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1.
Sensors (Basel) ; 24(7)2024 Apr 02.
Artículo en Inglés | MEDLINE | ID: mdl-38610476

RESUMEN

The advancement of unmanned aerial vehicles (UAVs) enables early detection of numerous disasters. Efforts have been made to automate the monitoring of data from UAVs, with machine learning methods recently attracting significant interest. These solutions often face challenges with high computational costs and energy usage. Conventionally, data from UAVs are processed using cloud computing, where they are sent to the cloud for analysis. However, this method might not meet the real-time needs of disaster relief scenarios. In contrast, edge computing provides real-time processing at the site but still struggles with computational and energy efficiency issues. To overcome these obstacles and enhance resource utilization, this paper presents a convolutional neural network (CNN) model with an early exit mechanism designed for fire detection in UAVs. This model is implemented using TSMC 40 nm CMOS technology, which aids in hardware acceleration. Notably, the neural network has a modest parameter count of 11.2 k. In the hardware computation part, the CNN circuit completes fire detection in approximately 230,000 cycles. Power-gating techniques are also used to turn off inactive memory, contributing to reduced power consumption. The experimental results show that this neural network reaches a maximum accuracy of 81.49% in the hardware implementation stage. After automatic layout and routing, the CNN hardware accelerator can operate at 300 MHz, consuming 117 mW of power.

2.
Magn Reson Med ; 81(2): 1434-1446, 2019 02.
Artículo en Inglés | MEDLINE | ID: mdl-30260501

RESUMEN

PURPOSE: An "RF-penetrable" PET insert that allows the MR body coil to be used for RF transmission was developed to make it easier for an existing MR center to achieve simultaneous PET/MRI. This study focuses on experiments and analyses to study PET/RF coil configurations for simultaneous PET/MR studies. METHODS: To investigate the appropriate RF coil design, a transmit/receive (TX/RX) birdcage coil and an RX-only phased-array coil (TX from body coil), both fitting inside the PET ring were built and characterized. For MR performance evaluation, B1 field uniformity and MR image SNR were calculated. PET photon attenuation due to each coil was studied by means of CT-based attenuation maps and reconstructed PET images. RESULTS: When using the RX-only phased-array coil (TX from body coil), compared with the TX/RX birdcage coil, the B1 field uniformity and the MR image (gradient echo and fast spin echo) SNR increased by 2.4±4.8%, 386.1±62.3%, and 205.0±56.5%, respectively. Although some components of the coil were distributed within the PET FOV, no significant PET photon attenuation was shown in the CT-based attenuation map and reconstructed PET images. CONCLUSION: RF coil configurations for an RF-penetrable PET insert for simultaneous PET/MRI were studied. The RX-only phased-array coil (TX from body coil) outperformed the TX/RX birdcage coil with improved MR performance as well as negligible PET photon attenuation.


Asunto(s)
Procesamiento de Imagen Asistido por Computador/métodos , Imagen por Resonancia Magnética/instrumentación , Tomografía de Emisión de Positrones/instrumentación , Ondas de Radio , Diseño de Equipo , Humanos , Imagen Multimodal/instrumentación , Fantasmas de Imagen , Fotones , Reproducibilidad de los Resultados , Relación Señal-Ruido
3.
Magn Reson Med ; 79(3): 1745-1752, 2018 03.
Artículo en Inglés | MEDLINE | ID: mdl-28585334

RESUMEN

PURPOSE: Magnetic resonance-compatible medical devices operate within the MR environment while benefitting from the superior anatomic information of MRI. Avoiding electromagnetic interference between such instrumentation and the MR system is crucial. In this work, various shielding configurations for positron emission tomography (PET) detectors were studied and analyzed regarding radiofrequency (RF) shielding effectiveness and gradient-induced eddy current performances. However, the results of this work apply to shielding considerations for any MR-compatible devices. METHODS: Six shielding enclosure configurations with various thicknesses, patterns, and materials were designed: solid and segmented copper, phosphor bronze mesh (PBM), and carbon fiber composite (CFC). A series of tests was performed on RF shielding effectiveness and the gradient-induced eddy current. RESULTS: For the shielding effectiveness, the solid copper with various thickness and PBM configurations yield significantly better shielding effectiveness (>15 dB) compared with CFC and segmented configurations. For the gradient-induced eddy current performance, the solid copper shielding configurations with different thicknesses showed significantly worse results, up to a factor of 3.89 dB, compared with the segmented copper, PBM, and the CFC configurations. CONCLUSIONS: We evaluated the RF shielding effectiveness and the gradient-induced eddy current artifacts of several shielding designs, and only the PBM showed positive outcomes for both aspects. Magn Reson Med 79:1745-1752, 2018. © 2017 International Society for Magnetic Resonance in Medicine.


