CT image denoising based on locally adaptive thresholding

The noise in reconstructed X-ray Computed Tomography (CT) slices is complex, non-stationary and indefinitely distributed. Subsequent image processing is needed in order to achieve a good-quality medical diagnosis. It requires a sufficiently great ratio between the detailed contrasts and the noise component amplitude. This paper presents an adaptive method for noise reduction in CT images, based on the local statistical evaluation of the noise component in the domain of Repagular Wavelet Transformation (RWT). Considering the spatial dependence of the noise strength, the threshold constant for processing the high frequency coefficients in the proposed shrinkage method is a function of the local standard deviation of the noise for each pixel of the image. Experimental studies have been conducted using different images in order to evaluate the effectiveness of the proposed algorithm

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information

Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term

Wavelet denoising of multiframe optical coherence tomography data

We introduce a novel speckle noise reduction algorithm for OCT images. Contrary to present approaches, the algorithm does not rely on simple averaging of multiple image frames or denoising on the final averaged image. Instead it uses wavelet decompositions of the single frames for a local noise and structure estimation. Based on this analysis, the wavelet detail coefficients are weighted, averaged and reconstructed. At a signal-to-noise gain at about 100% we observe only a minor sharpness decrease, as measured by a full-width-half-maximum reduction of 10.5%. While a similar signal-to-noise gain would require averaging of 29 frames, we achieve this result using only 8 frames as input to the algorithm. A possible application of the proposed algorithm is preprocessing in retinal structure segmentation algorithms, to allow a better differentiation between real tissue information and unwanted speckle noise

Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent developments in algorithm unrolling using deep neural networks (NNs), and relies on two distinct sub-networks. The first sub-network estimates the regularization parameter-map from the input data. The second sub-network unrolls T iterations of an iterative algorithm which approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is trained end-to-end in a supervised learning fashion using pairs of clean-corrupted data but crucially without the need of having access to labels for the optimal regularization parameter-maps. We prove consistency of the unrolled scheme by showing that the unrolled energy functional used for the supervised learning Γ-converges as T tends to infinity, to the corresponding functional that incorporates the exact solution map of the TV-minimization problem. We apply and evaluate our method on a variety of large scale and dynamic imaging problems in which the automatic computation of such parameters has been so far challenging: 2D dynamic cardiac MRI reconstruction, quantitative brain MRI reconstruction, low-dose CT and dynamic image denoising. The proposed method consistently improves the TV-reconstructions using scalar parameters and the obtained parameter-maps adapt well to each imaging problem and data by leading to the preservation of detailed features. Although the choice of the regularization parameter-maps is data-driven and based on NNs, the proposed algorithm is entirely interpretable since it inherits the properties of the respective iterative reconstruction method from which the network is implicitly defined

Learning Regularization Parameter-Maps for Variational Image Reconstruction Using Deep Neural Networks and Algorithm Unrolling

We introduce a method for the fast estimation of data-adapted, spatially and temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV) minimization. The proposed approach is inspired by recent developments in algorithm unrolling using deep neural networks (NNs) and relies on two distinct subnetworks. The first subnetwork estimates the regularization parameter-map from the input data. The second subnetwork unrolls iterations of an iterative algorithm which approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is then trained end-to-end in a supervised learning fashion using pairs of clean and corrupted data but crucially without the need for access to labels for the optimal regularization parameter-maps. We first prove consistency of the unrolled scheme by showing that the unrolled minimizing energy functional used for the supervised learning -converges, as tends to infinity, to the corresponding functional that incorporates the exact solution map of the TV-minimization problem. Then, we apply and evaluate the proposed method on a variety of large-scale and dynamic imaging problems with retrospectively simulated measurement data for which the automatic computation of such regularization parameters has been so far challenging using the state-of-the-art methods: a 2D dynamic cardiac magnetic resonance imaging (MRI) reconstruction problem, a quantitative brain MRI reconstruction problem, a low-dose computed tomography problem, and a dynamic image denoising problem. The proposed method consistently improves the TV reconstructions using scalar regularization parameters, and the obtained regularization parameter-maps adapt well to imaging problems and data by leading to the preservation of detailed features. Although the choice of the regularization parameter-maps is data-driven and based on NNs, the subsequent reconstruction algorithm is interpretable since it inherits the properties (e.g., convergence guarantees) of the iterative reconstruction method from which the network is implicitly defined