In this work, we propose three alternative methods to estimate noise map for CT images. Our methods are
generalizations to the existing even-and-odd views approach proposed by Hsieh and Thibault . Method one in this
work estimates noise map from images reconstructed from three sets of independent views. Method two deals with
images reconstructed by using two sets of correlated views. Our method three generates the noise map from two images
reconstructed from two sets of independent views while the number of views in each set is unequal. Physical phantom
data were employed to validate our proposed noise map estimation methods. In comparison to the existing method, our
alternative methods yield reasonably accurate noise map estimation.
A typical iterative CT reconstruction using SART involves ray-driven forward projection and voxel-driven back-
ward projection. Bilinear interpolation is usually applied on image data for forward projection, and linear
interpolation is usually applied on projection data for backward projection, when both data are represented
using discrete samples in 2D fan-beam geometry. The applied interpolations, however, may affect the spatial
resolution, bias and noise properties of the reconstruction. A basis function (such as blob and spline) is therefore
applied to formulate a continuous model for the image data to reduce bias. In this paper we propose to apply
the blob representation on the projection data and explore its effectiveness. In this way we use continuous model
for the data of projection difference during backward projection, and we avoid the linear interpolation in this
process. Experimental results show that the proposed scheme is able to provide higher spatial resolution than
linear interpolation, while introducing more local variations in the reconstruction. However, the introduced local
variations may be reduced with the combination of total variation (TV) minimization. The proposed scheme is
therefore able to provide improved spatial resolution while keeping low local variations in reconstructions.
Electronic noise becomes a major source of signal degradation in
low-dose clinical computed tomography (CT). In
current clinical scanners based on energy integrating x-ray detectors, electronic noise from the readout circuits adds a
noise of constant variance, which is negligible at high counts but can be significant at low count levels. On the other
hand, in a photon counting detector (PCD) with pulse height discrimination capability, electronic noise has little to no
impact on the measured signal. PCDs are known for their abilities to provide useful spectral information. In this work,
we investigate this dose reduction to improve low-dose single-energy CT. We perform low-dose single-energy CT
simulations using both energy integrating and photon counting detectors, and compare results with both analytical and
iterative reconstructions (IR). The results demonstrate the dose reduction potential of PCDs in conventional low-dose
single-energy CT examinations, when spectral information is not required.
In X-ray phase-contrast tomography imaging studies, the object of interest may be larger than the field of
view (FOV) of the imaging system, resulting in a set of truncated tomographic projections. In this work,
we adapt recent advancements in conventional reconstruction theory to X-ray phase-contrast tomography, and
demonstrate that the Laplacian of the refractive index distribution can be reconstructed exactly within certain
regions-of-interest from knowledge of truncated phase-contrast projection data.
Intensity diffraction tomography (I-DT) is a non-interferometric imaging method for reconstructing the complex-valued
refractive index distribution of a weakly scattering object. The original formulation of I-DT requires
measurement of two in-line intensity measurements on parallel detector planes at each tomographic view angle.
In this work, a reconstruction theory for multi-spectral is established and investigated for use with single material
objects whose dispersion characteristics are known a priori. Unlike other I-DT methods, the temporal frequency
of the illuminating plane-wave represents the degree-of-freedom of the imaging system that is varied to acquire
two independent intensity measurements on a fixed detector-plane. Moreover, the proposed method accounts for
Intensity diffraction tomography (IDT) is an imaging method for reconstructing the complex refractive index distribution of a weakly scattering three-dimensional object. Unlike classic diffraction tomography, which requires measurement of the transmitted wave-field phase, IDT accomplished this reconstruction from knowledge of wave-field intensity measurements on parallel detector planes at each tomographic view angle. In this work, novel scanning protocols and reconstruction algorithms for IDT are proposed that require two intensity measurements on a single detector plane positioned at a fixed distance from the object. Each measurement corresponds to a probing spherical wave field that possesses a distinct curvature. Accordingly, the form of the incident wavefield, rather than the detector position, represents the degree of freedom in the imaging system that is varied for acquisition of the necessary measurement data. Computer simulation studies are conducted to investigate the developed data acquisition and image reconstruction algorithms.
Photoacoustic tomography (PAT) is an emerging imaging technique with great potential for a wide range of biomedical imaging applications. The reconstruction problem of PAT is an inverse source problem, in which the photoacoustic source of interest is induced by a probing optical wavefield. In this work, we revisit the PAT reconstruction problem from a Fourier perspective. By use of standard analytic techniques from inverse source theory, we derive a mathematical relationship between the pressure wavefield data function and its normal derivative measured on an arbitrary aperture that encloses the object and the three-dimensional Fourier transform of the optical absorption distribution evaluated on concentric spheres. We refer to this relationship as a "Fourier-shell identity", which is analogous to the well-known Fourier-slice theorem of X-ray tomography. Potential applications of the Fourier-shell identity are identified
Propagation-based phase-contrast tomography is a coherent imaging method that seeks to reconstruct the
three-dimensional complex-valued refractive index distribution of an object. Measurements of the transmitted
wavefield intensities on two parallel detector-planes at each tomographic view angle are utilized to determine
the wavefield's complex amplitude, which represent the projection data utilized for tomographic reconstruction.
The mathematical formulas employed to determine the complex amplitude contain Fourier domain singularities
that can result in greatly amplified noise levels in the reconstructed images. In this article, statistically optimal
reconstruction methods that employ multiple (>2) detector-planes are developed that mitigate the noise
amplification effects due to singularities in the reconstruction formulas. These reconstruction methods permit
exploitation of statistically complementary information in a collection of in-line holographic measurement data,
resulting in images that can have dramatically reduced noise levels. Computer-simulation studies are conducted
to demonstrate and investigate quantitatively the developed reconstruction methods.