Asunto(s)
Imagen por Resonancia Magnética/instrumentación , Imagen por Resonancia Magnética/métodos , Cobre/química , Diseño de Equipo , Humanos , Fantasmas de Imagen , Tomografía de Emisión de Positrones/métodos , Ondas de Radio
4.
Phys Med Biol ; 69(18)2024 Sep 09.
Artículo en Inglés | MEDLINE | ID: mdl-39168156

RESUMEN

Simultaneous positron emission tomography (PET)/magnetic resonance imaging provides concurrent information about anatomic, functional, and molecular changes in disease. We are developing a second generation MR-compatible RF-penetrable TOF-PET insert. The insert has a smaller scintillation crystal size and ring diameter compared to clinical whole-body PET scanners, resulting in higher spatial resolution and sensitivity. This paper reports the initial system performance of this full-ring PET insert. The global photopeak energy resolution and global coincidence time resolution, 11.74 ± 0.03 % FWHM and 238.1 ± 0.5 ps FWHM, respectively, are preserved as we scaled up the system to a full ring comprising 12, 288 LYSO-SiPM channels (crystal size: 3.2 × 3.2 × 20 mm3). Throughout a ten-hour experiment, the system performance remained stable, exhibiting a less than 1% change in all measured parameters. In a resolution phantom study, the system successfully resolved all 2.8 mm diameter rods, achieving an average VPR of 0.28 ± 0.08 without TOF and 0.24 ± 0.07 with TOF applied. Moreover, the implementation of TOF in the Hoffman phantom study also enhanced image quality. Initial MR compatibility studies of the full PET ring were performed with it unpowered as a milestone to focus on looking for material and geometry-related artifacts. During all MR studies, the MR body coil functioned as both the transmit and receive coil, and no observable artifacts were detected. As expected, using the body coil also as the RF receiver, MR image signal-to-noise ratio exhibited degradation (∼30%), so we are developing a high quality receive-only coil that resides inside the PET ring.


Asunto(s)
Encéfalo , Imagen por Resonancia Magnética , Fantasmas de Imagen , Tomografía de Emisión de Positrones , Tomografía de Emisión de Positrones/instrumentación , Imagen por Resonancia Magnética/instrumentación , Encéfalo/diagnóstico por imagen , Ondas de Radio , Imagen Multimodal/instrumentación , Factores de Tiempo , Procesamiento de Imagen Asistido por Computador/métodos , Humanos
5.
Phys Med Biol ; 68(13)2023 Jun 30.
Artículo en Inglés | MEDLINE | ID: mdl-37321248

RESUMEN

Objective. This study aims to evaluate radiofrequency (RF) shielding effectiveness (SE), gradient-induced eddy current, magnetic resonance (MR) susceptibility, and positron emission tomography (PET) photon attenuation of six shielding materials: copper plate, copper tape, carbon fiber fabric, stainless steel mesh, phosphor bronze mesh, and a spray-on conductive coating.Approach. We evaluated the six shielding materials by implementing them on identical clear plastic enclosures. We measured the RF SE and eddy current in benchtop experiments (outside of the MR environment) and in a 3T MR scanner. The magnetic susceptibility performance was evaluated in the same MR scanner. Additionally, we measured their effects on PET detectors, including global coincidence time resolution, global energy resolution, and coincidence count rate.Main results. The RF SEs for copper plate, copper tape, carbon fiber fabric, stainless steel mesh, phosphor bronze mesh, and conductive coating enclosures were 56.8 ± 5.8, 63.9 ± 4.3, 33.1 ± 11.7, 43.6 ± 4.5, 52.7 ± 4.6, and 47.8 ±7.1 dB, respectively, in the benchtop experiment. Copper plate and copper tape experienced the most eddy current at 10 kHz in the benchtop experiment and also generated the largest ghosting artifacts in the MR scanner. Stainless steel mesh had the highest mean absolute difference (7.6 ±0.2 Hz) compared to the reference in the MR susceptibility evaluation. The carbon fiber fabric and phosphor bronze mesh enclosures caused the largest photon attenuation, reducing the coincidence count rate by 3.3%, while the rest caused less than 2.6%.Significance. The conductive coating proposed in this study is shown to be a high-performance Faraday cage material for PET/MRI applications based on its overall performance in all the experiments conducted in this study, as well as its ease and flexibility of manufacturing. As a result, it will be selected as the Faraday cage material for our second-generation MR-compatible PET insert.


