3D Modulation Transfer Function Research Articles

Theory, method, and test tools for determination of 3D MTF characteristics in cone-beam CT.

The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three-dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone-beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two-dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT. Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi-wire tool for measurement of the axial plane MTF [denoted as , where is the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g., =45°, denoted as ]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C-arm with CBCT capability, showing that yields an informative one-dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide "isotropic" resolution was evaluated by quantitative comparison of MTF at various . All three test tools provided consistent measurement of , and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane ( ) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C-arm system exhibited non-isotropic spatial resolution with conventional non-isotropic 1D apodization filters (i.e., frequency cutoff filters) - which is common in CBCT - and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non-isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D ). Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Experiments on a CBCT C-arm validated many intuitive aspects of 3D spatial resolution and quantified the extent to which a CBCT system may be considered to have isotropic resolution. Measurement of ) provided a practical 1D measure of the underlying 3D MTF characteristics and is extensible to other CT or CBCT systems offering high, isotropic spatial resolution.

Location and direction dependence in the 3D MTF for a high-resolution CT system.

The purpose of this study was to quantify location and direction-dependent variations in the 3D modulation transfer function (MTF) of a high-resolution CT scanner with selectable focal spot sizes and resolution modes. The Aquilion Precision CT scanner (Canon Medical Systems) has selectable 0.25mm or 0.5mm detectors (by binning) in both the axial (x-y) and detector array width (z) directions. For the x-y and z orientations, detectors are configured (x-y)=0.5 mm/(z)=0.5mm for normal resolution (NR), 0.25/0.5mm for high resolution (HR), and 0.25/0.25mm for super high resolution (SHR). Six focal spots (FS1-FS6) range in size from 0.4 (x-y)×0.5mm (z) for FS1 to 1.6×1.4mm for FS6. Phantoms fabricated from spherical objects were positioned at radial distances of 0, 4.0, 7.5, 11.0, 14.5, and 18.5cm. Axial and helical acquisitions were utilized and reconstructed using filtered back projection with the FC18 "Body," FC30 "Bone," and FC81 "Bone Sharp" kernels. The reconstructions were used to measure a 1D slice of the 3D MTF by oversampling the 3D ESF in the axial plane [MTF(fr ); φ=0°)], 45° out of the axial plane [MTF(fr ); φ=45°)], in the longitudinal direction [MTF(fr ); φ=80°)], and along the radial and azimuthal directions within the axial plane. The MTF(fr ); φ=45°) drops to 10% (f10 ) at 1.20, 1.45, and 2.06mm-1 for NR, HR, and SHR, respectively, for a helical acquisition with FS1, FC30, and r=4cm from the isocenter. The MTF(fr ); φ=45°) includes contributions of both the axial-plane MTF (f10 =1.10, 2.04, and 2.01mm-1 ) and the longitudinal MTF (f10 =1.17, 1.18, and 1.82mm-1 ) for the NR, HR, and SHR modes, respectively. For SHR, the axial scan mode showed a 15-25% improvement over helical mode in the longitudinal resolution. Helical pitch, ranging from 0.569 to 1.381, did not appreciably affect the 3D resolution (<2%). The radial MTFs across the axial field of view (FOV) showed dependencies on the focal spot length in z; for example, for SHR with FS2 (0.6×0.6mm), f10 at r=11cm was within 17% of the value at r=4cm, but for SHR with FS3 (0.6×1.3), the reduction in f10 was 46% from 4 to 11cm from the isocenter. The azimuthal MTF also decreased as r increased but less so for longer gantry rotation times and smaller focal spot dimensions in the axial plane. The longitudinal MTF was minimally affected (<11%) by position in the FOV and was principally affected by the focal spot length in the z-dimension. The 3D MTF was measured throughout the FOV of a high-resolution CT scanner, quantifying the advantages of different resolution modes and focal spot sizes on the axial-plane and longitudinal MTF. Reconstruction kernels were shown to impact axial-plane resolution, imparting non-isotropic 3D resolution characteristics. Focal spot size (both in x-y and in z) and gantry rotation time play important roles in preserving the high-resolution characteristics throughout the field of view for this new high-resolution CT scanner technology.

