Radon Projections Research Articles

Reconstruction of blood flow velocity with deep learning information fusion from spectral ct projections and vessel geometry

In this work, we investigate a new deep learning reconstruction method of blood flow velocity within deformed vessels from contrast enhanced X-ray projections and vessel geometry. The principle of the method is to perform linear or nonlinear dimension reductions on the Radon projections and on the mesh of the vessel. These low dimensional projections are then fused to obtain the velocity field in the vessel. The accuracy of the reconstruction method is proved using various neural network architectures with realistic unsteady blood flows. The approach leverages the vessel geometry information and outperforms the simple PCA-net.

Cerebrovascular segmentation in phase-contrast magnetic resonance angiography by a Radon projection composition network.

Cerebrovascular segmentation based on phase-contrast magnetic resonance angiography (PC-MRA) provides patient-specific intracranial vascular structures for neurosurgery planning. However, the vascular complex topology and spatial sparsity make the task challenging. Inspired by the computed tomography reconstruction, this paper proposes a Radon Projection Composition Network (RPC-Net) for cerebrovascular segmentation in PC-MRA, aiming to enhance distribution probability of vessels and fully obtain the vascular topological information. Multi-directional Radon projections of the images are introduced and a two-stream network is used to learn the features of the 3D images and projections. The projection domain features are remapped to the 3D image domain by filtered back-projection transform to obtain the image-projection joint features for predicting vessel voxels. A four-fold cross-validation experiment was performed on a local dataset containing 128 PC-MRA scans. The average Dice similarity coefficient, precision and recall of the RPC-Net achieved 86.12%, 85.91% and 86.50%, respectively, while the average completeness and validity of the vessel structure were 85.50% and 92.38%, respectively. The proposed method outperformed the existing methods, especially with significant improvement on the extraction of small and low-intensity vessels. Moreover, the applicability of the segmentation for electrode trajectory planning was also validated. The results demonstrate that the RPC-Net realizes an accurate and complete cerebrovascular segmentation and has potential applications in assisting neurosurgery preoperative planning.

Satellite Image Mosaics by Using Radon Projections

In this research a new mosaics method to build larg image from different satellite senses by using slide window technique is presented. That depend on using radon projections (line integrals) as features to compare instead of comparing each element in the slide windows. This new method and its faster version proved to be a fast matching method than the regular RMS method; therefore, it can be adopted in the satellite images mosaics to build a complete view from separated views for the same location.

Reflection symmetry detection of shapes based on shape signatures

We present two novel shape signature-based reflection symmetry detection methods with their theoretical underpinning and empirical evaluation. LIP-signature and R-signature share similar beneficial properties allowing to detect reflection symmetry directions in a high-performing manner. For the shape signature of a given shape, its merit profile is constructed to detect candidates of symmetry direction. A verification process is utilized to eliminate the false candidates by addressing Radon projections. The proposed methods can effectively deal with compound shapes which are challenging for traditional contour-based methods. To quantify the symmetric efficiency, a new symmetry measure is proposed over the range [0, 1]. Furthermore, we introduce two symmetry shape datasets with a new evaluation protocol and a lost measure for evaluating symmetry detectors. Experimental results using standard and new datasets suggest that the proposed methods prominently perform compared to state of the art.

Volume imaging by tracking sparse topological features in electron micrograph tilt series

The sensitive coherent interference of electron waves arising from a specimen is useful for revealing subtle structural information in electron micrographs, which can be important for minimising dose and for rapid imaging. In general, dynamical diffraction is expected due to the useful strong interactions of electrons with matter, which can create phase contrast that violates the requisite Radon projection assumption for tomography. It is for these reasons that incoherent imaging modalities such as high angle annular dark field have been favoured to date in electron tomography of crystalline specimens, to access a monotonic relationship between specimen thickness and micrograph intensity. Here we use a geometric approach to track topological features that are robust to perturbation of the imaging conditions, to enable 3D reconstructions from electron microscope tilt series under imaging conditions that violate the Radon projection assumption, with an emphasis on phase contrast. Invoking a sparsity assumption, we demonstrate that topological features can be reliably tracked in 3D using a differential geometric form of stereoscopy, to circumvent departures from the projection approximation and reduce noise by effecting segmentation of interest points from the outset. We demonstrate this approach on a variety of different specimen and data types, from polyhedral nanoparticles, to steel dislocation networks, cryo-EM cellular structures and 3D diffuse diffraction of a relaxor ferroelectric.

Polynomial interpolation of holomorphic functions based on Radon projections

ABSTRACT We study polynomial interpolation of Hermite type of holomorphic functions based on Radon projections. We give two kinds of interpolation schemes and show that the interpolation polynomials are continuous with respect to the angles and the distances. When the chords are suitably distributed, we prove that the interpolation polynomials converge geometrically on the closed unit disk to the functions.

Radon Inversion via Deep Learning.

