Theory Of Image Reconstruction Research Articles

Image Denoising by Deep Convolution Based on Sparse Representation

Noise filtering is a crucial task in digital image processing, performing the function of preprocessing. In this paper, we propose an algorithm that employs deep convolution and soft thresholding iterative algorithms to extract and learn the features of noisy images. The extracted features are acquired through prior and sparse representation theory for image reconstruction. Effective separation of the image and noise is achieved using an end-to-end network of dilated convolution and fully connected layers. Several experiments were performed on public images subject to various levels of Gaussian noise, in order to evaluate the effectiveness of the proposed approach. The results indicated that our algorithm achieved a high peak signal-to-noise ratio (PSNR) and significantly improved the visual effects of the images. Our study supports the effectiveness of our approach and substantiates its potential to be applied to a broad spectrum of image processing tasks.

A Method for Calculating Characteristic Value to Characterize the Induced Charge in Electrostatic Tomography

Electrostatic tomography (EST) is a technology that uses the induced charge on the electrode surface to reconstruct the parameter distribution of gas-solid two-phase flow. The induced signal is dynamic, whereas the induced charge required in the image reconstruction theory is static. Therefore, it is necessary to calculate the characteristic value of the signal to characterize the induced charge before image reconstruction. However, the calculation methods of characteristic value are different at present, and there is a lack of unified understanding. For the above problem, this article analyzes the mechanism of signal induced by the charged single particle, compares the differences between the charge-sensitive and current-sensitive preamplifiers, and comes to the conclusion that the current-sensitive preamplifier is more suitable for the measurement of induced charge. By further studying the output signal of the conditioning circuit with the current-sensitive preamplifier, root mean square of charge (RMSCE) is proposed to characterize the induced charge. Simulation and experimental results show that RMSCE has stronger characterization ability for the induced charge and can be used in EST system to obtain high-quality reconstructed images.

Reversible Autoencoder: A CNN-Based Nonlinear Lifting Scheme for Image Reconstruction

Emerging deep learning approaches have facilitated image reconstruction at the expense of excessive model complexities and lack of theoretical guarantees of stability. In this paper, we propose a theoretically sound deep architecture, named reversible autoencoder (Rev-AE), from the perspective of well-developed frame theory for image reconstruction. Reversible blocks (Rev-Blocks) are developed as fundamental building blocks to realize nonlinear dimension invariant transform, up-sampling (with dimension growth) and down-sampling (with dimension reduction) in Rev-AE. The Rev-Block integrates CNN-based operators with the two-stream structure of lifting scheme to introduce nonlinearity and achieve reversibility. Therefore, Rev-AE only requires training and storage of encoder parameters. Furthermore, Rev-AE bridges existing nonlinear CNNs and well-established traditional signal processing tools to realize end-to-end optimized reversible networks with a guarantee of stability for image reconstruction for the first time. Theoretical analysis demonstrates that reversible blocks guarantee perfect reconstruction with derived frame bounds and are robust to noise perturbation under restricted energy propagation of noise. Moreover, we prove that Rev-AE achieves stable reconstruction with bounded projection angle under the presence of down-sampling and up-sampling. The stability and robustness of Rev-Blocks are also validated with numerical evaluations. Experimental results demonstrate that Rev-AE achieves comparable performance with halved parameters in comparison to recent leading methods (e.g., 3-D CNN based autoencoder and ISTA-Net$^+$) in the applications of image compression and compressive sensing.

Time-resolved C-arm cone beam CT angiography (TR-CBCTA) imaging from a single short-scan C-arm cone beam CT acquisition with intra-arterial contrast injection

Time-resolved C-arm cone-beam CT (CBCT) angiography (TR-CBCTA) images can be generated from a series of CBCT acquisitions that satisfy data sufficiency condition in analytical image reconstruction theory. In this work, a new technique was developed to generate TR-CBCTA images from a single short-scan CBCT data acquisition with contrast media injection. The reconstruction technique enabling this application is a previously developed image reconstruction technique, synchronized multi-artifact reduction with tomographic reconstruction (SMART-RECON). In this new application, the acquired short-scan CBCT projection data were sorted into a union of several sub-sectors of view angles and each sub-sector of view angles corresponds to an individual image volume to be reconstructed. The SMART-RECON method was then used to jointly reconstruct all of these individual image volumes under two constraints: (1) each individual image volume is maximally consistent with the measured cone-beam projection data within the corresponding view angle sector and (2) the nuclear norm of the image matrix is minimized. The difference between these reconstructed individual image volumes is used to generated the desired subtracted angiograms. To validate the technique, numerical simulation data generated from a fractal tree angiogram phantom were used to quantitatively study the accuracy of the proposed method and retrospective in vivo human subject studies were used to demonstrate the feasibility of generating TR-CBCTA in clinical practice.

Accurate Transaxial Region-of-Interest Reconstruction in Helical CT?

