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Poster "Defect Detection from Compressed 3-D Ultrasonic Frequency Measurements", Sebastian Semper, Jan Kirchhof, Christoph Wagner, Fabian Krieg, Florian Römer, Giovanni Del Galdo
In this paper, we propose an efficient matrix-free algorithm to reconstruct locations and size of flaws in a specimen from volumetric ultrasound data by means of a native 3D Sparse Signal Recovery scheme using Orthogonal Matching Pursuit (OMP). The efficiency of the proposed approach is achieved in two ways. First, we formulate the dictionary matrix as a block multilevel Toeplitz matrix to minimize redundancy and thus memory consumption. Second, we exploit this specific structure in the dictionary to speed up the correlation step in OMP, which is implemented matrix-free. We compare our method to state-of-the- art, namely 3D Synthetic Aperture Focusing Technique, and show that it delivers a visually comparable performance, while it gains the additional freedom to use further methods such as Compressed Sensing.
More information at EUSIPCO 2019

Presentation "Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing", Florian Römer
In compressed sensing, the choice of the sensing matrix plays a crucial role: it defines the required hardware effort and determines the achievable recovery performance. Recent studies indicate that by optimizing a sensing matrix, one can potentially improve system performance compared to random ensembles. In this work, we analyze the sensitivity of a sensing matrix design to random perturbations, e.g., caused by hardware imperfections, with respect to the total (average) matrix coherence. We derive an exact expression for the average deterioration of the total coherence in the presence of Gaussian perturbations as a function of the perturbations' variance and the sensing matrix itself. We then numerically evaluate the impact it has on the recovery performance.
More information at EUSIPCO 2018

Poster "Defect Detection from 3D Ultrasonic Measurements Using Matrix-free Sparse Recovery Algorithms"
In this paper, we propose an efficient matrix-free algorithm to reconstruct locations and size of flaws in a specimen from volumetric ultrasound data by means of a native 3D Sparse Signal Recovery scheme using Orthogonal Matching Pursuit (OMP). The efficiency of the proposed approach is achieved in two ways. First, we formulate the dictionary matrix as a block multilevel Toeplitz matrix to minimize redundancy and thus memory consumption. Second, we exploit this specific structure in the dictionary to speed up the correlation step in OMP, which is implemented matrix-free. We compare our method to state-of-the- art, namely 3D Synthetic Aperture Focusing Technique, and show that it delivers a visually comparable performance, while it gains the additional freedom to use further methods such as Compressed Sensing.

Presentation "Design and Prototyping of a 3-D Positioner for Ultrasound Quality Control Measurements", Jan Kirchhof
We describe the development and build-up of a 3-D positioner for ultrasonic testing with single- and multi-element transducers, supporting a scan area of up to 300 × 300 mm. The machine is realized with a delta kinematic using many components from the consumer/maker area. It can be easily mounted onto a water basin, containing the test object to be scanned. Software control is realized via G-code, as popular in CNC. With additional components, the positioner can be re-configured and re-used as a high-quality 3-D printer.
More information at Symposium SHM-NDT 2018

Presentation "GPU-accelerated Matrix-free 3D Reconstruction for Ultrasonic Nondestructive Testing", Jan Kirchhof
In this paper, we propose a matrix-free 3D ultrasonic reconstruction scheme based on the Fast Iterative Shrinkage-Thresholding algorithm (FISTA) implemented on a GPU. The matrix-free implementation allows to reconstruct images even for problem sizes that would be intractable when explicitly calculating the matrix. However, due to the matrix-free implementation, additional steps are necessary to estimate the stepsize parameter required by FISTA, since the optimal stepsize depends on the largest singular value of the operator matrix, which in the matrix-free version is unavailable and cannot be built due to its size. The estimation is performed based on a priori knowledge of the model. We compare our method to 3D SAFT and OMP images of volumetric ultrasound measurement data of a steel specimen to show how FISTA leads to sharper images facilitating sizing and locating of defects within a specimen.
More information at IEEE IUS 2018