Asunto(s)
Cobre , Acero Inoxidable , Fibra de Carbono , Fantasmas de Imagen , Tomografía de Emisión de Positrones/métodos , Imagen por Resonancia Magnética/métodos
6.
Med Phys ; 50(6): 3389-3400, 2023 Jun.
Artículo en Inglés | MEDLINE | ID: mdl-36912373

RESUMEN

BACKGROUND: Simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) has shown promise in acquiring complementary multiparametric information of disease. However, designing these hybrid imaging systems is challenging due to the propensity for mutual interference between the PET and MRI subsystems. Currently, there are integrated PET/MRI systems for clinical applications. For neurologic imaging, a brain-dedicated PET insert provides superior spatial resolution and sensitivity compared to body PET scanners. PURPOSE: Our first-generation prototype brain PET insert ("PETcoil") demonstrated RF-penetrability and MR-compatibility. In the second-generation PETcoil system, all analog silicon photomultiplier (SiPM) signal digitization is moved inside the detectors, which results in substantially better PET detector performance, but presents a greater technical challenge for achieving MR-compatibility. In this paper, we report results from MR-compatibility studies of two fully assembled second-generation PET insert detector modules. METHODS: We studied the effect of the presence of the two second-generation TOF-PET insert detectors on parameters that affect MR image quality and evaluated TOF-PET detector performance under different MRI pulse sequence conditions. RESULTS: With the presence of operating PET detectors, no RF noise peaks were induced in the MR images, but the relative average noise level was increased by 15%, which led to a 3.1 to 4.2-dB degradation in MR image signal-to-noise ratio (SNR). The relative homogeneity of MR images degraded by less than 1.5% with the two operating TOF-PET detectors present. The reported results also indicated that ghosting artifacts (percent signal ghosting (PSG) ⩽ 1%) and MR susceptibility artifacts (0.044 ppm) were insignificant. The PET detector data showed a relative change of less than 5% in detector module performance between running outside and within the MR bore under different MRI pulse sequences except for energy resolution in EPI sequence (13% relative difference). CONCLUSIONS: The PET detector operation did not cause any significant artifacts in MR images and the performance and time-of-flight (TOF) capability of the former were preserved under different tested MR conditions.


Asunto(s)
Imagen por Resonancia Magnética , Imagen Multimodal , Imagen por Resonancia Magnética/métodos , Imagen Multimodal/métodos , Tomografía de Emisión de Positrones/métodos , Encéfalo/diagnóstico por imagen , Relación Señal-Ruido , Fantasmas de Imagen
7.
Phys Med Biol ; 68(8)2023 04 05.
Artículo en Inglés | MEDLINE | ID: mdl-36913739

RESUMEN

Objective. We are developing a portable, 'RF-penetrable', brain-dedicated time of flight (TOF)-PET insert (PETcoil) for simultaneous PET/MRI.Approach. In this paper, we evaluate the PET performance of two fully assembled detector modules for this insert design outside the MR room.Main results. The global coincidence time resolution, global 511 keV energy resolution, coincidence count rate, and detector temperature achieved over 2 h data collection were 242.2 ± 0.4 ps full width at half maximum (FWHM), 11.19% ± 0.02% FWHM, 22.0 ± 0.1 kcps, and 23.5 °C ± 0.3 °C, respectively. The intrinsic spatial resolutions in the axial and transaxial directions were 2.74 ± 0.01 mm FWHM and 2.88 ± 0.03 mm FWHM, respectively.Significance. These results demonstrate excellent TOF capability and the performance and stability necessary for scaling up to a full ring comprising 16 detector modules.


