Quantitative images showing the speed of sound proffle of the breast may be obtained by employing full-waveform inversion (FWI) methods on the measured data. These reconstruction methods work well for both dense and normal breasts. Contrast source inversion (CSI) is a frequency domain FWI method. In literature, many examples of successful application of CSI for breast imaging can be found. However, all these works are based on simulated data. In this work, we will present our first results obtained with employing CSI on experimental data. CSI was developed by Delft University of Technology and the experimental data was provided by FUJIFILM Healthcare Corporation. The experimental data is obtained using a ring-shaped transducer which scans a breast-mimicking gelatine phantom. Our initial results obtained with CSI look promising; all inclusions within the phantom are accurately reconstructed.

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Breast cancer is the most common type of cancer for women and in developed countries it forms one of their largest threats. Many studies have shown that early detection by screening is important for achieving a successful treatment and reducing the mortality rate. Nowadaysmammography is the gold standard for breast cancer screening. However, mammography has several drawbacks including the use of ionizing radiation, a painful procedure, and poor performance with dense breasts. Magnetic resonance imaging (MRI) could form an alternative as it has some powerful features. However, the high examination and equipment costs as well as the use of contrast agents limits its applicability. Another potential alternative for breast cancer screening is ultrasound. Ultrasound has the advantage over mammography orMRI that it is safe, cheap and patient-friendly. With ultrasound, a tumor can be detected since healthy breast tissues and cancerous tissues have different acoustic properties. All these features make ultrasound a promising candidate as a screening modality for breast cancer. Hand-held ultrasound scans are frequently used for breast imaging in hospitals. With these scanners reflectivity images are generated. These images typically show the boundaries between different tissues. Even when these exams are conducted by trained radiologists operator-dependency occurs. To eliminate this, automated full-breast ultrasound scanners have been developed where the transducer slides over the breast. However, as the imaging principle remains the same, only reflectivity images are generated. To avoid significant breast deformation as well as to scan the breast from as many sides as possible water-bath scanning systems have been developed. These systems have the additional advantage that both reflection and transmission measurements are obtained. This mixture of different measurement types make it feasible to obtain better images by employing advanced processing techniques. One promising imaging method is full-waveform inversion (FWI). FWI aims to match a modeled wavefield to a measured wavefield by adjusting the acoustic medium parameters. A minimization problem is constructed and solved to this aim. As a result, images showing quantitative information about the different tissues are obtained. This quantitative information aids to the characterization and identification of the different tissues. However, there are some challenges when applying FWI. One of the biggest challenges is its computational complexity. By the inclusion of wave phenomena such as diffraction, refraction, scattering and dispersion - needed to explain the measured data in great detail - the computational complexity of FWI has become significantly larger than conventional - mainly ray based - imaging methods. In this work, we investigate the applicability of contrast source inversion (CSI) as an FWI method for breast ultrasound. To this end, we first introduce our full-waveform forward modeling method which is based on solving an integral equation. With a synthetic example,we investigate howeach mediumparameter (compressibility, density, and attenuation) affects the scattered pressure field. The obtained results show that attenuation, in contrast to compressibility and density, has only little effect on the wavefield for frequencies below 1MHz. From that we conclude, that for these frequencies only attenuation can be neglected in our inversion. We also compare the results from our full-waveform modeling method with results obtained after commonly made approximations such as Born, ray-based and paraxial approximations. We observe from the presented numerical results that with each approximation important phenomena normally present in the full-wave data are absent. For this reason, we recommend to use a full-wave modeling method to compute synthetic measurement data. @en

Full-waveform inversion methods are widely used for breast imaging to provide quantitative information about the tissues such as the speed of sound. Full-waveform inversion faces a cycle-skipping problem when applied to large contrasts or large spatial domains. This problem leads to erroneous image reconstructions. To overcome this problem, low frequency measurements or good starting models are needed. In this work, we propose and test a frequency-hopping technique for our full-waveform inversion method (Contrast Source Inversion) to avoid the cycle-skipping problem. For a synthetic example, we first show the effect of cycle skipping in the reconstructed image. Next, we show for the same example that the implementation of the proposed frequency-hopping method solves this problem.

