Biomedical Image Reconstruction Research Articles

Translation invariant diagonal frame decomposition of inverse problems and their regularization

Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to data perturbations. To stabilize the reconstruction process, regularization methods have to be employed. Well-known regularization methods are based on frame expansions, such as the wavelet–vaguelette decomposition, which are well adapted to the underlying signal class and the forward model and furthermore allow efficient implementation. However, it is well known that the lack of translational invariance of wavelets and related systems leads to specific artifacts in the reconstruction. To overcome this problem, in this paper we introduce and analyze the translation invariant diagonal frame decomposition (TI-DFD) of linear operators as a novel concept generalizing the singular value decomposition. We characterize ill-posedness via the TI-DFD and prove that a TI-DFD combined with a regularizing filter leads to a convergent regularization method with optimal convergence rates. As illustrative example, we construct a wavelet-based TI-DFD for one-dimensional integration, where we also investigate our approach numerically. The results indicate that filtered TI-DFDs eliminate the typical wavelet artifacts when using standard wavelets and provide a fast, accurate, and stable solution scheme for inverse problems.

Advancements in Numerical Methods for Forward and Inverse Problems in Functional near Infra-Red Spectroscopy: A Review

In the field of biomedical image reconstruction, functional near infra-red spectroscopy (fNIRs) is a promising technology that uses near infra-red light for non-invasive imaging and reconstruction. Reconstructing an image requires both forward and backward problem-solving in order to figure out what the image’s optical properties are from the boundary data that has been measured. Researchers are using a variety of numerical methods to solve both the forward and backward problems in depth. This study will show the latest improvements in numerical methods for solving forward and backward problems in fNIRs. The physical interpretation of the forward problem is described, followed by the explanation of the state-of-the-art numerical methods and the description of the toolboxes. A more in-depth discussion of the numerical solution approaches for the inverse problem for fNIRs is also provided.

Sparse-view and limited-angle CT reconstruction with untrained networks and deep image prior

Background and objective: Neural network based image reconstruction methods are becoming increasingly popular. However, limited training data and the lack of theoretical guarantees for generalizability raised concerns, especially in biomedical imaging applications. These challenges are known to lead to an unstable reconstruction process that poses significant problems in biomedical image reconstruction. In this paper, we present a new framework that uses untrained generator networks to tackle this challenge, leveraging the structure of deep networks for regularizing solutions based on a technique known as Deep Image Prior (DIP).Methods: To achieve a high reconstruction accuracy, we propose a framework optimizing both the latent vector and the weights of a generator network during the reconstruction process. We also propose the corresponding reconstruction strategies to improve the stability and convergent performance of the proposed framework. Furthermore, instead of calculating forward projection in each iteration, we propose implementing its normal operator as a convolutional kernel under parallel beam geometry, thus greatly accelerating the calculation.Results: Our experiments show that the proposed framework has significant improvements over other state-of-the-art conventional, pre-trained, and untrained methods under sparse-view, limited-angle, and low-dose conditions.Conclusions: Applying to parallel beam X-ray imaging, our framework shows advantages in speed, accuracy, and stability of the reconstruction process. We also show that the proposed framework is compatible with all differentiable regularizations that are commonly used in biomedical image reconstruction literature. Our framework can also be used as a post-processing technique to further improve the reconstruction generated by any other reconstruction methods. Furthermore, the proposed framework requires no training data and can be adjusted on-demand to adapt to different conditions (e.g. noise level, geometry, and imaged object).

Deep learning for biomedical image reconstruction: a survey

Medical imaging is an invaluable resource in medicine as it enables to peer inside the human body and provides scientists and physicians with a wealth of information indispensable for understanding, modelling, diagnosis, and treatment of diseases. Reconstruction algorithms entail transforming signals collected by acquisition hardware into interpretable images. Reconstruction is a challenging task given the ill-posed of the problem and the absence of exact analytic inverse transforms in practical cases. While the last decades witnessed impressive advancements in terms of new modalities, improved temporal and spatial resolution, reduced cost, and wider applicability, several improvements can still be envisioned such as reducing acquisition and reconstruction time to reduce patient's exposure to radiation and discomfort while increasing clinics throughput and reconstruction accuracy. Furthermore, the deployment of biomedical imaging in handheld devices with small power requires a fine balance between accuracy and latency.

AI transforms image reconstruction

A deep-learning-based approach improves the speed, accuracy, and robustness of biomedical image reconstruction.

THE FOURIER RADIAL ERROR SPECTRUM PLOT: A MORE NUANCED QUANTITATIVE EVALUATION OF IMAGE RECONSTRUCTION QUALITY.

In the modern biomedical image reconstruction literature, the quality of a reconstructed image is often numerically quantified using scalar error measures such as mean-squared error or the structural similarity index. While such measures provide a rough summary of image quality, they also suffer from well-known limitations. For example, a substantial amount of information is necessarily lost whenever the characteristics of a high-dimensional image are summarized by a single number. In this work, we introduce the Fourier radial Error Spectrum Plot (ESP), which provides a novel and more nuanced assessment of error by decomposing the error into its different spatial frequency components. The usefulness of ESP is illustrated in the context of MRI reconstruction from under-sampled data. In addition, we demonstrate that the extra dimension of insight provided by ESP can be used to improve the performance of existing image reconstruction techniques.

Fast reconstruction of 3D volumes from 2D CT projection data with GPUs.

BackgroundBiomedical image reconstruction applications require producing high fidelity images in or close to real-time. We have implemented reconstruction of three dimensional conebeam computed tomography(CBCT) with two dimensional projections. The algorithm takes slices of the target, weights and filters them to backproject the data, then creates the final 3D volume. We have implemented the algorithm using several hardware and software approaches and taken advantage of different types of parallelism in modern processors. The two hardware platforms used are a Central Processing Unit (CPU) and a heterogeneous system with a combination of CPU and GPU. On the CPU we implement serial MATLAB, parallel MATLAB, C and parallel C with OpenMP extensions. These codes are compared against the heterogeneous versions written in CUDA-C and OpenCL.FindingsOur results show that GPUs are particularly well suited to accelerating CBCT. Relative performance was evaluated on a mathematical phantom as well as on mouse data. Speedups of up to 200x are observed by using an AMD GPU compared to a parallel version in C with OpenMP constructs.ConclusionsIn this paper, we have implemented the Feldkamp-Davis-Kress algorithm, compatible with Fessler’s image reconstruction toolbox and tested it on different hardware platforms including CPU and a combination of CPU and GPU. Both NVIDIA and AMD GPUs have been used for performance evaluation. GPUs provide significant speedup over the parallel CPU version.