Asunto(s)
Encéfalo , Imagen por Resonancia Magnética , Imagen por Resonancia Magnética/métodos , Encéfalo/diagnóstico por imagen , Tomografía de Emisión de Positrones/métodos , Fantasmas de Imagen , Temperatura
8.
IEEE Trans Radiat Plasma Med Sci ; 2(5): 422-431, 2018 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-30911706

RESUMEN

Hybrid positron emission tomography (PET)/magnetic resonance imaging (MRI) has risen to the cutting edge of medical imaging technology as it allows simultaneous acquisition of structural, functional and molecular information of the patient. A PET insert that can be installed into existing MR systems can in principle reduce the cost barriers for an existing MR site to achieve simultaneous PET/MRI compared to procuring an integrated PET+MRI system. The PET insert systems developed so far for PET/MRI require the RF transmitter coil to reside inside the PET ring as those PET inserts block the RF fields from the MRI system. Here we report for the first time on the performance of a full-ring brain-sized "RF-penetrable" PET insert we have recently completed. This insert allows the RF fields generated by the built-in body coil to penetrate the PET ring. The PET insert comprises a ring of 16 detector modules employing electro-optical coupled signal transmission and a multiplexing framework based on compressed sensing. Energy resolution, coincidence timing resolution (CTR), photopeak position, and coincidence count rate were acquired outside and inside a 3-Tesla MRI system under simultaneous acquisition to evaluate the impact of MRI on the PET performance. Coincidence count rate performance was evaluated by acquiring a cylinder source with high initial activity decaying over time. Tomographic imaging of two phantoms, a custom 6.5-cm diameter resolution phantom with hot rods of four different sizes (2.8 mm, 3.2 mm, 4.2 mm, and 5.2 mm diameter) and a 3D Hoffman brain phantom, were performed to evaluate the imaging capability of the PET insert. The energy resolution at 511 keV and CTR acquired by the PET insert were 16.2±0.1% and 5.3±0.1 ns FWHM, respectively, and remained stable during MRI operation except when the EPI sequence was applied. The PET system starts to show saturation in coincidence count rate at 2.76 million photon counts per second. Most of the 2.8-mm diameter hot rods and main features of the 3D Hoffman brain phantom were resolved by the PET insert, demonstrating its high spatial resolution and capability to image a complex tracer distribution mimicking that seen in the human brain.

9.
IEEE Trans Med Imaging ; 37(9): 2060-2069, 2018 09.
Artículo en Inglés | MEDLINE | ID: mdl-29993864

RESUMEN

Despite the great promise of integrated positron emission tomography (PET)/magnetic resonance (MR) imaging to add molecular information to anatomical and functional MR, its potential impact in medicine is diminished by a very high cost, limiting its dissemination. An RF-penetrable PET ring that can be inserted into any existing MR system has been developed to address this issue. Employing optical signal transmission along with battery power enables the PET ring insert to electrically float with respect to the MR system. Then, inter-modular gaps of the PET ring allow the RF transmit field from the standard built-in body coil to penetrate into the PET fields-of-view (FOV) with some attenuation that can be compensated for. MR performance, including RF noise, magnetic susceptibility, RF penetrability through and $B_{1}$ uniformity within the PET insert, and MR image quality, were analyzed with and without the PET ring present. The simulated and experimentally measured RF field attenuation factors with the PET ring present were -2.7 and -3.2 dB, respectively. The magnetic susceptibility effect (0.063 ppm) and noise emitted from the PET ring in the MR receive channel were insignificant. $B_{1}$ homogeneity of a spherical agar phantom within the PET ring FOV dropped by 8.4% and MR image SNR was reduced by 3.5 and 4.3 dB with the PET present for gradient-recalled echo and fast-spin echo, respectively. This paper demonstrates, for the first time, an RF-penetrable PET insert comprising a full ring of operating detectors that achieves simultaneous PET/MR using the standard built-in body coil as the RF transmitter.


