We consider the scenario of finding the transfer function of an aberrating layer in front of a receiving ultrasound (US) array, assuming a separate non-aberrated transmit source. We propose a method for blindly estimating this transfer function without exact knowledge of the ultrasound sources or acoustic contrast image, and without directly measuring the transfer function using a separate controlled calibration experiment. Instead, the measurement data of many unknown random images is collected, such as from blood flow, and its second-order statistics are exploited. A measurement model is formulated that explicitly defines the layer's transfer function. A covariance domain problem is then defined to eliminate the image variable, and it is solved for the layer's transfer function using manifold-based optimization. The proposed approach and calibration algorithm are evaluated on a range of challenging and realistic simulations using the k-Wave toolbox. Our results show that, given a sufficiently efficient parameterization of the layer's transfer function, and by jointly estimating the transfer function at multiple frequencies, the proposed algorithm is able to obtain an accurate estimate. Subsequent simulated imaging experiments using the obtained transfer function also show increased imaging performance in various aberrating layers, including a skull layer.

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Whereas aberrating layers are typically viewed as an impediment to medical ultrasound imaging, they can, surprisingly, also be used to our benefit. As long as we can model the effect of an aberrating layer, we can utilize ‘model-based imaging’, the imaging technique explored throughout this thesis, to reconstruct ultrasound images where traditional beamforming methods would fail, employing the ever increasing computational power available to us nowadays. Not only does this allow us to image through layers, but it also leads to interesting applications, such as 3D ultrasound imaging with spatially undersampled data, using an aberrating ‘coding mask’. The formulation of a measurementmodel, a fundamental part ofmodel-based imaging, also gives insight into the imaging problem mathematically, and allows us to investigate methods for estimating the effect of an aberrating layer ‘blindly’, i.e., without explicitly measuring it. In this thesis, we thus investigate (a), imaging through a layer when the layer’s aberration effect is known, and how it can be applied to imaging with spatially undersampled data, and (b), methods and algorithms for estimating the effect of the aberrating layer without knowing it a priori. In the first part of this thesis, we illustrate how using model-based imaging can be utilized for 3D ultrasound imaging using a single ultrasound transducer, and equipping it with a plastic coding mask. The plastic mask acts as an analog coder, that scrambles the transmitted and received waves in a manner that is location dependent. As a result, the temporal shape of an ultrasound echo can be used instead of the traditional method of using phase differences between sensors in a sensor array. Imaging is instead accomplished using model-based imaging. By measuring the pulse-echo response of each pixel, we can form an image by solving a regularized linear least squares problem, which takes into account the measured pixel-specific pulse-echo signals. The proposed device and imaging method is then verified experimentally. In the following chapter, a coding mask design method is proposed for the aforementioned imaging device. A measurement model is formulatedwhere themask geometry is an explicit parameter to be optimized. After forming this model, a numerical optimization method is proposed and numerically tested. Our numerical experiments show that optimized mask geometries exhibit an energy focusing effect on the region-of-interest, whilst simultaneously decorrelating echo signals between pixels. In the second part of this thesis, in contrast, we consider methods for calibrating propagation models when the pulse-echo response per pixel is not known. The most important calibration challenge we consider is that of imaging through an aberrating layer in front of an ultrasound array. This could be subcutaneous fat or the human skull, for example. In this thesiswe formulate ameasurement model consisting of a partwhere wave propagation is known (i.e., the assumed homogeneous region behind the aberrating layer, where the contrast image of interest is located), and an unknown propagation part, consisting of the Green’s functions from an array sensor to any point on the the interface of the aberrating layer and the imaging medium. We then investigate methods for finding this set of Green’s functions without explicitly measuring them (so called ‘blind’ calibration). The first proposed method exploits the singular value decomposition of the measurement data in combination with the assumed Toeplitz structure of the matrices representing the aberrating layer’s Green’s functions. However, the method is lacking in practicality since an additional set ofmeasurements is required with a phase screen mounted on the interface of the aberration layer and the imaging medium. The second method resolves these practical issues by utilizing a covariance matching technique. A sufficiently large set of measurements is obtained where each measurement is different due to e.g. moving particles such as blood flow or micro-bubbles. Using the covariance of the data, algorithms are then defined that can estimate the transfer functions of the aberrating layer from the measurement covariance data. Finally,we propose amethod for estimating the electro-mechanical impulse response of an ultrasound sensor, by simply measuring its pulse-echo response from a flat plate reflector in front of the sensor. Estimating the one-way (electro-mechanical) impulse response then becomes a de-autoconvolution problem, for which we propose a method by solving a semi-definite relaxation of the de-autoconvolution problem. @en