3D MTF estimation using sphere phantoms for cone-beam computed tomography systems.

For cone-beam computed tomography (CBCT) systems, we propose a sphere phantom based method to estimate the full three-dimensional (3D) modulation transfer function (MTF). The FDK reconstruction of CBCT system in a local region was modeled by a triple convolution operator. Afterward, we calculated the directional projections of ideal and reconstructed sphere phantoms into a two-dimensional (2D) plane for multiple views. To estimate the projected 3D point spread function (PSF), we applied the 2D Richardson-Lucy deconvolution with Tikhonov-Miller (RL-TM). After estimating the projected 3D PSF from multiple views, the full 3D PSF was estimated by performing filtered backprojection. Then, the full 3D MTF was calculated by taking the modulus of the Fourier transform of the estimated 3D PSF. To validate the proposed method, we reconstructed sphere phantoms from simulation and experiment data. We simulated ideal 3D MTFs and compared them with the estimated 3D MTFs along the -, -, and -directions. The full-width at half-maximum (FWHM) and full-width at tenth-maximum (FWTM) values were compared between ideal and estimated 3D MTFs. The estimated 3D MTFs from both the simulation and experiment results show qualitative similarity in their shapes with the ideal 3D MTFs; FWHM and FWTM results quantitatively show that the proposed method provides reliable estimation performance. In particular, the estimated 3D MTF in a missing cone region was correctly matched with the corresponding ideal 3D MTF. In this work, we proposed a full 3D MTF estimation method for CBCT systems. Based on the results, we believe that the proposed method can be used to evaluate the spatial resolution performance of CBCT systems.

Characterizing 3D sensors using the 3D modulation transfer function

The fields of optical 3D measurement system applications are continuously expanding and becoming more and more diverse. To evaluate appropriate systems for various measurement tasks, comparable parameters are necessary, whereas the 3D modulation transfer function (3D-MTF) has been established as a further criterion. Its aim is the determination of the system response between the measurement of a straight, sharp-edged cube and its opposite ideal calculated one. Within the scope of this work simulations and practical investigations regarding the 3D-MTF’s influences and its main issues are specifically investigated. Therefore, different determined edge radii representing the high-frequency spectra lead to various decreasing 3D-MTF characteristics. Furthermore, rising sampling frequencies improve its maximum transfer value to a saturation point in dependence of the radius. To approve these results of previous simulations, three fringe projection scanners were selected to determine the diversity. As the best 3D-MTF characteristic, a saturated transfer value of has been identified at a sufficient sampling frequency, which is reached at four times the Nyquist limit. This high 3D resolution can mainly be achieved due to an improved camera projector interaction. Additionally, too small sampling ratios lead to uncertainties in the edge function determination, while higher ratios do not show major improvements. In conclusion, the 3D-MTF algorithm has thus been practically verified and its repeatability as well as its robustness have been confirmed.

Three-dimensional cascaded system analysis of a 50 µm pixel pitch wafer-scale CMOS active pixel sensor x-ray detector for digital breast tomosynthesis

High-resolution, low-noise x-ray detectors based on the complementary metal-oxide-semiconductor (CMOS) active pixel sensor (APS) technology have been developed and proposed for digital breast tomosynthesis (DBT). In this study, we evaluated the three-dimensional (3D) imaging performance of a 50 µm pixel pitch CMOS APS x-ray detector named DynAMITe (Dynamic Range Adjustable for Medical Imaging Technology). The two-dimensional (2D) angle-dependent modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE) were experimentally characterized and modeled using the cascaded system analysis at oblique incident angles up to 30°. The cascaded system model was extended to the 3D spatial frequency space in combination with the filtered back-projection (FBP) reconstruction method to calculate the 3D and in-plane MTF, NNPS and DQE parameters. The results demonstrate that the beam obliquity blurs the 2D MTF and DQE in the high spatial frequency range. However, this effect can be eliminated after FBP image reconstruction. In addition, impacts of the image acquisition geometry and detector parameters were evaluated using the 3D cascaded system analysis for DBT. The result shows that a wider projection angle range (e.g. ±30°) improves the low spatial frequency (below 5 mm−1) performance of the CMOS APS detector. In addition, to maintain a high spatial resolution for DBT, a focal spot size of smaller than 0.3 mm should be used. Theoretical analysis suggests that a pixelated scintillator in combination with the 50 µm pixel pitch CMOS APS detector could further improve the 3D image resolution. Finally, the 3D imaging performance of the CMOS APS and an indirect amorphous silicon (a-Si:H) thin-film transistor (TFT) passive pixel sensor (PPS) detector was simulated and compared.