Asunto(s)
Imagen por Resonancia Magnética , Imagen Multimodal , Tomografía de Emisión de Positrones , Encéfalo/diagnóstico por imagen , Diseño de Equipo , Humanos , Procesamiento de Imagen Asistido por Computador , Imagen por Resonancia Magnética/instrumentación , Imagen por Resonancia Magnética/métodos , Imagen Multimodal/instrumentación , Imagen Multimodal/métodos , Fantasmas de Imagen , Tomografía de Emisión de Positrones/instrumentación , Tomografía de Emisión de Positrones/métodos
10.
Phys Med Biol ; 62(1): 258-271, 2017 01 07.
Artículo en Inglés | MEDLINE | ID: mdl-27991437

RESUMEN

It is well known that a PET detector capable of measuring both photon time-of-flight (TOF) and depth-of-interaction (DOI) improves the image quality and accuracy. Phoswich designs have been realized in PET detectors to measure DOI for more than a decade. However, PET detectors based on phoswich designs put great demand on the readout circuits, which have to differentiate the pulse shape produced by different crystal layers. A simple pulse shape discrimination approach is required to realize the phoswich designs in a clinical PET scanner, which consists of thousands of scintillation crystal elements. In this work, we studied time-over-threshold (ToT) as a pulse shape parameter for DOI. The energy, timing and DOI performance were evaluated for a phoswich detector design comprising [Formula: see text] mm LYSO:Ce crystal optically coupled to [Formula: see text] mm calcium co-doped LSO:Ce,Ca(0.4%) crystal read out by a silicon photomultiplier (SiPM). A DOI accuracy of 97.2% has been achieved for photopeak events using the proposed time-over-threshold (ToT) processing. The energy resolution without correction for SiPM non-linearity was [Formula: see text]% and [Formula: see text]% FWHM at 511 keV for LYSO and LSO crystal layers, respectively. The coincidence time resolution for photopeak events ranges from 164.6 ps to 183.1 ps FWHM, depending on the layer combinations. The coincidence time resolution for inter-crystal scatter events ranges from 214.6 ps to 418.3 ps FWHM, depending on the energy windows applied. These results show great promises of using ToT for pulse shape discrimination in a TOF phoswich detector since a ToT measurement can be easily implemented in readout electronics.


Asunto(s)
Tomografía de Emisión de Positrones/instrumentación , Equipos y Suministros Eléctricos , Fotones , Silicio , Factores de Tiempo
11.
Med Phys ; 44(1): 112-120, 2017 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-28102949

RESUMEN

PURPOSE: A brain sized radio frequency (RF)-penetrable PET insert has been designed for simultaneous operation with MRI systems. This system takes advantage of electro-optical coupling and battery power to electrically float the PET insert relative to the MRI ground, permitting RF signals to be transmitted through small gaps between the modules that form the PET ring. This design facilitates the use of the built-in body coil for RF transmission and thus could be inserted into any existing MR site wishing to achieve simultaneous PET/MR imaging. The PET detectors employ nonmagnetic silicon photomultipliers in conjunction with a compressed sensing signal multiplexing scheme, and optical fibers to transmit analog PET detector signals out of the MRI room for decoding, processing, and image reconstruction. METHODS: The PET insert was first constructed and tested in a laboratory benchtop setting, where tomographic images of a custom resolution phantom were successfully acquired. The PET insert was then placed within a 3T body MRI system, and tomographic resolution/contrast phantom images were acquired both with only the B0 field present, and under continuous pulsing from different MR imaging sequences. RESULTS: The resulting PET images have comparable contrast-to-noise ratios (CNR) under all MR pulsing conditions: The maximum percent CNR relative difference for each rod type among all four PET images acquired in the MRI system has a mean of 14.0 ± 7.7%. MR images were successfully acquired through the RF-penetrable PET shielding using only the built-in MR body coil, suggesting that simultaneous imaging is possible without significant mutual interference. CONCLUSIONS: These results show promise for this technology as an alternative to costly integrated PET/MR scanners; a PET insert that is compatible with any existing clinical MRI system could greatly increase the availability, accessibility, and dissemination of PET/MR.