Photoacoustic (PA) imaging can be used to monitor flowing blood inside the microvascular and capillary bed. Ultrasound speckle decorrelation based velocimetry imaging was previously shown to accurately estimate blood flow velocity in mouse brain (micro-)vasculature. Translating this method to photoacoustic imaging will allow simultaneous imaging of flow velocity and extracting functional parameters like blood oxygenation. In this study, we use a pulsed laser diode and a quantitative method based on normalized first order field autocorrelation function of PA field fluctuations to estimate flow velocities in an ink tube phantom and in the microvasculature of the chorioallantoic membrane of a chicken embryo. We demonstrate how the decorrelation time of signals acquired over frames are related to the flow speed and show that the PA flow analysis based on this approach is an angle independent flow velocity imaging method.

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We consider the scenario of finding the transfer function of an aberrating layer in front of an ultrasound array. We are interested in blindly estimating this transfer function without prior knowledge of the unknown ultrasound sources or ultrasound contrast image. The algorithm gives an exact solution if the matrix representing the aberration layer’s transfer function is full rank, up to a scaling and reordering of its columns, which has to be resolved using some prior knowledge of the matrix structure. We provide conditions for the robustness of blind calibration in noise. Numerical simulations show that the method becomes more robust for shorter wavelengths, as the transfer function matrices then tend to be less ill-conditioned. Image reconstruction from simulated data using the k-Wave toolbox show that a well calibrated model removes some of the distortions introduced by an uncalibrated model, and improves the resolution for some of the sources.@en

We study the design of a coding mask for pulse-echo ultrasound imaging. We are interested in the scenario of a single receiving transducer with an aberrating layer, or ‘mask,’ in front of the transducer's receive surface, with a separate co-located transmit transducer. The mask encodes spatial measurements into a single output signal, containing more information about a reflector's position than a transducer without a mask. The amount of information in such measurements is dependent on the mask geometry, which we propose to optimize using an image reconstruction mean square error (MSE) criterion. We approximate the physics involved to define a linear measurement model, which we use to find an expression for the image error covariance matrix. By discretizing the mask surface and defining a discrete number of mask thickness levels per point on its surface, we show how finding the best mask can be posed as a variation of a sensor selection problem. We propose a convex relaxation in combination with randomized rounding, as well as a greedy optimization algorithm to solve this problem. We show empirically that both algorithms come close to the global optimum. Our simulations further show that the optimized masks have better a MSE than nearly all randomly shaped masks. We observe that an optimized mask amplifies echoes coming from within the region of interest (ROI), and strongly reduces the correlation between echoes of pixels within the ROI.@en

We consider a model-based ultrasound imaging scenario using a single transducer with a coding mask, and assume that the pulse-echo model is erroneously estimated, resulting in decreased imaging performance. Although the pulse-echo Green's function to each pixel has to be measured to obtain a good model, typically only forward-field measurements are obtained for better SNR, from which the pulse-echo Green's functions are estimated. However, if the transducer's receive transfer function is different from the transmit transfer function, the forward-field measurements do not incorporate the receive transfer function, resulting in an incorrect pulse-echo model. We propose two calibration techniques that start with this erroneous model, and update it using pulse-echo measurements. In the first technique we assume the calibration phantom is known a priori, whereas in the second technique we use multiple random calibration phantoms of which only the second-order statistics are assumed to be known beforehand. Both methods are able to significantly improve the pulse-echo model, strongly improving imaging performance. Our simulation results show that the first technique works best, since there is no uncertainty about the calibration image, whereas the blind calibration technique requires no exact knowledge of the calibration phantom, making it robust to positioning or manufacturing errors.

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We present a form of acoustic microscopy, called Structured Ultrasound Microscopy (SUM). It creates a volumetric image by recording reflected echoes of ultrasound waves with a structured phase front using a moving single-element transducer and computational reconstruction. A priori knowledge of the acoustic field produced by the single element allows us to relate the received echoes to a 3D scatter map within the acoustic beam itself, leading to an isotropic resolution at all depths. An aberration mask in front of the acoustic element imposes the phase structure, broadening the beam and breaking the spatial coherence between different voxels at equal acoustic propagation delay, increasing the uniqueness of the reconstruction. By translating the transducer across the 3D volume, we synthetically enlarge the imaging aperture by using multiple overlapping and spatially sparsely sampled measurements to solve for the entire image. In this paper, we explain the SUM technique and demonstrate microscopic imaging at 20 MHz of a 2.3 × 2.3 × 1.2 mm object in water, with an isotropic resolution below 100 μm. The proposed approach allows for wide-field 3D imaging at isotropic microscopic resolution using a small unfocused ultrasound sensor and multiple spatially sparsely sampled measurements. This technique may find applications in many other fields where space is constrained, device simplicity is desired, and wide-field isotropic high-resolution imaging is required.