Optimization of contrast-enhanced breast imaging: Analysis using a cascaded linear system model.

Contrast-enhanced (CE) breast imaging involves the injection contrast agents (i.e., iodine) to increase conspicuity of malignant lesions. CE imaging may be used in conjunction with digital mammography (DM) or digital breast tomosynthesis (DBT) and has shown promise in improving diagnostic specificity. Both CE-DM and CE-DBT techniques require optimization as clinical diagnostic tools. Physical factors including x-ray spectra, subtraction technique, and the signal from iodine contrast, must be considered to provide the greatest object detectability and image quality. We developed a cascaded linear system model (CLSM) for the optimization of CE-DM and CE-DBT employing dual energy (DE) subtraction or temporal (TE) subtraction. We have previously developed a CLSM for DBT implemented with an a-Se flat panel imager (FPI) and filtered backprojection (FBP) reconstruction algorithm. The model is used to track image quality metrics - modulation transfer function (MTF) and noise power spectrum (NPS) - at each stage of the imaging chain. In this study, the CLSM is extended for CE breast imaging. The effect of x-ray spectrum (varied by changing tube potential and the filter) and DE and TE subtraction techniques on breast structural noise was measured was studied and included as a deterministic source of noise in the CLSM. From the two-dimensional (2D) and three-dimensional (3D) MTF and NPS, the ideal observer signal-to-noise ratio (SNR), also known as the detectability index (d'), may be calculated. Using d' as a FOM, we discuss the optimization of CE imaging for the task of iodinated contrast object detection within structured backgrounds. Increasing x-ray energy was determined to decrease the magnitude of structural noise and not its correlation. By performing DE subtraction, the magnitude of the structural noise was further reduced at the expense of increased stochastic (quantum and electronic) noise. TE subtraction exhibited essentially no residual structural noise at the expense of increased quantum noise, even over that of the DE case. For DE subtraction, optimization of dose weighting to the HE view (fh ) results in the minimization of quantum noise. Both subtraction weighting factor (wSub ) and the iodine contrast signal were dependent on the LE and HE x-ray spectra. To best detect a 5 mm Gaussian lesion with 5 mg/ml of iodine within a 4 cm thick breast, it was found that the high energy (HE) view should be acquired with a tube potential of 47 kVp (W/Ti spectrum) and the low energy (LE) view with a potential of 23 kVp (W/Rh spectrum). Due to the complete removal of structural noise, TE subtraction produced much higher d' than DE subtraction both as a function of mean glandular dose and iodine concentration. We have shown the effect of increasing x-ray energy as well as projection domain subtraction on breast structural noise. Further, we have exhibited the utility of the CLSM for DE and TE subtraction CE imaging in the optimization of imaging parameters such as x-ray energy, fh , and wSub as well as guiding the understanding of their effects on image contrast and noise.

Cone-beam micro computed tomography dedicated to the breast

We developed a scanner for micro computed tomography dedicated to the breast (BµCT) with a high resolution flat-panel detector and a microfocus X-ray tube. We evaluated the system spatial resolution via the 3D modulation transfer function (MTF). In addition to conventional absorption-based X-ray imaging, such a prototype showed capabilities for propagation-based phase-contrast and related edge enhancement effects in 3D imaging. The system limiting spatial resolution is 6.2mm−1 (MTF at 10%) in the vertical direction and 3.8mm−1 in the radial direction, values which compare favorably with the spatial resolution reached by mini focus breast CT scanners of other groups. The BµCT scanner was able to detect both microcalcification clusters and masses in an anthropomorphic breast phantom at a dose comparable to that of two-view mammography. The use of a breast holder is proposed in order to have 1–2min long scan times without breast motion artifacts.