In conventional helical computed tomography (CT), the field-of-view is a cylinder centered on the axis of the helix. Here, we consider the situation where all measurement lines are blocked except those intersecting a small cylindrical region-of-interest (ROI) not necessarily centered on the axis of the system. We address the question of image reconstruction inside the ROI. The patient boundary is assumed known, and we avoid the “interior problem” by assuming that the ROI includes part of the patient boundary. By applying analytic image reconstruction theory, we show that the entire cylindrical ROI can be reconstructed provided the pitch of the helix does not violate the well-known Tam–Danielsson detector condition. Using an iterative algorithm, we performed ROI reconstruction from simulated phantom data and from real patient data, and compared the results with full-field reconstructions. Visually, the ROI reconstructed images perfectly matched the full-field reconstructions. However, there were small quantitative discrepancies near the interior boundaries of the ROIs, which we attribute to the known reduced stability at one side of the inverse truncated Hilbert transform. In conclusion, we have demonstrated mathematically that accurate transverse ROI reconstruction is possible for helical CT, although care must be taken near the interior boundary to achieve quantitative accuracy.

Generalized Fourier slice theorem for cone-beam image reconstruction.

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is <formula>O(N^4)</formula>, which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Sub-surface elastography based on the dynamic shear strain analysis

Quantitative acoustical imaging methods estimate the characteristics of the tissue elasticity of a region of interest having somewhat inhomogeneity contrasted to the surrounding soft tissues. The aim of this research is to propose a novel near-field imaging method for the shear wave elastography and sub-wavelength imaging. The proposed imaging methodology utilizes the determinant of a covariance matrix which is composed of the orthogonal pair of the shear strain variations. The image reconstruction theory can be summarized as follows. 1) The distributions of the normal displacement of the skin surface is governed by the 2-dimensional wave equation in the Lamb-wave field. 2) When the single propagating wave front exists on the surface of the tissue without any stiffer regions, therefore, the orthogonal pair of the out-of-surface shear strains are linearly dependent each other. Therefore the determinant of a covariance matrix which is composed of the orthogonal pair of the shear strains becomes zero. 3) When a region of interest having somewhat inhomogeneity exists, scattered wave field arises in the Lamb-wave field. Consequently, the determinant becomes larger than zero because of the independency between the orthogonal pair over the region of the scattered and incident wave field.

Dual‐source spiral CT with pitch up to 3.2 and 75 ms temporal resolution: Image reconstruction and assessment of image quality

To present the theory for image reconstruction of a high-pitch, high-temporal-resolution spiral scan mode for dual-source CT (DSCT) and evaluate its image quality and dose. With the use of two x-ray sources and two data acquisition systems, spiral CT exams having a nominal temporal resolution per image of up to one-quarter of the gantry rotation time can be acquired using pitch values up to 3.2. The scan field of view (SFOV) for this mode, however, is limited to the SFOV of the second detector as a maximum, depending on the pitch. Spatial and low contrast resolution, image uniformity and noise, CT number accuracy and linearity, and radiation dose were assessed using the ACR CT accreditation phantom, a 30 cm diameter cylindrical water phantom or a 32 cm diameter cylindrical PMMA CTDI phantom. Slice sensitivity profiles (SSPs) were measured for different nominal slice thicknesses, and an anthropomorphic phantom was used to assess image artifacts. Results were compared between single-source scans at pitch = 1.0 and dual-source scans at pitch = 3.2. In addition, image quality and temporal resolution of an ECG-triggered version of the DSCT high-pitch spiral scan mode were evaluated with a moving coronary artery phantom, and radiation dose was assessed in comparison with other existing cardiac scan techniques. No significant differences in quantitative measures of image quality were found between single-source scans at pitch = 1.0 and dual-source scans at pitch = 3.2 for spatial and low contrast resolution, CT number accuracy and linearity, SSPs, image uniformity, and noise. The pitch value (1.6 pitch 3.2) had only a minor impact on radiation dose and image noise when the effective tube current time product (mA s/pitch) was kept constant. However, while not severe, artifacts were found to be more prevalent for the dual-source pitch = 3.2 scan mode when structures varied markedly along the z axis, particularly for head scans. Images of the moving coronary artery phantom acquired with the ECG-triggered high-pitch scan mode were visually free from motion artifacts at heart rates of 60 and 70 bpm. However, image quality started to deteriorate for higher heart rates. At equivalent image quality, the ECG-triggered high-pitch scan mode demonstrated lower radiation dose than other cardiac scan techniques on the same DSCT equipment (25% and 60% dose reduction compared to ECG-triggered sequential step-and-shoot and ECG-gated spiral with x-ray pulsing). A high-pitch (up to pitch = 3.2), high-temporal-resolution (up to 75 ms) dual-source CT scan mode produced equivalent image quality relative to single-source scans using a more typical pitch value (pitch = 1.0). The resultant reduction in the overall acquisition time may offer clinical advantage for cardiovascular, trauma, and pediatric CT applications. In addition, ECG-triggered high-pitch scanning may be useful as an alternative to ECG-triggered sequential scanning for patients with low to moderate heart rates up to 70 bpm, with the potential to scan the heart within one heart beat at reduced radiation dose.