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We study the optimal design of an aperture coding mask, and the optimal sensing positions of a single ultrasound sensor with a scanning configuration. In previous works, we have shown that 3D ultrasound imaging is possible using a randomly shaped coding mask with randomly chosen sensing positions. Here we propose an optimization algorithm for the joint design of the coding mask and the sensing positions. We first define a linear measurement model and parameterize it with respect to the mask shape. To optimize the shape of the mask, we use a greedy descent algorithm to minimize the imaging MSE, assuming a Wiener estimate is used for image reconstruction. To optimize the sensing positions, we pre-define a set of such sensing positions by gridding the measurement plane, and regard each sensing position as a virtual sensor candidate. We then use a greedy sensor selection algorithm to find a good selection of sensing positions. To jointly optimize for both the mask and the sensing positions, we alternatingly optimize between them, keeping either the mask shape or the sensing positions fixed. Using simulations we show that the joint optimization results in better imaging performance than optimizing for the mask or the sensing positions alone, or using a completely random design.@en

High quality three dimensional ultrasound imaging is typically attained by increasing the amount of sensors, resulting in complex hardware. Compressing measurements before sensing addresses this problem, and could enable new clinical applications. We have developed an analogue compression technique, by positioning a plastic coding mask in front of the aperture, which distorts the ultrasound field by inducing varying local echo delays. This results in a compression of the spatial ultrasound field across the sensor surface, while retaining sufficient information for 3D imaging. Using only a single sensor, complementary measurements can be obtained by rotation of the sensor and the mask to increase the conditioning of the reconstruction problem. In this work, we study a method to optimize the shape of the coding mask. To this end, we define an approximate signal model that captures the ultrasound response of the mask, and use it to pose mask shape optimization as a sensor selection problem. We solve it by relaxing it to a convex problem, as well as by using a greedy selection method. Our simulation results show that these approaches are able to outperform the random design strategy, in particular when mask rotations are included in the problem.

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Most techniques that are used to reconstruct images from raw ultrasound signals are based on pre-defined geometrical processing. This type of image reconstruction typically has a low computational complexity and allows for real-time visualization. Since these techniques do not account for situation-specific parameters such as transducer characteristics and medium in-homogeneities, they cannot make proper use of the information that is contained in the raw ultrasound signals. In this paper, we explore the possibility of reconstructing images that best explain the measured ultrasound signals given the full ultrasound propagation model including all parameters. We build this model by measuring the spatiotemporal impulse response of the imaging transducer and, using the angular spectrum approach, estimate the ultrasound signal as it would originate from each individual image pixel position. An iterative search for the pixel combination that best explains the recorded signals provides the final image. We discuss the details of this model, provide experimental proof that this reconstruction allows for improved image quality, and extend our ideas to other imaging schemes such as compressive imaging.@en

3D ultrasound (US) requires expensive transducers comprising thousands of elements and complicated hardware. This complexity originates from the classical idea on spatial sampling requirements for US imaging. The discovery of compressive sensing allows to ease this sampling constraint, enabling smarter ways of recording the required information. Inspired by this work we introduce a US imager that can perform 3D imaging using one acoustic sensor. Our device sends and detects US waves through a random coding mask that enables unique signals at every voxel. Rotation of the mask allows for several compressed measurements. By knowing the voxel signals, a full 3D reconstruction of the object can be obtained, as we demonstrate in this work.@en

We present a method for estimating the one-way electro-mechanical impulse response or transfer function of self-reciprocal ultrasound transducers. The one-way impulse response is needed for forward field simulations, or for pulseecho simulations and excitation code design when the oneway impulse response per array element is different. Using a flat plate reflector that is positioned parallel to the transducer surface, the resulting pulse-echo signal is measured. Since the transducer is self-reciprocal, the transmit and receive impulse responses are equivalent. Consequently, the measured signal is the autoconvolution of the one-way impulse response. We propose a new de-autoconvolution algorithm to obtain the one-way impulse response from such a signal. The proposed measurement procedure is especially time-efficient for large arrays, and does not rely on hydrophones or additional transducers. Experimental results are shown to demonstrate the effectiveness of the proposed method.@en