Imaging characteristics of Zernike and annular polynomial aberrations

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

Fundamental relationship between the noise properties of grating-based differential phase contrast CT and absorption CT: Theoretical framework using a cascaded system model and experimental validation

Using a grating interferometer, a conventional x-ray cone beam computed tomography (CT) data acquisition system can be used to simultaneously generate both conventional absorption CT (ACT) and differential phase contrast CT (DPC-CT) images from a single data acquisition. Since the two CT images were extracted from the same set of x-ray projections, it is expected that intrinsic relationships exist between the noise properties of the two contrast mechanisms. The purpose of this paper is to investigate these relationships. First, a theoretical framework was developed using a cascaded system model analysis to investigate the relationship between the noise power spectra (NPS) of DPC-CT and ACT. Based on the derived analytical expressions of the NPS, the relationship between the spatial-frequency-dependent noise equivalent quanta (NEQ) of DPC-CT and ACT was derived. From these fundamental relationships, the NPS and NEQ of the DPC-CT system can be derived from the corresponding ACT system or vice versa. To validate these theoretical relationships, a benchtop cone beam DPC-CT/ACT system was used to experimentally measure the modulation transfer function (MTF) and NPS of both DPC-CT and ACT. The measured three-dimensional (3D) MTF and NPS were then combined to generate the corresponding 3D NEQ. Two fundamental relationships have been theoretically derived and experimentally validated for the NPS and NEQ of DPC-CT and ACT: (1) the 3D NPS of DPC-CT is quantitatively related to the corresponding 3D NPS of ACT by an inplane-only spatial-frequency-dependent factor 1∕f (2), the ratio of window functions applied to DPC-CT and ACT, and a numerical factor C(g) determined by the geometry and efficiency of the grating interferometer. Note that the frequency-dependent factor is independent of the frequency component f(z) perpendicular to the axial plane. (2) The 3D NEQ of DPC-CT is related to the corresponding 3D NEQ of ACT by an f (2) scaling factor and numerical factors that depend on both the attenuation and refraction properties of the image object, as well as C(g) and the MTF of the grating interferometer. The performance of a DPC-CT system is intrinsically related to the corresponding ACT system. As long as the NPS and NEQ of an ACT system is known, the corresponding NPS and NEQ of the DPC-CT system can be readily estimated using additional characteristics of the grating interferometer.

Measurements of system sharpness for two digital breast tomosynthesis systems

The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF0.50) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm−1 for the Inspiration system and from 2.50 to 1.20 mm−1 for the Dimensions unit. The maximum deviation of measured MTF0.50 from the calculated value was 13%. MTF0.50 measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm−1 for the Inspiration system and from 2.21 to 1.31 mm−1 for the Dimensions system. The full-width half-maximum for the in-depth PSF was 3.0 and 5.9 mm for the Inspiration and Dimensions systems, respectively. There was no difference in the 3D MTF curves, sectioned in the tube-travel direction, for bead heights of 15 and 65 mm above the table. A 25 µm tungsten wire held within a 15 mm thick PMMA plate was found to be a suitable test object for measurement of in-plane MTF. Evaluation of MTF as a function of height above the table, both in the projection images and in the reconstructed planes, provides important information on the impact of focus size and focus motion on the DBT system's imaging performance.

Modulation transfer function of spatially variant sampling retina-like sensor

Space-variant sensors are of great importance in both machine and biological vision, and they have superior imaging property than the rectilinear sensors during high-speed forward motion. We focus on the modulation transfer function (MTF) of a particular spatially variant sampling retina-like sensor, pixels of which are arranged in a log-polar fashion. The 3D MTF of the sensor has been built using Hankel Transformation (HT) based on sampling and imaging property of the sensor. Moreover, the output image is simulated in the light of MTF. This research helps to model the imaging process of an imaging system containing retina-like sensor.

