Tomas Olofsson

Synthetic aperture imaging using sources with finite aperture: Deconvolution of the spatial impulse response

A method for ultrasonic synthetic aperture imaging using finite-sized transducers is introduced that is based on a compact, linear, discrete model of the ultrasonic measurement system developed using matrix formalism. Using this model a time-domain algorithm for deconvolution of the transducers spatial impulse responses (SIRs) is developed that is based on a minimum mean square error (MMSE) criterion. The algorithm takes the form of a spatiotemporal filter that compensates for the SIRs associated with a finite-sized transducer at every point of the processed image. A major advantage of the proposed method is that it can be used for any transducer, provided that its associated SIRs are known. This is in contrast to the synthetic aperture focusing technique (SAFT), which treats the transducer as a point source. The performance of the method is evaluated with simulations and experiments, performed in water using a linear phased array. The results obtained using the proposed method are compared to those obtained with a classical time-domain SAFT algorithm. For a finite aperture source, it is clearly shown that the resolution obtained using the proposed method is superior to that obtained using the SAFT algorithm.

Synthetic aperture focusing of ultrasonic data from multilayered media using an omega-K algorithm

The synthetic aperture focusing technique (SAFT) is used to create focused images from ultrasound scans. SAFT has traditionally been applied only for imaging in a single medium, but the recently introduced phase shift migration (PSM) algorithm has expanded the use of SAFT to multilayer structures. In this article we present a similar focusing algorithm called multi-layer omega-k (MULOK), which combines PSM and the ω-k algorithm to perform multilayer imaging more efficiently. The asymptotic complexity is shown to be lower for MULOK than for PSM, and this is confirmed by comparing execution times for implementations of both algorithms. To facilitate the complexity analysis, a detailed description of algorithm implementation is included, which also serves as a guide for readers interested in practical implementation. Using data from an experiment with a multilayered structure, we show that there is essentially no difference in image quality between the two algorithms.

Phase shift migration for imaging layered objects and objects immersed in water

This paper proposes the use of phase shift migration for ultrasonic imaging of layered objects and objects immersed in water. The method, which was developed in reflection seismology, is a frequency domain technique that in a computationally efficient way restores images of objects that are isotropic and homogeneous in the lateral direction but inhomogeneous in depth. The performance of the proposed method was evaluated using immersion test data from a block with side-drilled holes with an additional scatterer residing in water. In this way, the methods capability of simultaneously imaging scatterers in different media and at different depths was investigated. The method was also applied to a copper block with flat bottom holes. The results verify that the proposed method is capable of producing high-resolution and lownoise images for layered or immersed objects.

On Time-Domain Model-Based Ultrasonic Array Imaging

This paper treats time-domain model-based Bayesian image reconstruction for ultrasonic array imaging and, in particular, two reconstruction methods are presented. These two methods arc based on a linear model of the array imaging system and they perform compensation in both the spatial and temporal domains using a minimum mean squared error (MMSE) criterion and a maximum a posteriori MAP) estimation approach, respectively. The presented estimators perform compensation for both the electrical and acoustical wave propagation effects for the ultrasonic array system at hand. The estimators also take uncertainties into account, and, by the incorporation of proper prior knowledge, high-contrast superresolution reconstruction results are obtained. The novel nonlinear MAP estimator constrains the scattering amplitudes to be positive, which applies in applications where the scatterers have higher acoustic impedance than the surrounding medium. The linear MMSE and nonlinear MAP estimators are compared to the traditional delay-and-sum (DAS) beamformer with respect to both resolution and signal-to-noise ratio. The algorithms are compared using both simulated and measured data. The results show that the model-based methods can successfully compensate for both side-lobes and grating lobes, and they have a superior temporal and lateral resolution compared to DAS beamforming. The ability of the nonlinear MAP estimator to suppress noise is also superior compared to both the linear MMSE estimator and the DAS beamformer.

Deconvolution and model-based restoration of clipped ultrasonic signals

This paper presents a simple and general approach for deconvolving ultrasonic signals for which some of the samples have been clipped at the maximum and minimum saturation levels of the analog-to-digital converter. Furthermore, it shows how the deconvolution results can be used to restore the clipped amplitudes. By using the presented methods, the artifacts that typically arise when applying standard deconvolution methods on clipped data can be avoided. The deconvolution problem is stated as maximum a posteriori estimation of the reflection sequence under an assumption of uncorrelated Gaussian measurement noise and with the signal clipping explicitly taken into account in the signal generation model. Apart from the exact solution, two simplified approximate solutions are considered. The first approximation leads to solving a quadratic programming problem with inequality constraints and the second yields a simple closed form linear solution. A comparison under varying noise and clipping distortion conditions shows that the exact solution consistently yields the best performance, but the accuracies of both the approximative solutions are almost as good as the exact solution for low clipping distortion levels. At larger distortion levels, only the first approximative solution can compete in accuracy with the exact solution. Signal restoration results using real ultrasonic data further verify the above conclusions.

