Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

3D microwave tomography with huber regularization applied to realistic numerical breast phantoms

Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Generalized Inpainting Method for Hyperspectral Image Acquisition

A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a reduced spatial resolution and the need for a demosaicing procedure on its interleaved data. In this work, we address both issues and propose an approach inspired by recent developments in compressed sensing and analysis sparse models. We formulate our superresolution and demosaicing task as a 3-D generalized inpainting problem. Interestingly, the target spatial resolution can be adjusted for mitigating the compression level of our sensing. The reconstruction procedure uses a fast greedy method called Pseudo-inverse IHT. We also show on simulations that a random arrangement of the spectral filters on the sensor is preferable to regular mosaic layout as it improves the quality of the reconstruction. The efficiency of our technique is demonstrated through numerical experiments on both synthetic and real data as acquired by the snapshot imager.Comment: Keywords: Hyperspectral, inpainting, iterative hard thresholding, sparse models, CMOS, Fabry-P\'ero

Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a pre-collected dataset of example image patches, and then for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image non-local self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI

EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200