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Breast cancer is the most common form of cancer diagnosed with women. To reduce its mortality rate, early diagnosis is important. In the past, this has led to the introduction of national screening programs using mammography. The disadvantages of mammography (application of ionizing radiation and low detection rate in dense breast) resulted in the demand for an alternative. This demand has led to the development of ultrasonic water bath scanning systems. Those systems scan the breast from all sides and aim for reconstructing the acoustic tissue properties from the measured pressure fields by employing among others full-waveform inversion methods. However, full-wave inversion is computationally expensive, especially in 3-D, and scales almost linear with the size of the spatial domain. To reduce the computational load, we propose a method that reduces the size of the spatial computational domain by back-propagating the field measured on the surface of the 3-D scanning geometry to a surface enclosing a reduced volume. To this end, the measured field is first decomposed into spherical Hankel functions with complex coefficients and subsequently redatumed to a new surface closer by the object. The proposed redatuming method is tested successfully for 3-D synthetic examples.

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Whole breast ultrasound scanning systems are used to screen a women’s breast for suspicious lesions. Typically, the transducers are located at fixed positions at relatively large distances from the breast to avoid any contact with the breast. Unfortunately, these large distances give rise to large spatial domains to be imaged. These large domains hamper the applicability of imaging by inversion. To reduce the size of the spatial computational domain, we present a two-dimensional redatuming method based on Hankel decomposition of the measured field. With this method, the field measured over an arbitrary-shaped closed curve can be redatumed to a new curve enclosing a smaller spatial domain. Additional advantages of the proposed method are that it allows to account for the finite size and orientation of a transducer and that it is robust to noise. The proposed method is successfully validated using synthetic and measured data and the results show that the recorded field can be redatumed to any position in the embedding.@en

Multi-parameter inversion for medical ultrasound leads to an improved tissue classification. In general, simultaneous reconstruction of volume density of mass and compressibility would require knowledge of the particle velocity field along with the pressure field. However, in practice the particle velocity field is not measured. Here, the authors propose a method for multi-parameter inversion where the particle velocity field is reconstructed from the measured pressure field. To this end, the measured pressure field is described using outward propagating Hankel functions. For a synthetic setup, it is shown that the reconstructed particle velocity field matches the forward modelled particle velocity field. Next, the reconstructed particle velocity field is used together with the synthetically measured pressure field to reconstruct density and compressibility profiles with the aid of contrast source inversion. Finally, comparing the reconstructed speed of sound profiles obtained via single-parameter versus multi-parameter inversion shows that multi-parameter outperforms single-parameter inversion with respect to accuracy and stability.

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Transcranial ultrasound has been used to image the brain since 1942. Currently, it is regaining interest and full-waveform inversion (FWI) methods are now employed to reconstruct speed-of-sound profiles of the brain. Many of these methods require a good starting model. Here, we test the applicability of contrast source inversion (CSI) as a FWI method to reconstruct two-dimensional speed-of-sound profiles of the soft brain tissue enclosed by the skull. The advantage of CSI is that it can handle large acoustic contrasts without the need for a good starting model. To test the performance of CSI, we first compute synthetic data. The resulting pressure field clearly shows a significant amount of multiple scattering caused by the skull that acts as a hard acoustic contrast. Next we invert the resulting synthetic data within the Born approximation as well as by applying CSI as a FWI method. The results clearly show that Born inversion can only image the soft brain tissue in the absence of the skull whereas it generates erroneous results when the skull is present. On the other hand, with CSI it is feasible to reconstruct both the skull and the soft brain tissue accurately. Importantly, as compared to other methods CSI does not require any a priori information about the contrast, a mask or a heterogeneous starting model to reconstruct the soft tissue enclosed by the skull.

