Real-time dynamic image reconstruction in time-domain diffuse optical tomography

In diffuse optical tomography (DOT), real-time image reconstruction of oxy- and deoxy-haemoglobin changes occurring in the brain could give valuable information in clinical care settings. Although non-linear reconstruction techniques could provide more accurate results, their computational burden makes them unsuitable for real-time applications. Linear techniques can be employed under the assumption that the expected change in absorption is small. Several approaches exist, differing primarily in their handling of regularization and the noise statistics. In real experiments, it is impossible to compute the true noise statistics, because of the presence of physiological oscillations in the measured data. This is even more critical in real-time applications, where no off-line filtering and averaging can be performed to reduce the noise level. Therefore, many studies substitute the noise covariance matrix with the identity matrix. In this paper, we examined two questions: does using the noise model with realistic, imperfect data yield an improvement in image quality compared to using the identity matrix; and what is the difference in quality between online and offline reconstructions. Bespoke test data were created using a novel process through which simulated changes in absorption were added to real resting-state DOT data. A realistic multi-layer head model was used as the geometry for the reconstruction. Results validated our assumptions, highlighting the validity of computing the noise statistics from the measured data for online image reconstruction, which was performed at 2 Hz. Our results can be directly extended to a real application where real-time imaging is required.

We describe a method to increase the speed of convergence for the simultaneous reconstruction of absorption and scattering images in Diffuse Optical Tomography (DOT). We used the diffusion approximation of the radiative transfer equation and the Finite Element Method (FEM) to solve the forward problem. The absorption and reduced scattering images are reconstructed by inverting the distribution of the moments of the time-dependent detected light flux. The inverse problem is solved with an optimization algorithm like ART or Conjugate Gradient. This ill-posed inverse problem can be simplified by using a priori knowledge of the studied objects. In this paper, we consider that DOT is a functional imaging technique that can be complemented by an anatomical imaging technique like Magnetic Resonance Imaging (MRI). We used anatomic information obtained from MRI as prior knowledge to compute optical absorption and scattering images. In a first step, MRI segmented images were only used to mesh our phantoms, with a finer resolution around boundaries. In a second step, we computed optical images with homogeneous properties from the segmented MRI image, in order to initialise our optimisation process. These two initialisations yield better reconstructed images. Reconstruction from simulated and experimental data will be presented.

We describe a method to increase the speed of convergence for the simultaneous reconstruction of absorption and scattering images in Diffuse Optical Tomography (DOT). We used the diffusion approximation of the radiative transfer equation and the Finite Element Method (FEM) to solve the forward problem. The absorption and reduced scattering images are reconstructed by inverting the distribution of the moments of the time-dependent detected light flux. The inverse problem is solved with an optimization algorithm like ART or Conjugate Gradient. This ill-posed inverse problem can be simplified by using <i>a priori</i> knowledge of the studied objects. In this paper, we consider that DOT is a functional imaging technique that can be complemented by an anatomical imaging technique like Magnetic Resonance Imaging (MRI). We used anatomic information obtained from MRI as prior knowledge to compute optical absorption and scattering images. In a first step, MRI segmented images were only used to mesh our phantoms, with a finer resolution around boundaries. In a second step, we computed optical images with homogeneous properties from the segmented MRI image, in order to initialise our optimisation process. These two initialisations yield better reconstructed images. Reconstruction from simulated and experimental data will be presented.

Effective optode configuration for the image reconstruction in diffuse optical tomography