Analysis of 3D SPECT image reconstruction and its extension to ultrasonic diffraction tomography

We present a detailed investigation of the theory for image reconstruction in 3D SPECT with uniform attenuation and distance-dependent spatial resolution. In particular, we present an alternative approach for derivation of relationships between the ideal and modified sinograms, and we investigate systematically the implication of the spatial resolution function for these relationships as well as on the ideal-sinogram estimation methods that are developed from these relationships. In our theory, the optical transfer function (OTF) of the resolution function is required to have a specific form. This form is satisfied by the OTF of the 3D Cauchy (or 3D Gaussian) exactly (or approximately). In this work, we develop a formula for converting a general OTF into that specific form so that our theory can be applied. Finally, we point out that the theory developed for SPECT can readily be generalized to 2D ultrasound diffraction tomography.

The P-transform and photoacoustic image reconstruction

Photoacoustic imaging is a new imaging modality which converts pressure signals received by an array of transducers to a regional distribution of electromagnetic absorption density. This paper presents a rigorous theory for photoacoustic image reconstruction in a concise format. A new type of transform, the P-transform, is proposed, analysed and presented as the main mathematical tool for reconstruction. It is proved that photoacoustic image reconstruction is intrinsically a three-dimensional (3D) procedure. The spatial smear function (SSF) is introduced. To complete photoacoustic image reconstruction an integral equation must be solved, which is replaced by a matrix approach in a discretized space. An example using synthetic data proves the validity of the photoacoustic image reconstruction theory proposed in the paper. The example shows that even the first-order approximation of photoacoustic image reconstruction gives good agreement with reality. It is also seen from the example that the accuracy and noise immunity of the reconstruction procedure depend on the experimental arrangement.

An iterative filtered backprojection inverse treatment planning algorithm for tomotherapy

An inverse treatment planning algorithm for tomotherapy is described. The algorithm iteratively computes a set of nonnegative beam intensity profiles that minimizes the least-square residual dose defined in the target and selected normal tissue regions of interest. At each iteration the residual dose distribution is transformed into a set of residual beam profiles using an inversion method derived from filtered backprojection image reconstruction theory. These "residual" profiles are used to correct the current beam profile estimates resulting in new profile estimates. Adaptive filtering is incorporated into the inversion model so that the gross structure of the dose distribution is optimized during initial iterations of the algorithm, and the fine structure corresponding to edges is obtained at later iterations. A three dimensional, kernel based, convolutions/superposition dose model is used to compute dose during each iteration. Two clinically relevant treatment planning examples are presented illustrating the use of the algorithm for planning conformal radiotherapy of the breast and the prostate. Solutions are generally achieved in 10-20 iterations requiring about 20 h of CPU time using a midrange workstation. The majority of the calculation time is spent on the three-dimensional dose calculation. The inverse treatment planning algorithm is a useful research tool for exploring the potential of tomotherapy for conformal radiotherapy. Further work is needed to (a) achieve clinically acceptable computation times; (b) verify the algorithm using multileaf collimator technology; and (c) extend the method to biological objectives.

Theory of image reconstruction in laser scanned acoustic microscopy : Mueller, R.K.; Soumekh, B. IEEE 1985 Ultrasonics Symposium, San Francisco, California (United States), 16–18 Oct. 1985, pp. 720–724. Edited by B.R. McAvoy. IEEE, Piscataway, New Jersey (1985)

Theory of image reconstruction in laser scanned acoustic microscopy : Mueller, R.K.; Soumekh, B. IEEE 1985 Ultrasonics Symposium, San Francisco, California (United States), 16–18 Oct. 1985, pp. 720–724. Edited by B.R. McAvoy. IEEE, Piscataway, New Jersey (1985)

Image reconstruction and restoration: overview of common estimation structures and problems

Developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined. Particular attention is paid to common estimation structures and to practical problems not properly solved yet. The problem of image reconstruction and restoration is first formulated. Some of the current regularization approaches used to solve the problem are then described. The concepts of a priori information and compound criterion are introduced. A Bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated. The practical aspects of computing the solution, first when the hyperparameters are known and second when they must be estimated, are then considered. Conclusions are drawn, and points that still need to be investigated are outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nuclear Magnetic Resonance Tomography, NMR Scanner Techniques and the Theory of Image Reconstruction by V. Bangert

<i>Nuclear Magnetic Resonance Tomography, NMR Scanner Techniques and the Theory of Image Reconstruction</i> by V. Bangert

Theory of image reconstruction in computed tomography.

Mathematical methods are of central importance in the new technologies of radiographic and radioisotopic image reconstruction. The most important procedures are classified as Back-projection, iterative, and analytical (Two-dimensional Fourier, Filtered Back-projection). Back-projection played an important historical role but is no longer used because of sizable artifacts. Analytical methods excel in speed and accuracy when a large number of projections are available and are extensively used in x-ray imaging. Iterative reconstruction is more attractive when the number of views is limited, if noise is significant, and if additional factors, e.g., gamma-ray attenuation, are present. For these reasons, iterative methods are widely used in radioisotope imaging.