Intensity diffraction tomography (I-DT) is an imaging method that reconstructs the complex-valued refractive index distribution of a weakly scattering object without explicit knowledge of the wavefield phase. In this work, a novel scanning protocol for I-DT is proposed that involves the use of plane-wave and spherical wave probing wavefields. A useful feature of the scanning protocol is that two in-line intensity measurements are acquired on a detector-plane whose distance from the object remains fixed. Accordingly, the translation of the detector that is required in classic in-line measurement geometries is avoided. A reconstruction algorithm that exploits tomographic symmetries is developed and demonstrated by use of computer-simulation studies.
Diffraction tomography (DT) is an established imaging technique for use with diffracting wavefields, which
represents a generalized form of x-ray tomography. In this work, we revisit the three-dimensional reconstruction
problem of DT for variable density acoustic media. Novel reconstruction algorithms are developed for
reconstructing separate images that depict a weakly scattering object's compressibility and density variations.
If tomographic measurement data are acquired at four distinct temporal frequencies, we demonstrate that
the effects of object dispersion can be accounted for completely by use of analytic reconstruction formulas.
Computer-simulation studies are conducted to demonstrate the developed image reconstruction methods.
Intensity diffraction tomography (IDT)is a propagation-based phase-contrast tomography imaging method. In this work, we develop an IDT reconstruction theory for measurement geometries that employ tilted detector planes. The conventional IDT reconstruction theory is contained as a special case where the detector planes are perpendicular to the direction of the probing plane-waves. The resulting reconstruction algorithms are implemented numerically, and computer-simulation studies are conducted to demonstrate their validity and robustness to data noise.
Acoustic diffraction tomography (DT) is an inversion scheme that can reconstruct the spatially variant acoustic properties of a scattering object. In this work, we develop and investigate a novel reconstruction algorithm for reconstructing separate images of the
density and compressibility fluctuations of nonviscoelastic scattering objects. The reconstruction algorithm is derived by identifying and exploiting tomographic symmetries and the rotational
invariance of the problem. The proposed reconstruction algorithm is implemented numerically and demonstrated by use of computer-simulation studies.
Propagation-based phase-contrast tomography is a non-interferometric
imaging technique that can reconstruct the complex refractive
index distribution of an object. To accomplish such a reconstruction,
however, the measured phase-contrast projections must be untruncated.
We have demonstrated recently that the mathematical theory of local
computed tomography (CT), which was originally developed for absorption CT, can be applied naturally for understanding the problem of reconstructing the location of image boundaries from truncated phase-contrast projections. In this work, we reveal that, for two-dimensional objects, the magnitude of refractive index discontinuities can be reconstructed from truncated phase-contrast projections acquired in the near-Fresnel zone. We show that these magnitudes can be reliably reconstructed using algorithms that were developed originally for local absorption CT.
In this work we investigate the phase-contrast tomography reconstruction problem assuming an incident (paraxial) spherical-wave. Starting from linearized inverse scattering theory, we develop an intensity diffraction tomography (I-DT) reconstruction algorithm that is relevant to scanning geometries that have a fixed source-to-object distance. This reconstruction algorithm accounts for first-order scattering effects introduced by the object and provides a
relationship between the intensity measurements made on two parallel detector planes and the desired complex refractive index distribution. A preliminary numerical investigation of the developed
reconstruction algorithm is presented.
Diffraction tomography (DT) is a well-known method for reconstructing the complex-valued refractive index distribution of weakly scattering objects. A reconstruction theory of intensity DT (I-DT) has been proposed [Gbur and Wolf, JOSA A, 2002] that can accomplish such a reconstruction from knowledge of only the wavefield intensities on two different transverse planes at each tomographic view angle. In this work, we elucidate the relationship between I-DT and phase-contrast tomography and demonstrate that I-DT reconstruction theory contains some of the existing reconstruction algorithms for phase-contrast tomography as special cases.
In this work, we examine the application of intensity diffraction tomography (I-DT) for imaging three-dimensional (3D) phase objects. We develop and investigate two algorithms for reconstructing phase objects that utilize only half of the measurements that would be needed to reconstruct a complex-valued object function. Each reconstruction algorithm reconstructs the phase object by use of different sets of intensity measurements. We demonstrate that the numerical and noise propagation properties of the two reconstruction algorithms differ considerably.
A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits for the reconstruction of a weakly-scattering object without explicity knowledge of phase information. In this work, we examine the noise properties of I-DT. An explicit expression for the variance of the estimated object function as a function of spatial frequency is derived and employed for understanding the noise properties of images reconstruction in I-DT. It is demonstrated analytically and numerically that the noise properties of I-DT are significantly different from those of conventional diffraction tomography (DT).
We investigate the problem of reconstructing a 3D image of a tumor
volume from a set of truncated MV cone-beam projections. Our proposed approach is distinct from previously investigated approaches in that it utilizes a local tomography reconstruction algorithm. Using simulated and experimental MV projection data, we demonstrate
that a local cone-beam tomography algorithm can reconstruct accurate
images that contain information regarding boundaries and edges
inside a localized region of interest. We also demonstrate that
the conventional Feldkamp-Davis-Kress cone-beam reconstruction algorithm is not well-suited for reconstructing images of
low-contrast structures from truncated cone-beam projections.