Registration of Standardized Histological Images in Feature Space

In this paper, we propose three novel and important methods for the registration of histological images for 3D reconstruction. First, possible intensity variations and nonstandardness in images are corrected by an intensity standardization process which maps the image scale into a standard scale where the similar intensities correspond to similar tissues meaning. Second, 2D histological images are mapped into a feature space where continuous variables are used as high confidence image features for accurate registration. Third, we propose an automatic best reference slice selection algorithm that improves reconstruction quality based on both image entropy and mean square error of the registration process. We demonstrate that the choice of reference slice has a significant impact on registration error, standardization, feature space and entropy information. After 2D histological slices are registered through an affine transformation with respect to an automatically chosen reference, the 3D volume is reconstructed by co-registering 2D slices elastically.Comment: SPIE Medical Imaging 2008 - submissio

Maximum-a-posteriori estimation with Bayesian confidence regions

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a result, while most modern mathematical imaging methods produce impressive point estimation results, they are generally unable to quantify the uncertainty in the solutions delivered. This paper presents a new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional. The approximations are derived by using recent concentration of measure results related to information theory for log-concave random vectors. A remarkable property of the approximations is that they can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques. In particular, they are available as a by-product in problems solved by maximum-a-posteriori estimation. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where the approximations are used to perform Bayesian hypothesis tests and explore the uncertainty about the solutions, and where proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error

Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions

Purpose: A time-efficient strategy to acquire high-quality multi-contrast images is to reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause leakage of uncommon features among contrasts, compromising diagnostic utility. The goal of this study is to develop a compressive sensing method for multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Theory: Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi-channel multi-contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. Methods: The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single-channel simulated and multi-channel in-vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. Results: The proposed method demonstrates rapid convergence and improved image quality for both simulated and in-vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage-of-features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms. Conclusion: The proposed compressive sensing method performs fast reconstruction of multi-channel multi-contrast MRI data with improved image quality. It offers reliability against feature leakage in joint reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio

Solving ill-posed inverse problems using iterative deep neural networks

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against FBP and TV reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the TV reconstruction while being significantly faster, giving reconstructions of 512 x 512 volumes in about 0.4 seconds using a single GPU

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Deep learning in computational microscopy

We propose to use deep convolutional neural networks (DCNNs) to perform 2D and 3D computational imaging. Specifically, we investigate three different applications. We first try to solve the 3D inverse scattering problem based on learning a huge number of training target and speckle pairs. We also demonstrate a new DCNN architecture to perform Fourier ptychographic Microscopy (FPM) reconstruction, which achieves high-resolution phase recovery with considerably less data than standard FPM. Finally, we employ DCNN models that can predict focused 2D fluorescent microscopic images from blurred images captured at overfocused or underfocused planes.Published versio