The Radon transform is widely used in physical and life sciences, and one of its major applications is in medical X-ray computed tomography (CT), which is significantly important in disease screening and diagnosis. In this paper, we propose a novel reconstruction framework for Radon inversion with deep learning (DL) techniques. For simplicity, the proposed framework is denoted as iRadonMAP, i.e., inverse Radon transform approximation. Specifically, we construct an interpretable neural network that contains three dedicated components. The first component is a fully connected filtering (FCF) layer along the rotation angle direction in the sinogram domain, and the second one is a sinusoidal back-projection (SBP) layer, which back-projects the filtered sinogram data into the spatial domain. Next, a common network structure is added to further improve the overall performance. iRadonMAP is first pretrained on a large number of generic images from the ImageNet database and then fine-tuned with clinical patient data. The experimental results demonstrate the feasibility of the proposed iRadonMAP framework for Radon inversion.

Video classification and retrieval through spatio-temporal Radon features

The rise in the availability of video content for access via the Internet and the medium of television has resulted in the development of automatic search procedures to retrieve the desired video. Searches can be simplified and hastened by employing automatic classification of videos. This paper proposes a descriptor called the Spatio-Temporal Histogram of Radon Projections (STHRP) for representing the temporal pattern of the contents of a video and demonstrates its application to video classification and retrieval. The first step in STHRP pattern computation is to represent any video as Three Orthogonal Planes (TOPs), i.e., XY, XT and YT, signifying the spatial and temporal contents. Frames corresponding to each plane are partitioned into overlapping blocks. Radon projections are obtained over these blocks at different orientations, resulting in weighted transform coefficients that are normalized and grouped into bins. Linear Discriminant Analysis (LDA) is performed over these coefficients of the TOPs to arrive at a compact description of STHRP pattern. Compared to existing classification and retrieval approaches, the proposed descriptor is highly robust to translation, rotation and illumination variations in videos. To evaluate the capabilities of the invariant STHRP pattern, we analyse the performance by conducting experiments on the UCF-101, HMDB51, 10contexts and TRECVID data sets for classification and retrieval using a bagged tree model. Experimental evaluation of video classification reveals that STHRP pattern can achieve classification rates of 96.15%, 71.7%, 93.24% and 97.3% for the UCF-101, HMDB51,10contexts and TRECVID 2005 data sets respectively. We conducted retrieval experiments on the TRECVID 2005, JHMDB and 10contexts data sets and the results revealed that STHRP pattern is able to provide the videos relevant to the user's query in minimal time (0.05s) with a good precision rate.

Nonconvex image reconstruction via expectation propagation.

The problem of efficiently reconstructing tomographic images can be mapped into a Bayesian inference problem over the space of pixels densities. Solutions to this problem are given by pixels assignments that are compatible with tomographic measurements and maximize a posterior probability density. This maximization can be performed with standard local optimization tools when the log-posterior is a convex function, but it is generally intractable when introducing realistic nonconcave priors that reflect typical images features such as smoothness or sharpness. We introduce a new method to reconstruct images obtained from Radon projections by using expectation propagation, which allows us to approximate the intractable posterior. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, expectation propagation paired with very simple but non-log-concave priors is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing the solution of this problem in terms of the measured data, under the assumption of the constant and known speed of sound. However, almost all of these formulas require data to be measured either on an unbounded surface, or on a closed surface completely surrounding the object. This is too restrictive for practical applications. The alternative approach we present, under certain restriction on geometry, yields a theoretically exact reconstruction of the standard Radon projections of the source from the data measured on a finite open surface. In addition, this technique reduces the time interval where the data should be known. In general, our method requires a pre-computation of densities of certain single-layer potentials. However, in the case of a truncated circular or spherical acquisition surface, these densities are easily obtained analytically, which leads to fully explicit asymptotically fast algorithms. We test these algorithms in a series of numerical simulations.

Harmonic interpolation of Hermite type based on Radon projections with constant distances

ABSTRACTWe study harmonic interpolation of Hermite type of harmonic functions based on Radon projections with constant distances of chords. We show that the interpolation polynomials are continuous with respect to the angles and the distances. When the chords coalesce to some points on the unit circle, we prove that the interpolation polynomials tend to a Hermite interpolation polynomial at the coalescing points.

Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix

Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a natural sparsity, one can directly employ compressive sensing (CS) techniques to reconstruct the CT images. In CS, sensing matrices having low coherence (a measure providing correlation among columns) provide better image reconstruction. However, the sensing matrix constructed through the incomplete angular set of Radon projections typically possesses large coherence. In this paper, we attempt to reduce the coherence of the sensing matrix via a square and invertible preconditioner possessing a small condition number, which is obtained through a convex optimization technique. The stated properties of our preconditioner imply that it can be used effectively even in noisy cases. We demonstrate empirically that the preconditioned sensing matrix yields better signal recovery than the original sensing matrix.

