstructions from the low-rate measurements. Compared to conventional DAS, this allows us to formulate a fully physically motivated forward model matrix. To enable this, the projection operations of the forward model matrix are implemented matrix-free by exploiting the underlying two-level Toeplitz structure. Finally, we show that high-resolution reconstructions from as low as a single Fourier coefficient per A-scan are possible based on simulated data and measurements from a steel specimen.

A guideline for atomistic design and understanding of ultrahard nanomagnets.

Magnetic nanoparticles are of immense current interest because of their possible use in biomedical and technological applications. Here we demonstrate that the large magnetic anisotropy of FePt nanoparticles can be significantly modified by surface design. We employ X-ray absorption spectroscopy offering an element-specific approach to magnetocrystalline anisotropy and the orbital magnetism. Experimental results on oxide-free FePt nanoparticles embedded in Al are compared with large-scale density functional theory calculations of the geometric- and spin-resolved electronic structure, which only recently have become possible on world-leading supercomputer architectures. The combination of both approaches yields a more detailed understanding that may open new ways for a microscopic design of magnetic nanoparticles and allows us to present three rules to achieve desired magnetic properties. In addition, concrete suggestions of capping materials for FePt nanoparticles are given for tailoring both magnetocrystalline anisotropy and magnetic moments.