There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

CA : A Cancer Journal for Clinicians

Introduction to linear and nonlinear programming

Bilateral teleoperation: An historical survey

Registration of trans-perineal template mapping biopsy cores to volumetric ultrasound

We introduce two model-based iterative methods to obtain shear modulus images of tissue using magnetic resonance elastography. The first method jointly finds the displacement field that best fits tissue displacement data and the corresponding shear modulus. The displacement satisfies a viscoelastic wave equation constraint, discretized using the finite element method. Sparsifying regularization terms in both shear modulus and displacement are used in the cost function minimized for the best fit. The second method extends the first method for multifrequency tissue displacement data. The formulated problems are bi-convex. Their solution can be obtained iteratively by using the alternating direction method of multipliers. Sparsifying regularizations and the wave equation constraint filter out sensor noise and compressional waves. Our methods do not require bandpass filtering as a preprocessing step and converge fast irrespective of the initialization. We evaluate our new methods in multiple in silico and phantom experiments, with comparisons with existing methods, and we show improvements in contrast to noise and signal-to-noise ratios. Results from an in vivo liver imaging study show elastograms with mean elasticity comparable to other values reported in the literature.

Model-Based Quantitative Elasticity Reconstruction Using ADMM

We define a deconvolution based photoacoustic reconstruction with sparsity regularization (DPARS) algorithm for image restoration from projections. The proposed method is capable of visualizing tissue in the presence of constraints such as the specific directivity of sensors and limited-view Photoacoustic Tomography (PAT). The directivity effect means that our algorithm treats the optically-generated ultrasonic waves based on which direction they arrive at the transducer. Most PA image reconstruction methods assume that sensors have omni-directional response; however, in practice, the sensors show higher sensitivity to the ultrasonic waves coming from one specific direction. In DPARS, the sensitivity of the transducer to incoming waves from different directions are considered. Thus, the DPARS algorithm takes into account the relative location of the absorbers with respect to the transducers, and generates a linear system of equations to solve for the distribution of absorbers. The numerical conditioning and computing times are improved by the use of a sparse Discrete Fourier Transform (DCT) representation of the distribution of absorption coefficients. Our simulation results show that DPARS outperforms the conventional Delay-and-Sum reconstruction method in terms of CNR and RMS errors. Experimental results confirm that DPARS provides images with higher resolution than DAS.

Deconvolution based photoacoustic reconstruction for directional transducer with sparsity regularization

Imaging and detection of brachytherapy seeds using transrectal ultrasound (TRUS) remains a challenge for prostate brachytherapy, mainly due to the small size of brachytherapy seeds in relatively low-quality B-mode TRUS images. In this paper, we propose a new solution for brachytherapy seed detection using 3D ultrasound. We use 3D reflected power images computed from ultrasound radio-frequency signals, instead of using conventional B-mode images. Then implanted seeds are detected in 3D local search spaces that are determined by a priori knowledge. Experimental results showed that the proposed solution works well for seed localization in the prostate phantom.

Detection of brachytherapy seeds using 3D ultrasound

This paper presents a fast image synthesis procedure inside elastic volumes under deformation simulated by the finite element method (FEM). Given the node displacements of a mesh and the 3D image voxel data of a volume prior to deformation, the method maps the image pixels, to be synthesized, from the deformed configuration back to the nominal pre-deformed configuration, where the pixel intensities are obtained easily through interpolation in the regular-grid structure of the voxel volume. This mapping requires the identification of the mesh element enclosing each image pixel, in order to use its corresponding shape function for smooth interpolation. To accelerate this point location operation, a fast method of marking the projection of the deformed mesh on the image pixels at every frame is introduced. In order to evaluate our method, a deformable tissue phantom was constructed and its 3D ultrasound volume was acquired in its nominal state. B-mode images of the phantom were then synthesized under the simulated deformation of an ultrasound probe. Results show that realistic B-mode images can be simulated in real-time with the proposed technique, even under large deformations. The technique is also implemented on a real-time system for ultrasound exploration with deformation.

/pdf/fast-b-mode-ultrasound-image-simulation-of-deformed-tissue-3k7z7j019l.pdf

Septimiu E. Salcudean

Papers

Registration of trans-perineal template mapping biopsy cores to volumetric ultrasound

Model-Based Quantitative Elasticity Reconstruction Using ADMM

Deconvolution based photoacoustic reconstruction for directional transducer with sparsity regularization

Detection of brachytherapy seeds using 3D ultrasound

Fast B-Mode Ultrasound Image Simulation of Deformed Tissue