Maximum a posteriori deconvolution of sparse ultrasonic signals using genetic optimization

Deconvolution of sparse spike sequences has received much attention in the field of seismic exploration. In certain situations in ultrasonic non-destructive testing (NDT) of materials, similar conditions as those found in seismic exploration occur. One example is the problem of detecting disbonds in layered aluminum structures. The reflection sequence convolved with the impulse response of the transducer results in masking closely spaced reflections. Deconvolution of these signals may reveal the reflection sequence and thus make the interpretation easier. In this paper we use the Bernoulli-Gaussian (BG) distribution for modeling the signal generation. This relatively simple model allows maximum a posteriori (MAP) estimation of the reflection sequence. A derivation of the MAP criterion is given for clarity. We propose a genetic algorithm for optimizing the MAP criterion. The genetic algorithm approach is motivated by the fact that the criterion is non-convex, implying that the criterion may have more than one local minimum point. The probability of obtaining the global optimal solution is increased by using the proposed genetic algorithm. One of the key features in genetic algorithms, the so-called cross-over operator, has been modified and adapted to the structure of the BG deconvolution problem to improve the efficiency of the search. The algorithm is tested on simulated data using the probability of detection (PD) and probability of false alarm (PFA) as evaluation criteria. The algorithm is also tested on real ultrasonic data from a layered aluminum structure. The results show considerable improvements in the possibility of interpreting the signals.

Sparse Deconvolution of B-Scan Images

In this paper, a new computationally efficient sparse deconvolution algorithm for the use on B-scan images from objects with relatively few scattering targets is presented. It is based on a linear image formation model that has been used earlier in connection with linear minimum mean squared error (MMSE) two-dimensional (2-D) deconvolution. The MMSE deconvolution results have shown improved resolution compared to synthetic aperture focusing technique (SAFT), but at the cost of increased computation time. The proposed algorithm uses the sparsity of the image, reducing the degrees of freedom in the reconstruction problem, to reduce the computation time and to improve the resolution. The dominating task in the algorithm consists in detecting the set of active scattering targets, which is done by iterating between one up-dating pass that detects new points to include in the set, and a down-dating pass that removes redundant points. In the up-date, a spatio-temporal matched filter is used to isolate potential candidates. A subset of those are chosen using a detection criterion. The amplitudes of the detected scatterers are found by MMSE. The algorithm properties are illustrated using synthetic and real B-scan. The results show excellent resolution enhancement- and noise-suppression capabilities. The involved computation times are analyzed.

Long Term Channel Characterization for Energy Efficient Transmission in Industrial Environments

One of the challenges for a successful use of wireless sensor networks in process industries is to design networks with energy efficient transmission, to increase the lifetime of the deployed network while maintaining the required latency and bit-error rate. The design of such transmission schemes depend on the radio channel characteristics of the region. This paper presents an investigation of the statistical properties of the radio channel in a typical process industry, particularly when the network is meant to be deployed for a long time duration, e.g., days, weeks, and even months. Using 17-20-h-long extensive measurement campaigns in a rolling mill and a paper mill, we highlight the non-stationarity in the environment and quantify the ability of various distributions, given in the literature, to describe the variations on the links. Finally, we analyze the design of an optimal received signal-to-noise ratio (SNR) for the deployed nodes and show that improper selection of the distribution for modeling of the variations in the channel can lead to an overuse of energy by a factor of four or even higher.

Minimum entropy deconvolution of pulse-echo signals acquired from attenuative layered media

In this article deconvolution of ultrasonic pulse-echo data acquired from attenuative layered media is considered. The problem is divided in two subproblems: treating the sparse reflection sequence caused by the layered structure of the media and treating the frequency-dependent attenuation. The first subproblem is solved by means of joint maximum a posteriori estimation of the assumed zero mean, white, nonstationary reflection sequence and its corresponding sequence of unknown standard deviations. This approach leads to an algorithm that seeks minimum entropy solutions for the reflection sequence and therefore the algorithm serves as a novel link between the classical Wiener filter and methods for sparse or minimum entropy deconvolution. The second subproblem is solved by introducing a new signal processing-oriented, linear discrete-time model for frequency-dependent attenuation in isotropic and homogeneous media. The deconvolution algorithm is tested using simulated data and its performance for real normal incidence pulse-echo data from a composite material is also demonstrated. The results show that the algorithm, in combination with the attenuation model, yields estimates that reveal the internal structure of the composite and, thus, simplify the interpretation of the ultrasonic data.

Imaging and suppression of Lamb modes using adaptive beamforming

Lamb waves have proven to be very useful for plate inspection because large areas of a plate can be covered from a fixed position. This capability makes them suitable for both inspection and structural health monitoring (SHM) applications. During the last decade, research on the use of active arrays in combination with beamforming techniques has shown that a fixed array can be used to perform omni-directional monitoring of a plate structure. The dispersion and multiple propagating modes are issues that need to be addressed when working with Lamb waves. Previous work has mainly focused on conventional, delay-and-sum (DAS) beamforming, while reducing the effects of multiple modes through frequency selectivity and transducer design. The paper describes an adaptive beamforming technique using a minimum variance distortionless response beamforming (MVBF) approach for spatial Lamb wave filtering with multiple-transmitter‐multiple-receiver arrays. Dispersion is compensated for by using theoretically calculated dispersion curves. Simulations are used for evaluating the performance of the technique for suppression of interfering Lamb modes, both with and without the presence of mode conversion using different array configurations. A simple simulation model of the plate is used to compare the performance of different sizes of active arrays. An aluminum plate with artificial defects is used for the experimental evaluation. The results show that the MVBF approach performs a lot better in terms of resolution and suppression of interfering modes than the widely used standard beamformer.