Dual-track spectrometer design for 1D gas-phase Raman spectroscopy.

In this study, a new design for a 1D gas-phase Raman spectrometer is presented, utilizing two dedicated tracks to image different properties of the measured signal onto a single charge-coupled device (CCD) chip. Two possible configurations are shown: a polarization-separation configuration, which separates the detected Raman signal into s- and p-polarized shares; and a dual-resolution configuration, which captures all process-relevant species in a range of approximately 515-4650 cm on one track and the highly resolved nitrogen spectrum on the other. This new spectrometer design offers several advantages when compared to traditional polarization-separation/dual-resolution systems, which often use switchable filters or two different spectrometers in tandem to achieve comparable measurements.

An Efficient Algorithm for the Piecewise Affine-Linear Mumford-Shah Model Based on a Taylor Jet Splitting.

We propose an algorithm to efficiently compute approximate solutions of the piecewise affine Mumford-Shah model. The algorithm is based on a novel reformulation of the underlying optimization problem in terms of Taylor jets. A splitting approach leads to linewise segmented jet estimation problems for which we propose an exact and efficient solver.

Total Variation Regularization of Pose Signals with an Application to 3D Freehand Ultrasound.

Three-dimensional freehand imaging techniques are gaining wider adoption due to their ?exibility and cost ef?ciency. Typical examples for such a combination of a tracking system with an imaging device are freehand SPECT or freehand 3D ultrasound. However, the quality of the resulting image data is heavily dependent on the skill of the human operator and on the level of noise of the tracking data.

Fast Piecewise-Affine Motion Estimation Without Segmentation.

Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme.

Model-based learning of local image features for unsupervised texture segmentation.

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images.

Fast Segmentation From Blurred Data in 3D Fluorescence Microscopy.

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of dealing with 3D images defined on non-cubic grids. Our discretization allows us to utilize a specific splitting approach, which results in decoupled subproblems of moderate size.

Fast Median Filtering for Phase or Orientation Data.

Median filtering is among the most utilized tools for smoothing real-valued data, as it is robust, edge-preserving, value-preserving, and yet can be computed efficiently. For data living on the unit circle, such as phase data or orientation data, a filter with similar properties is desirable. For these data, there is no unique means to define a median; so we discuss various possibilities.

Joint Segmentation and Shape Regularization With a Generalized Forward-Backward Algorithm.

This paper presents a method for the simultaneous segmentation and regularization of a series of shapes from a corresponding sequence of images. Such series arise as time series of 2D images when considering video data, or as stacks of 2D images obtained by slicewise tomographic reconstruction. We first derive a model where the regularization of the shape signal is achieved by a total variation prior on the shape manifold.

Edge Preserving and Noise Reducing Reconstruction for Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is an emerging medical imaging modality which is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. It is an important feature of MPI that even fast dynamic processes can be captured for 3D volumes. The high temporal resolution in turn leads to large amounts of data which have to be handled efficiently.

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional.

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements.

Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities.