Regularizing Image Reconstruction for Gradient-Domain Rendering with Feature Patches

We present a novel algorithm to reconstruct high-quality images from sampled pixels and gradients in gradient-domain rendering. Our approach extends screened Poisson reconstruction by adding additional regularization constraints. Our key idea is to exploit local patches in feature images, which contain per-pixels normals, textures, position, etc., to formulate these constraints. We describe a GPU implementation of our approach that runs on the order of seconds on megapixel images. We demonstrate a significant improvement in image quality over screened Poisson reconstruction under the L1 norm. Because we adapt the regularization constraints to the noise level in the input, our algorithm is consistent and converges to the ground truth.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Three-dimensional image reconstruction of dephosphorylated smooth muscle heavy meromyosin reveals asymmetry in the interaction between myosin heads and placement of subfragment 2

Regulation of the actin-activated ATPase of smooth muscle myosin II is known to involve an interaction between the two heads that is controlled by phosphorylation of the regulatory light chain. However, the three-dimensional structure of this inactivated form has been unknown. We have used a lipid monolayer to obtain two-dimensional crystalline arrays of the unphosphorylated inactive form of smooth muscle heavy meromyosin suitable for structural studies by electron cryomicroscopy of unstained, frozen-hydrated specimens. The three-dimensional structure reveals an asymmetric interaction between the two myosin heads. The ATPase activity of one head is sterically “blocked” because part of its actin-binding interface is positioned onto the converter domain of the second head. ATPase activity of the second head, which can bind actin, appears to be inhibited through stabilization of converter domain movements needed to release phosphate and achieve strong actin binding. When the subfragment 2 domain of heavy meromyosin is oriented as it would be in an actomyosin filament lattice, the position of the heads is very different from that needed to bind actin, suggesting an additional contribution to ATPase inhibition in situ.

Image reconstruction in full-field Fourier-domain optical coherence tomography

Full-field Fourier-domain optical coherence tomography (3F-OCT) is a full-field version of spectral domain/swept source optical coherence tomography. A set of two-dimensional Fourier holograms is recorded at discrete wavenumbers spanning the swept source tuning range. The resultant three-dimensional data cube contains comprehensive information on the three-dimensional spatial properties of the sample, including its morphological layout and optical scatter. The morphological layout can be reconstructed in software via three-dimensional discrete Fourier transformation. The spatial resolution of the 3F-OCT reconstructed image, however, is degraded due to the presence of a phase cross-term, whose origin and effects are addressed in this paper. We present a theoretical and experimental study of the imaging performance of 3F-OCT, with particular emphasis on elimination of the deleterious effects of the phase cross-term.

High-resolution image reconstruction from multiple low-resolution images.

In this paper, we demonstrate a digital signal processing (DSP) algorithm for improving spatial resolution of images captured by CMOS cameras. The basic approach is to reconstruct a high resolution (HR) image from a shift-related low resolution (LR) image sequence. The aliasing relationship of Fourier transforms between discrete and continuous images in the frequency domain is used for mapping LR images to a HR image. The method of projection onto convex sets (POCS) is applied to trace the best estimate of pixel matching from the LR images to the reconstructed HR image. Computer simulations and preliminary experimental results have shown that the algorithm works effectively on the application of post-image-captured processing for CMOS cameras. It can also be applied to HR digital image reconstruction, where shift information of the LR image sequence is known.

Prior image-constrained l(1)-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography

A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in multimodal diffuse optical tomographic imaging is introduced. This approach is based on a prior image-constrained-l(1) minimization scheme and has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the proposed framework is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information. (C) 2012 Optical Society of America

Data-resolution based optimal choice of minimum required measurements for image-guided diffuse optical tomography

Image-guided diffuse optical tomography has the advantage of reducing the total number of optical parameters being reconstructed to the number of distinct tissue types identified by the traditional imaging modality, converting the optical image-reconstruction problem from underdetermined in nature to overdetermined. In such cases, the minimum required measurements might be far less compared to those of the traditional diffuse optical imaging. An approach to choose these optimally based on a data-resolution matrix is proposed, and it is shown that such a choice does not compromise the reconstruction performance. (C) 2013 Optical Society of America

Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography

Typical image-guided diffuse optical tomographic image reconstruction procedures involve reduction of the number of optical parameters to be reconstructed equal to the number of distinct regions identified in the structural information provided by the traditional imaging modality. This makes the image reconstruction problem less ill-posed compared to traditional underdetermined cases. Still, the methods that are deployed in this case are same as those used for traditional diffuse optical image reconstruction, which involves a regularization term as well as computation of the Jacobian. A gradient-free Nelder-Mead simplex method is proposed here to perform the image reconstruction procedure and is shown to provide solutions that closely match ones obtained using established methods, even in highly noisy data. The proposed method also has the distinct advantage of being more efficient owing to being regularization free, involving only repeated forward calculations. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Projection Error Propagation-based Regularization (PEPR) method for resistivity reconstruction in Electrical Impedance Tomography (EIT)

A novel Projection Error Propagation-based Regularization (PEPR) method is proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error developed by difference between experimental measurements and calculated data. The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. Resistivity imaging of practical phantoms in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm as well as with Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS) with PEPR. The effect of PEPR method is also studied with phantoms with different configurations and with different current injection methods. All the resistivity images reconstructed with PEPR method are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the projection error and solution error in each iterations both for simulated and experimental data in both the algorithms and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP). (C) 2013 Elsevier Ltd. All rights reserved.

A MatLAB Based Virtual Phantom for 2D Electrical Impedance Tomography (MatVP2DEIT): Studying the Medical Electrical Impedance Tomography Reconstruction in Computer

Electrical Impedance Tomography (EIT) is a computerized medical imaging technique which reconstructs the electrical impedance images of a domain under test from the boundary voltage-current data measured by an EIT electronic instrumentation using an image reconstruction algorithm. Being a computed tomography technique, EIT injects a constant current to the patient's body through the surface electrodes surrounding the domain to be imaged (Omega) and tries to calculate the spatial distribution of electrical conductivity or resistivity of the closed conducting domain using the potentials developed at the domain boundary (partial derivative Omega). Practical phantoms are essentially required to study, test and calibrate a medical EIT system for certifying the system before applying it on patients for diagnostic imaging. Therefore, the EIT phantoms are essentially required to generate boundary data for studying and assessing the instrumentation and inverse solvers a in EIT. For proper assessment of an inverse solver of a 2D EIT system, a perfect 2D practical phantom is required. As the practical phantoms are the assemblies of the objects with 3D geometries, the developing of a practical 2D-phantom is a great challenge and therefore, the boundary data generated from the practical phantoms with 3D geometry are found inappropriate for assessing a 2D inverse solver. Furthermore, the boundary data errors contributed by the instrumentation are also difficult to separate from the errors developed by the 3D phantoms. Hence, the errorless boundary data are found essential to assess the inverse solver in 2D EIT. In this direction, a MatLAB-based Virtual Phantom for 2D EIT (MatVP2DEIT) is developed to generate accurate boundary data for assessing the 2D-EIT inverse solvers and the image reconstruction accuracy. MatVP2DEIT is a MatLAB-based computer program which simulates a phantom in computer and generates the boundary potential data as the outputs by using the combinations of different phantom parameters as the inputs to the program. Phantom diameter, inhomogeneity geometry (shape, size and position), number of inhomogeneities, applied current magnitude, background resistivity, inhomogeneity resistivity all are set as the phantom variables which are provided as the input parameters to the MatVP2DEIT for simulating different phantom configurations. A constant current injection is simulated at the phantom boundary with different current injection protocols and boundary potential data are calculated. Boundary data sets are generated with different phantom configurations obtained with the different combinations of the phantom variables and the resistivity images are reconstructed using EIDORS. Boundary data of the virtual phantoms, containing inhomogeneities with complex geometries, are also generated for different current injection patterns using MatVP2DEIT and the resistivity imaging is studied. The effect of regularization method on the image reconstruction is also studied with the data generated by MatVP2DEIT. Resistivity images are evaluated by studying the resistivity parameters and contrast parameters estimated from the elemental resistivity profiles of the reconstructed phantom domain. Results show that the MatVP2DEIT generates accurate boundary data for different types of single or multiple objects which are efficient and accurate enough to reconstruct the resistivity images in EIDORS. The spatial resolution studies show that, the resistivity imaging conducted with the boundary data generated by MatVP2DEIT with 2048 elements, can reconstruct two circular inhomogeneities placed with a minimum distance (boundary to boundary) of 2 mm. It is also observed that, in MatVP2DEIT with 2048 elements, the boundary data generated for a phantom with a circular inhomogeneity of a diameter less than 7% of that of the phantom domain can produce resistivity images in EIDORS with a 1968 element mesh. Results also show that the MatVP2DEIT accurately generates the boundary data for neighbouring, opposite reference and trigonometric current patterns which are very suitable for resistivity reconstruction studies. MatVP2DEIT generated data are also found suitable for studying the effect of the different regularization methods on reconstruction process. Comparing the reconstructed image with an original geometry made in MatVP2DEIT, it would be easier to study the resistivity imaging procedures as well as the inverse solver performance. Using the proposed MatVP2DEIT software with modified domains, the cross sectional anatomy of a number of body parts can be simulated in PC and the impedance image reconstruction of human anatomy can be studied.

Toward Real-Time Availability of 3D Temperature Maps Created with Temporally Constrained Reconstruction

PurposeTo extend the previously developed temporally constrained reconstruction (TCR) algorithm to allow for real-time availability of three-dimensional (3D) temperature maps capable of monitoring MR-guided high intensity focused ultrasound applications. MethodsA real-time TCR (RT-TCR) algorithm is developed that only uses current and previously acquired undersampled k-space data from a 3D segmented EPI pulse sequence, with the image reconstruction done in a graphics processing unit implementation to overcome computation burden. Simulated and experimental data sets of HIFU heating are used to evaluate the performance of the RT-TCR algorithm. ResultsThe simulation studies demonstrate that the RT-TCR algorithm has subsecond reconstruction time and can accurately measure HIFU-induced temperature rises of 20 degrees C in 15 s for 3D volumes of 16 slices (RMSE = 0.1 degrees C), 24 slices (RMSE = 0.2 degrees C), and 32 slices (RMSE = 0.3 degrees C). Experimental results in ex vivo porcine muscle demonstrate that the RT-TCR approach can reconstruct temperature maps with 192 x 162 x 66 mm 3D volume coverage, 1.5 x 1.5 x 3.0 mm resolution, and 1.2-s scan time with an accuracy of 0.5 degrees C. ConclusionThe RT-TCR algorithm offers an approach to obtaining large coverage 3D temperature maps in real-time for monitoring MR-guided high intensity focused ultrasound treatments. Magn Reson Med 71:1394-1404, 2014. (c) 2013 Wiley Periodicals, Inc.