The image reconstruction for Fourier-domain optical coherence tomography (FD-OCT) could be achieved by iterative methods, which offer a more accurate estimation than the traditional inverse discrete Fourier transform (IDFT) reconstruction. However, the existing iterative methods are mostly A-line-based and are developed on CPU, which causes slow reconstruction. Besides, A-line-based reconstruction makes the iterative methods incompatible with most existing image-level image processing techniques. In this paper, we proposed an iterative method that enables B-scan-based OCT image reconstruction, which has three major advantages: (1) Large-scale parallelism of the OCT dataset is achieved by using GPU acceleration. (2) A novel image-level cross-domain regularizer was developed, such that the image processing could be performed simultaneously during the image reconstruction; an enhanced image could be directly generated from the OCT interferogram. (3) The scalability of the proposed method was demonstrated for 3D OCT image reconstruction. Compared with the state-of-the-art (SOTA) iterative approaches, the proposed method achieves higher image quality with reduced computational time by orders of magnitude. To further show the image enhancement ability, a comparison was conducted between the proposed method and the conventional workflow, in which an IDFT reconstructed OCT image is later processed by a total variation-regularized denoising algorithm. The proposed method can achieve a better performance evaluated by metrics such as signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), while the speed is improved by more than 30 times. Real-time image reconstruction at more than 20 B-scans per second was realized with a frame size of 4096 (axial) × 1000 (lateral), which showcases the great potential of the proposed method in real-world applications.

The underdeterminedness of the inverse problems encountered in diffuse optical tomography (DOT) becomes especially severe when detecting breast cancers, because much more variables are needed to be reconstructed due to the big-size. With the addition of ill-condition caused by the diffusive nature of light propagation, the ill-posedness makes it very difficult to improve the image reconstruction. Fortunately, from the anatomy viewpoint, we have known that the cancer is distributed locally and only amounts to a small percentage of the whole breast. This makes it possible to employ the compressive sensing theory to mitigate the ill-posedness, based on the prior knowledge about the sparsity of the signal to be reconstructed. Specifically speaking, sparsity regularizations can be used in DOT to improve the image reconstruction under the premise that un-increase the number of measurements required in the reconstruction. In this paper, we primarily focus on comparing the performances of different kinds of L_p-norm-based regularizations in terms of theory and real effects, respectively. The numerical and phantom experiments have proven that the sparsity regularizations can dramatically improve the image reconstruction. Furthermore, as the p in the L_p-norm decreasing to zero, the solutions become sparser and the corresponding image quality gets higher, with smooth L₀-norm-based regularization providing the highest image quality.

Ultrasound computed tomography is an inexpensive and radiation-free medical imaging technique used to quantify the tissue acoustic properties for advanced clinical diagnosis. Image reconstruction in ultrasound tomography is often modeled as an optimization scheme solved by iterative methods like full-waveform inversion. These iterative methods are computationally expensive, while the optimization problem is ill-posed and nonlinear. To address this problem, we propose to use deep learning to overcome the computational burden and ill-posedness, and achieve near real-time image reconstruction in ultrasound tomography. We aim to directly learn the mapping from the recorded time-series sensor data to a spatial image of acoustical properties. To accomplish this, we develop a deep learning model using two cascaded convolutional neural networks with an encoder–decoder architecture. We achieve a good representation by first extracting the intermediate mapping-knowledge and later utilizing this knowledge to reconstruct the image. This approach is evaluated on synthetic phantoms where simulated ultrasound data are acquired from a ring of transducers surrounding the region of interest. The measurement data is acquired by forward modeling the wave equation using the k-wave toolbox. Our simulation results demonstrate that our proposed deep-learning method is robust to noise and significantly outperforms the state-of-the-art traditional iterative method both quantitatively and qualitatively. Furthermore, our model takes substantially less computational time than the conventional full-wave inversion method.

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

Current fluorescence diffuse optical tomography (fDOT) systems can provide large data sets and, in addition, the unknown parameters to be estimated are so numerous that the sensitivity matrix is too large to store. Alternatively, iterative methods can be used, but they can be extremely slow at converging when dealing with large matrices. A few approaches suitable for the reconstruction of images from very large data sets have been developed. However, they either require explicit construction of the sensitivity matrix, suffer from slow computation times, or can only be applied to restricted geometries. We introduce a method for fast reconstruction in fDOT with large data and solution spaces, which preserves the resolution of the forward operator whilst compressing its representation. The method does not require construction of the full matrix, and thus allows storage and direct inversion of the explicitly constructed compressed system matrix. The method is tested using simulated and experimental data. Results show that the fDOT image reconstruction problem can be effectively compressed without significant loss of information and with the added advantage of reducing image noise.