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Breast ultrasound is gaining interest as an alternative to mammography. To improve its diagnostic value, full waveform inversion methods are developed. These methods aim for reconstructing speed of sound maps of the breast. When the inversion is performed in the frequency domain, computation time is reduced by limiting the number of frequency components at the cost of retrieving noisy images. To compensate for the lack of frequency information and to reduce the noise in the reconstruction, we propose two solutions. First, we select the frequency components randomly out of the entire available bandwidth for each source-receiver combination separately. Next, a regularization method is applied that takes advantage of the sparseness of the reconstructed contrast in the wavelet domain.

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Synthetic-aperture (SA) imaging is a popular method to visualize the reflectivity of an object from ultrasonic reflections. The method yields an image of the (volume) contrast in acoustic impedance with respect to the embedding. Typically, constant mass density is assumed in the underlying derivation. Due to the band-limited nature of the recorded data, the image is blurred in space, which is quantified by the associated point spread function. SA volume imaging is valid under the Born approximation, where it is assumed that the contrast is weak. When objects are large with respect to the wavelength, it is questionable whether SA volume imaging should be the method-of-choice. Herein, we propose an alternative solution that we refer to as SA interface imaging. This approach yields a vector image of the discontinuities of acoustic impedance at the tissue interfaces. Constant wave speed is assumed in the underlying derivation. The image is blurred in space by a tensor, which we refer to as the interface spread function. SA interface imaging is valid under the Kirchhoff approximation, where it is assumed that the wavelength is small compared to the spatial dimensions of the interfaces. We compare the performance of volume and interface imaging on synthetic data and on experimental data of a gelatin cylinder with a radius of 75 wavelengths, submerged in water. As expected, the interface image peaks at the gelatin-water interface, while the volume image exposes a peak and trough on opposing sides of the interface.

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Ultrasound has been widely used for detecting breast cancer in woman. Currently, full-wave inversion methods become increasingly popular as they provide better reconstructions and tissue characterizations as compared to standard imaging methods such as SAFT. One problem with full-wave inversion is the long computation time, that is proportional to the size of the image domain. To reduce computation time we developed a new 2-D redatuming method that allows to redatum the data measured on an arbitrary curved contour to a new contour enclosing a smaller spatial domain. The new method uses Hankel function decomposition to describe the measured wave field. The applicability of the proposed method is tested successfully by using a synthetic and an a real experimental example. With the experimental example, we also show an additional advantage that redatuming brings us; it allows us to relocate the receivers at the actual grid points of our computational domain.@en

To design breast ultrasound scanning systems or to test new imaging methods, various computer models are used to simulate the acoustic wave field propagation through a breast. The computer models vary in complexity depending on the applied approximations. The objective of this paper is to investigate how the applied approximations affect the resulting wave field. In particular, we investigate the importance of taking three-dimensional (3-D) spatial variations in the compressibility, volume density of mass, and attenuation into account. In addition, we compare four 3-D solution methods: a full-wave method, a Born approximation method, a parabolic approximation method, and a ray-based method. Results show that, for frequencies below 1 MHz, the amplitude of the fields scattering off the compressibility or density contrasts are at least 24 dB higher than the amplitude of the fields scattering off the attenuation contrasts. The results also show that considering only speed of sound as a contrast is a valid approximation. In addition, it is shown that the pressure field modeled with the full-wave method is more accurate than the fields modeled using the other three methods. Finally, the accuracy of the full-wave method is location independent whereas the accuracy of the other methods strongly depends on the point of observation.

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We present a novel microwave imaging technique for sparse domain imaging applications. In the proposed method, inverse scattering algorithm modified gradient method (MGM) is combined with a fast iterative shrinkage-thresholding algorithm to improve the resolution and robustness of the MGM by enforcing the sparsity in the imaging domain. The numerical experiments show that the proposed method achieves higher resolution and robustness compared with that of classical MGM. For nonsparse domain reconstruction, the wavelet transformation is adopted to convert nonsparse spatial domain into a sparse wavelet coefficient domain. The feasibility of the proposed method in the wavelet domain is demonstrated through the numerical experiments.

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