SU‐D‐301‐06: Impact of Non‐Stationarity in Breast Tomosynthesis on Task‐Based Imaging Performance

Purpose: Reconstructed tomosynthesis data is known to exhibit non‐stationarity, (i.e., the pixel mean and standard deviation depends on location), which is expected to impact our ability to accurately assess imaging performance. The purpose of this study was to characterize the magnitude and impact of non‐stationarity on various imaging tasks. Method and Materials:A phantom consisting of an array of 15 aluminum oxide beads was constructed to measure the 3D modulation transfer function (MTF) across a range of locations in the breast. Similarly, a uniform breast phantom was used to measure the noise‐power spectrum (NPS) across the same range of locations. Simulated tomosynthesis and real tomosynthesis images were acquired to characterize independently the impact of non‐stationarity on quantum and anatomical noise measurements and the impact of scatter on non‐stationarity. The MTF and NPS were compared across locations in terms of measures of sharpness and noise and furthermore combined with a task function to measure task‐based performance indices including the detection, localization, and size estimation of a 4 mm mass. The variability and range of the indices were characterized across the different regions of the breast. Results: The 3D MTF and NPS varied in shape and orientation across location. The measure of sharpness and noise was found to vary by 3% and 2%, respectively, from the center to the edge (located 4 cm from center). The task‐based performance also depended on location, with 4% variation for a detection task and 3% variation for a size estimation task. Overall, variation was mostly along the lateral direction of the breast. Conclusions: This work provides guidelines for the application of Fourier‐based metrics in breast tomosyntehsis. While the shape and orientation of the 3D MTF and NPS are dependent on location, variability of the task‐based performance indices was found to be minimal.

WE‐G‐110‐03: Directional MTF Measurement of Tomosynthesis Images Using a Cone‐Based Technique

Purpose: To develop a cone‐based modulation transfer function (MTF) measurement technique for tomosynthesis using a sphere phantom. Methods: Projections were simulated for a voxelized breast phantom with 12 mm sphere inserts using a fluence modeled from 28 kVp beam and incident upon an indirect flat‐panel detector with 200 um pixel size. Characteristic noise and blurring for each projection were added using cascaded systems analysis. The projections were reconstructed using standard filtered backprojection techniques, producing a 3D volume with an isotropic voxel size of 200 um. ROIs that completely encompassed single spheres were extracted, and conical regions were prescribed along the three axes extending from the centroids. Pixels within the cones were used to form edge spread functions (ESF), from which directional “raw” MTFs were calculated. Binning size and conical range were considered for maximizing accuracy and minimizing noise of the MTF. A method for removing out‐of‐plane artifacts of the ESFs in x and y directions was investigated and yielded an “effective” MTF. Results: Comparisons of the cone‐based MTF along the different axes and the true 3D MTF yielded good agreement. A 30 degree angle was found to provide ideal trade‐off between measurement noise and accuracy. Drop‐off frequencies in the x‐ and y‐directional “raw” MTFs were 1.5 cycles/mm and 2.5 cycles/mm, respectively. As expected, the z‐directional MTF had a much lower drop‐off due to the lack of angular sampling. The removal of artifacts in ESF yielded a “modified” MTFs which enabled a novel characterization of in‐slice resolution for tomosynthesis. Conclusion: The directional MTF of tomosynthesis reconstruction with FBP was determined by using the cone‐based MTF technique. The presented method of separating the effective resolution and artifacts from the measured ESF is expected to facilitate the interpretation of MTF measurements in tomosynthesis.

The effect of angular dose distribution on the detection of microcalcifications in digital breast tomosynthesis

