We present a bent ray reconstruction algorithm for an ultrasound tomography (UT) scanner designed for breast
screening. The scanner consists of a circular array of transmitters and receivers which encloses the object to be
imaged. By solving a nonlinear system of equations, the reconstruction algorithm estimates the sound speed of
the object using the set of travel-time measurements. The main difficulty in this inverse problem is to ensure the
convergence and robustness to noise. In this paper, we propose a gradient method to find a solution for which
the corresponding travel-times are closest to the measured travel-times in the least squares sense. To this end,
first the gradient of the cost function is derived using Fermat's Principle. Then, the iterative nonlinear conjugate
gradient algorithm solves the minimization problem. This is combined with the backtracking line search method
to efficiently find the step size in each iteration. This approach is guaranteed to converge to a local minimum
of the cost function where the convergence point depends on the initial guess. Moreover, the method has the
potential to easily incorporate regularity constraints such as sparsity as a priori information on the model. The method is tested both numerically and using in vivo data obtained from a UT scanner. The results confirm the stability and robustness of our approach for breast screening applications.
We present preliminary results obtained using a time domain wave-based reconstruction algorithm for an ultrasound
transmission tomography scanner with a circular geometry. While a comprehensive description of this type of algorithm has already been given elsewhere, the focus of this work is on some practical issues arising with this approach. In fact, wave-based reconstruction methods suffer from two major drawbacks which limit their application in a practical setting: convergence is difficult to obtain and the computational cost is prohibitive. We address the first problem by appropriate initialization using a ray-based reconstruction. Then, the complexity of the method is reduced by means of an efficient parallel implementation on graphical processing units (GPU). We provide a mathematical derivation of the wave-based method under consideration, describe some details of our implementation and present simulation results obtained with a numerical phantom designed for a breast cancer detection application. The source code of our GPU implementation is freely available on the web at www.usense.org.
A major limitation of thermal therapies is the lack of detailed thermal information needed to monitor the
therapy. Temperatures are routinely measured invasively with thermocouples, but only sparse measurements
can be made. Ultrasound tomography is an attractive modality for temperature monitoring because it is noninvasive,
non-ionizing, convenient and inexpensive. It capitalizes on the fact that the changes in temperature
cause the changes in sound speed. In this work we investigate the possibility of monitoring large temperature
changes, in the interval from body temperature to -40°C. The ability to estimate temperature in this interval is
of a great importance in cryosurgery, where freezing is used to destroy abnormal tissue. In our experiment, we
freeze locally a tissue-mimicking phantom using a combination of one, two or three cryoprobes. The estimation of
sound speed is a difficult task because, first, the sound is highly attenuated when traversing the frozen tissue; and
second, the sound speed to be reconstructed has a high spatial bandwidth, due to the dramatic change in speed
between the frozen and unfrozen tissue. We show that the first problem can be overcome using a beamforming
technique. As the classical reconstruction algorithms inherently smooth the reconstruction, we propose to solve
the second problem by applying reconstruction techniques based on sparsity.
Recent results in compressed sensing or compressive sampling suggest that a relatively small set of measurements
taken as the inner product with universal random measurement vectors can well represent a source that is
sparse in some fixed basis. By adapting a deterministic, non-universal and structured sensing device, this paper
presents results on using the annihilating filter to decode the information taken in this new compressed sensing
environment. The information is the minimum amount of nonadaptive knowledge that makes it possible to go
back to the original object. We will show that for a k-sparse signal of dimension n, the proposed decoder needs 2k
measurements and its complexity is of O(k2) whereas for the decoding based on the l1 minimization, the number
of measurements needs to be of O(k log(n)) and the complexity is of O(n3). In the case of noisy measurements,
we first denoise the signal using an iterative algorithm that finds the closest rank k and Toeplitz matrix to the
measurements matrix (in Frobenius norm) before applying the annihilating filter method. Furthermore, for a
k-sparse vector with known equal coefficients, we propose an algebraic decoder which needs only k measurements
for the signal reconstruction. Finally, we provide simulation results that demonstrate the performance of our
algorithm.
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