The relationship between conventional reference measurement correction and approximation error modelling in linear reconstruction in diffuse optical tomography is considered.

Parallel Image Reconstruction in Real-Time Ultrasound Process Tomography for Two-phased Flow Measurements

Time-domain diffuse optical tomography (TD-DOT) is interested to many scholars due to its unique features such as rich information in each measured pulse, elimination of cross-talk in the reconstruction, and no need for the measurement calibration, although TD-DOT imaging system requires very expensive equipment. Usually, the generalized pulse spectrum technique (GPST) is applied to transform the real domain optical diffusion forward model into its Laplacian domain. However, the application of TD-DOT has been limited by the low spatial resolution due to strong optical scattering in tissues. In this study, we introduced the anatomical guidance from computed tomography (CT) and positron emission tomography (PET) into TD-DOT to improve the quality of the reconstructed TD-DOT images with the soft prior method. Furthermore, we have investigated to maximize the utilization of the rich information contained in the measured pulses by increasing the frequency number in the Laplacian transformation. To validate the proposed method, we have performed numerical simulation studies by using the CT/PET breast images of a breast cancer patient, in which we generated the breast mesh from CT images and obtained the breast tumor position and size from the PET images. The soft prior guidance based TD-DOT reconstruction was performed in the Laplacian domain. Our simulation results indicate that the spatial resolution and the accuracy of the reconstructed TD-DOT images have been improved substantially after applying the anatomical guidance.

Malignant breast lesions manifest in a variety of shapes and configurations. Here we propose an algorithm utilizing anisotropic-tumor-prior guided diffuse optical tomography (DOT) reconstructions to recover an unknown tumor’s orientation and shape anisotropy.

Based on a 3D pre-treatment magnetic resonance (MR) scan, we developed DREME-MR to jointly reconstruct the reference patient anatomy and solve a data-driven, patient-specific cardiorespiratory motion model. Via a motion encoder simultaneously learned during the reconstruction, DREME-MR further enables real-time volumetric MR imaging and cardiorespiratory motion tracking with minimal intra-treatment k-space data.&#xD;&#xD;Approach: DREME-MR integrates dynamic MRI reconstruction and real-time MR imaging into a unified, dual-task learning framework. From a 3D radial-spoke-based pre-treatment MR scan, DREME-MR uses spatiotemporal implicit-neural-representation (INR) to reconstruct pre-treatment dynamic volumetric MR images (learning task 1). The INR-based reconstruction takes a joint image reconstruction and deformable registration approach, yielding a reference anatomy and a corresponding cardiorespiratory motion model. The motion model adopts a low-rank, multi-resolution representation to approximate motion fields as products of motion coefficients and motion basis components (MBCs). Via a progressive, frequency-guided strategy, DREME-MR decouples cardiac MBCs from respiratory MBCs to resolve the two distinct motion modes. Simultaneously with the pre-treatment dynamic MRI reconstruction, DREME-MR also trains a multilayer perceptron (MLP)-based motion encoder to infer cardiorespiratory motion coefficients directly from the raw k-space data (learning task 2), allowing real-time, intra-treatment volumetric MR imaging and motion tracking with minimal k-space data (20-30 spokes) acquired after the pre-treatment MRI scan.&#xD;&#xD;Main results: Evaluated using data from a digital phantom (XCAT) and a human scan, DREME-MR solves real-time 3D cardiorespiratory motion with a latency of < 165 ms (= 150-ms data acquisition + 15-ms inference time), fulfilling the temporal constraint of real-time imaging. The XCAT study achieves mean(±S.D.) center-of-mass tracking errors of 0.73±0.38mm for a lung tumor and 1.69±1.12mm for the left ventricle. The human study shows good motion correlations (liver: 0.96; left ventricle: 0.65) between DREME-MR-solved motion and extracted surrogate signals.&#xD;&#xD;Significance: DREME-MR allows real-time 3D MRI and cardiorespiratory motion tracking with low latency, advancing intra-treatment MR-guided adaptive radiotherapy, including real-time multileaf collimator (MLC) tracking.

12 - Direct image reconstruction in electrical tomography and its applications