A sequential search-space shrinking using CNN transfer learning and a Radon projection pool for medical image retrieval

Closing the semantic gap in medical image analysis is critical. Access to large-scale datasets might help to narrow the gap. However, large and balanced datasets may not always be available. On the other side, retrieving similar images from an archive is a valuable task to facilitate better diagnosis. In this work, we concentrate on forming a search space, consisting of the most similar images for a given query, to be used for a similarity-based search technique in a retrieval system. We propose a two-step hierarchical shrinking search space when local binary patterns are used. Transfer learning via convolutional neural networks is utilized for the first stage of search space shrinking, followed by creating a selection pool using Radon transform for further reduction. The difference between two orthogonal Radon projections is considered in the selection pool to extract more information. The IRMA dataset, from ImageCLEF initiative, containing 14,400 X-ray images, is used to validate the proposed scheme. We report a total IRMA error of 168.05 (or 90.30% accuracy) which is the best result compared with existing methods in the literature for this dataset when real-time processing is considered.

A Reweighted Joint Spatial-Radon Domain CT Image Reconstruction Model for Metal Artifact Reduction

High density implants such as metals often lead to serious artifacts in the reconstructed CT images which hampers the accuracy of image based diagnosis and treatment planning. In this paper, we propose a novel wavelet frame based CT image reconstruction model to reduce metal artifacts. This model is built on a joint spatial and Radon (projection) domain (JSR) image reconstruction framework with a built-in weighting and re-weighting mechanism in Radon domain to repair degraded projection data. The new weighting strategy used in the proposed model not only makes the regularization in Radon domain by wavelet frame transform more effective, but also makes the commonly assumed linear model for CT imaging a more accurate approximation of the nonlinear physical problem. The proposed model, which will be referred to as the re-weighted JSR model, combines the ideas of the recently proposed wavelet frame based JSR model \cite{Dong2013} and the normalized metal artifact reduction model \cite{meyer2010normalized}, and manages to achieve noticeably better CT reconstruction quality than both methods. To solve the proposed re-weighted JSR model, an efficient alternative iteration algorithm is proposed with guaranteed convergence. Numerical experiments on both simulated and real CT image data demonstrate the effectiveness of the re-weighted JSR model and its advantage over some of the state-of-the-art methods.

Using Few Radon Projections to Recover 3-D NMR Spectrum

Given a regular binary function f on R2 with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.Keywords: Radon transforms, transformation of an image, Back projection.

A parameter for the assessment of the segmentation of TEM tomography reconstructed volumes based on mutual information

A method is proposed and verified for selecting the optimum segmentation of a TEM reconstruction among the results of several segmentation algorithms. The selection criterion is the accuracy of the segmentation. To do this selection, a parameter for the comparison of the accuracies of the different segmentations has been defined. It consists of the mutual information value between the acquired TEM images of the sample and the Radon projections of the segmented volumes. In this work, it has been proved that this new mutual information parameter and the Jaccard coefficient between the segmented volume and the ideal one are correlated. In addition, the results of the new parameter are compared to the results obtained from another validated method to select the optimum segmentation.

Novel phase-based descriptor using bispectrum for texture classification

In this paper, we propose a novel rotation invariant and noise tolerant descriptor for texture classification. This descriptor is based on circular statistics of Fourier phase. This one is recovered from the third order spectrum namely the bispectrum, known to provide invariance properties and to preserve phase information. The computational complexity of two dimensional image is reduced using Radon transform. At first, the input image is decomposed into a set of 1D radon projections. Then, for each projection the bispectrum is computed and the phase vector is recovered. Features vectors contain circular statistics of each phase vector recovered from bispectrum of each 1D projection. The proposed descriptor is evaluated on three test suites from the database “Outex” and compared with three descriptors also based on the phase. According to the classification experiments, our descriptor achieves highest rates under noise, illumination and rotation changes.

On Tomography with Limited Data

We give an algorithm for reconstructing a density function f in the plane from limited number of Radon projections on a range of angles −𝝋∗<𝝋<𝝋∗ together with a few well selected angles outside this range. In doing so, we assume that f is subjected to a linear transformation that produces g, and actually recover g. Interpolation is a basic tool in our calculations

Linear Transformation Recognition Using Radon Transform

Given two regular functions (images) f and g on R2 where g is formed from f by a general linear transformation, g(x) = f (Ax + b). We present a procedure to determine the transformation ‘parameters’ A and b using Radon projections of f and only two projections of g. We use these projections together with simple facts on matrix vector multiplication to recover the matrix A. The assumptions we have here are: f is nonnegative and A is nonsingular. Commonly used transformations in image processing such as rotation, scaling and others are special cases of our approach.

Harmonic interpolation of Hermite type based on Radon projections in two directions

We study Hermite-type interpolation based on Radon projections. We give necessary and sufficient conditions for regularity in the cases in which chords lie in two directions. We also prove that the interpolation polynomials are continuous with respect to the distance from the origin to the chords.