Substantial effort has been devoted to the clinical development of digital breast tomosynthesis (DBT). DBT is a three-dimensional (3D) x-ray imaging modality that reconstructs a number of thin image slices parallel to a stationary detector plane. Preliminary clinical studies have shown that the removal of overlapping breast tissue reduces image clutter and increases detectability of large, low contrast lesions. However, some studies, as well as anecdotal evidence, suggested decreased conspicuity of small, high contrast objects such as microcalcifications. Several investigators have proposed alternative imaging methods for improving microcalcification detection by delivering half of the total dose to the central view in addition to a separate DBT scan. Preliminary observer studies found possible improvement by either viewing the central projection alone or combining all views with a reconstruction algorithm. In this paper, we developed a generalized imaging theory based on a cascaded linear-system model for DBT to calculate the effect of variable angular dose distribution on the 3D modulation transfer function (MTF) and noise power spectrum (NPS). Using the ideal observer signal-to-noise ratio (SNR), d', as a figure-of-merit (FOM) for a signal embedded in a uniform background, we compared the detectability of objects with different sizes under different imaging conditions (e.g., angular dose distribution and reconstruction filters). Experimental investigation was conducted for three different angular dose schemes (ADS) using a Siemens Novation(TOMO) prototype unit. Our results show excellent agreement between modeled and experimental measurements of 3D NPS with different angular dose distribution. The ideal observer detectability index for the detection of Gaussian objects with different angular dose distributions depends strongly on the applied reconstruction filter as well as the imaging task. For detection tasks of small calcifications with reconstruction filters used typically in a clinical setting, variable angular dose distribution with more dose delivered to the central views may lead to higher d' than a uniform angular dose distribution. The conspicuity of the detection of small calcifications may be improved, under certain imaging conditions, by delivering higher dose toward the central views of a tomosynthesis scan, while also reducing the dose at peripheral angles to keep total administered radiation dose equivalent. The degree of improvement depends on the choice of reconstruction filters as well as the imaging task. The improvement is more substantial for high-frequency imaging tasks and when an aggressive slice-thickness (ST) filter is applied to reduced the high-frequency noise at peripheral angles.

Three‐dimensional tomosynthetic image restoration for brachytherapy source localization

Tomosynthetic image reconstruction allows for the production of a virtually infinite number of slices from a finite number of projection views of a subject. If the reconstructed image volume is viewed in toto, and the three‐dimensional (3D) impulse response is accurately known, then it is possible to solve the inverse problem (deconvolution) using canonical image restoration methods (such as Wiener filtering or solution by conjugate gradient least squares iteration) by extension to three dimensions in either the spatial or the frequency domains. This dissertation presents modified direct and iterative restoration methods for solving the inverse tomosynthetic imaging problem in 3D. The significant blur artifact that is common to tomosynthetic reconstructions is deconvolved by solving for the entire 3D image at once. The 3D impulse response is computed analytically using a fiducial reference schema as realized in a robust, self‐calibrating solution to generalized tomosynthesis. 3D modulation transfer function analysis is used to characterize the tomosynthetic resolution of the 3D reconstructions. The relevant clinical application of these methods is 3D imaging for brachytherapy source localization. Conventional localization schemes for brachytherapy implants using orthogonal or stereoscopic projection radiographs suffer from scaling distortions and poor visibility of implanted seeds, resulting in compromised source tracking (reported errors: 2–4 mm) and dosimetric inaccuracy. 3D image reconstruction (using a well‐chosen projection sampling scheme) and restoration of a prostate brachytherapy phantom is used for testing. The approaches presented in this work localize source centroids with submillimeter error in two Cartesian dimensions and just over one millimeter error in the third.

An investigation of the stationarity of the 3D modulation transfer function of SPECT

The authors evaluated the rotational symmetry and stationarity of the three-dimensional (3-D) modulation transfer function (MTF) of single-photon-emission computed tomography (SPECT). Point spread functions (PSF) in scattering media were obtained by placing a point source at varying radial distances from the center of three differently shaped water-filled phantoms. Results indicate that at the center of a nonisotropic phantom, the 3-D MTF is anisotropic. For off-axis source locations the 3-D MTF becomes increasingly anisotropic as the point source is moved radially off center. 3-D MTFs obtained using arithmetic mean averaging of opposing projections showed less low- to mid-frequency but more high-frequency variation with position than 3-D MTFs obtained using geometric mean averaging. It is concluded that the postreconstruction 3-D MTF is anisotropic and nonstationary, and that the inconsistency of the projection data with angle due to nonisotropic attenuation is the major cause of the low- and mid-frequency variation in the transfer functions. >