Asunto(s)
Procesamiento de Imagen Asistido por Computador , Imagen por Resonancia Magnética/instrumentación , Tomografía de Emisión de Positrones/instrumentación , Ondas de Radio , Humanos , Fantasmas de Imagen , Relación Señal-Ruido , Factores de Tiempo
12.
Phys Med Biol ; 60(16): 6407-21, 2015 Aug 21.
Artículo en Inglés | MEDLINE | ID: mdl-26237671

RESUMEN

In the field of information theory, compressed sensing (CS) had been developed to recover signals at a lower sampling rate than suggested by the Nyquist-Shannon theorem, provided the signals have a sparse representation with respect to some base. CS has recently emerged as a method to multiplex PET detector readouts thanks to the sparse nature of 511 keV photon interactions in a typical PET study. We have shown in our previous numerical studies that, at the same multiplexing ratio, CS achieves higher signal-to-noise ratio (SNR) compared to Anger and cross-strip multiplexing. In addition, unlike Anger logic, multiplexing by CS preserves the capability to resolve multi-hit events, in which multiple pixels are triggered within the resolving time of the detector. In this work, we characterized the time, energy and intrinsic spatial resolution of two CS detectors and a data acquisition system we have developed for a PET insert system for simultaneous PET/MRI. The CS detector comprises a 2 x 4 mosaic of 4 x 4 arrays of 3.2 x 3.2 x 20 mm(3) lutetium-yttrium orthosilicate crystals coupled one-to-one to eight 4 x 4 silicon photomultiplier arrays. The total number of 128 pixels is multiplexed down to 16 readout channels by CS. The energy, coincidence time and intrinsic spatial resolution achieved by two CS detectors were 15.4±0.1% FWHM at 511 keV, 4.5 ns FWHM and 2.3 mm FWHM, respectively. A series of experiments were conducted to measure the sources of time jitter that limit the time resolution of the current system, which provides guidance for potential system design improvements. These findings demonstrate the feasibility of compressed sensing as a promising multiplexing method for PET detectors.


Asunto(s)
Tomografía de Emisión de Positrones/instrumentación , Lutecio/química , Tomografía de Emisión de Positrones/métodos , Relación Señal-Ruido , Silicatos/química
13.
Phys Med Biol ; 60(9): 3459-78, 2015 May 07.
Artículo en Inglés | MEDLINE | ID: mdl-25856511

RESUMEN

The simultaneous acquisition of PET and MRI data shows promise to provide powerful capabilities to study disease processes in human subjects, guide the development of novel treatments, and monitor therapy response and disease progression. A brain-size PET detector ring insert for an MRI system is being developed that, if successful, can be inserted into any existing MRI system to enable simultaneous PET and MRI images of the brain to be acquired without mutual interference. The PET insert uses electro-optical coupling to relay all the signals from the PET detectors out of the MRI system using analog modulated lasers coupled to fiber optics. Because the fibers use light instead of electrical signals, the PET detector can be electrically decoupled from the MRI making it partially transmissive to the RF field of the MRI. The SiPM devices and low power lasers were powered using non-magnetic MRI compatible batteries. Also, the number of laser-fiber channels in the system was reduced using techniques adapted from the field of compressed sensing. Using the fact that incoming PET data is sparse in time and space, electronic circuits implementing constant weight codes uniquely encode the detector signals in order to reduce the number of electro-optical readout channels by 8-fold. Two out of a total of sixteen electro-optical detector modules have been built and tested with the entire RF-shielded detector gantry for the PET ring insert. The two detectors have been tested outside and inside of a 3T MRI system to study mutual interference effects and simultaneous performance with MRI. Preliminary results show that the PET insert is feasible for high resolution simultaneous PET/MRI imaging for applications in the brain.


Asunto(s)
Imagen por Resonancia Magnética/instrumentación , Imagen Multimodal/instrumentación , Tomografía de Emisión de Positrones/instrumentación , Imagen por Resonancia Magnética/métodos , Imagen Multimodal/métodos , Tomografía de Emisión de Positrones/métodos
15.
16.
J Acoust Soc Am ; 112(3 Pt 1): 811-21, 2002 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-12243167

RESUMEN

The inverse calculation of material parameters of a thin-layer system is investigated using transient elastic waves. The inverse problem is formulated as an optimization problem in which the norm of the discrepancies between the calculated and measured normal surface displacements is minimized through the simplex algorithm. The theoretical result is first solved using the Laplace transform and the transient response is then implemented analytically by Cagniard's method. In the experiment, the source time function is generated by the brittle fracture of a pencil lead on the surface of the thin-layer system, and a National Bureau of Standards (NBS) conical transducer is used to record the surface responses. To obtain reliable inverse results for material parameters, a two-step inverse calculation procedure is proposed. The recovered material parameters of the specimens agree well with the theoretical values and experimental results.

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