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This paper presents an adaptive progressive image acquisition algorithm based on the concept of kernel construction. The algorithm takes the conventional route of blind progressive sampling to sample and reconstruct the ground truth image in an iterative manner. During each iteration, an equivalent kernel is built for each unsampled pixel to capture the spatial structure of its local neighborhood...
In this paper, we introduce a novel technique of deriving Fisher kernels from the Gaussian Bernoulli restricted Boltzmann machine (GBRBM) and factored 3-way restricted Boltzmann machine (FRBM) to yield better texture classification results. GBRBM and FRBM, both, are stochastic probabilistic models that have already shown their suitability for modelling real valued continuous data, however, they are...
The rise of big data, which need computationally demanding manipulation has posed unprecedented challenges in the machine learning community. In this context, a variety of dimensionality reduction methods has been introduced in order to deal with the large-scale aspect of the data. However, their employment in very large scales often becomes impractical due to memory and computation limitations. In...
Regularization of iterative reconstruction for fully dynamic PET has often been achieved implicitly by estimating coefficients relating to temporal basis functions, such as data-derived temporal basis functions, wavelet temporal basis functions, or compartmental model based temporal basis functions (direct kinetic parameter estimation). In this work, we propose and evaluate a method for anatomy-guided...
Whole-body (WB) PET parametric imaging has recently become clinically feasible with the introduction of multi-bed dynamic acquisition protocols, benefiting from the latest technologies in clinical PET scanners. Currently, Time-of-Flight (TOF) capabilities of modern PET systems allow for more accurate localization of the annihilation position along the line of response (LOR). As a result, TOF can prevent...
PET acquisition requires prolonged scan times, and during the scan a large magnitude of patient motion can occur. Breathing may result in a significant displacement of organs and consequent blurring of clinically relevant features. Various non-rigid motion corrections that act in the image space were proposed to address this problem. TOF data can be considered to be histo-images. Therefore, non-rigid...
PET reconstruction results in images with correlations between neighbouring image voxels. Alternative reconstruction algorithms, such as OSEM reconstruction incorporating resolution modelling (RM) can significantly alter this voxel covariance. While RM has been demonstrated to reduce voxel variance, it has been suggested that the increased covariance results in increased region-based ensemble variance...
We present an image-domain point spread function (PSF) modeling approach for resolution recovery where spatially varying PSF kernel widths are adjusted based on data quality. This approach attempts to maximize contrast recovery while minimizing edge artifacts (ringing) associated with PSF modeling. We choose broader PSF kernels for noisier datasets where the extent of ringing is comparable to noise...
The Laue diffraction microscopy experiment uses the polychromatic Laue micro-diffraction technique to examine the structure of materials with sub-micron spatial resolution in all three dimensions. During this experiment, local crystallographic orientations, orientation gradients and strains are measured as properties which will be recorded in HDF5 image format. The recorded images will be processed...
Heterogeneity among cells is a common characteristic of living systems. For mathematical modeling of heterogeneous cell populations, one typically has to reconstruct the underlying heterogeneity from measurements on the population level. Based on recent insights into the mathematical nature of this problem as an inverse problem of tomographic type, we evaluate numerical methods to perform such a reconstruction...
Compressive Sensing (CS) signal reconstruction can be implemented using convex relaxation, non-convex, or local optimization algorithms. Though the reconstruction using convex optimization, such as the Iterative Hard Thresholding algorithm, is more accurate than matching pursuit algorithms, most researchers focus on matching pursuit algorithms because they are less computationally complex. Orthogonal...
A novel Kernel PCA/Kernel KLT transform (S-KPCA) is introduced which incorporates higher order statistics into the design of the transform matrix using a Reproducing Kernel Hilbert Space (RKHS) approach. The goal is to arrive at an orthonormal transform matrix E with column eigenvectors that allow reconstruction of an input vector with few coefficients and superior signal fidelity. In contrast to...
A vector space approach to image reconstruction is derived and introduced. The continuous-domain image is assumed to belong to a reproducing kernel Hilbert space and the sampling process is shown to correspond to an appropriate orthogonal projection. The values at the interpolating grid are shown to correspond to a set of inner product calculations, giving rise to a minimax solution for an ℓ2 approximation...
In this paper we describe a novel method for finding non-negative solutions to linear inverse problems. Such problems include image reconstruction where one is required to deconvolve a known point spread function from the image to produce a clearer image. The method described here is related to the truncated singular function expansion for solving linear inverse problems. The method consists of choosing...
Compressed Sensing (CS) is a new paradigm in signal processing and reconstruction from sub-nyquist sampled data. CS has shown promising results in accelerating dynamic Magnetic Resonance Imaging (dMRI). CS based approaches hugely rely on sparsifying transforms to reconstruct the dynamic MR images from its undersampled k-space data. Recent developments in dictionary learning and nonlinear kernel based...
In this paper, we propose a new reconstruction framework that utilizes nonlinear models to sparsely represent the MR parameter-weighted image in a high dimensional feature space. Different from the prior work with nonlinear models where the image series is reconstructed simultaneously, each image at a specific time point is assumed to lie in a low-dimensional manifold and is reconstructed individually...
Dipole inversion is the final step of the QSM algorithm. In this step, the zero cone surface in the dipole kernel makes the field-to-susceptibility inverse problem ill-posed. Current solutions are mostly based on the Bayesian approach. Compared to the L1-norm, which has been used in previous techniques, the L2-norm converges faster. Therefore, we propose to employ a reweighted L2-norm using weights...
Due to all kinds of need of customers and the complicated transmitting environment of digital image and video resources, numerous practical applications emerge, e.g. Image in painting, interpolation, super-resolution and the removal of salt and pepper noise. One thing these cases all have in common is that there are plenty of missing pixels randomly distributed in an image. Existing image restoration...
We propose a low rank structured matrix completion algorithm for image inpainting problems originated from scanning microscopy. The proposed method exploits the annihilation property observed in Gaussian Markov Random Field (GMRF) or partial differential equation (PDE)-based inpainting approaches. By utilizing the commutative property of the convolution, the annihilation property is embodied into...
The quality of high-resolution Echo Planar images of the human brain has improved greatly in recent years, enabled by novel multi-channel receiver coil arrays and parallel imaging. However, in regions with local field inhomogeneity, EPI artifacts limit which parts of the brain can be imaged successfully. In this work, we present evidence that certain image artifacts can be attributed to nonlinear...
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