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Oblique reconstructions in tomosynthesis. II. Super-resolution.

ABSTRACT: In tomosynthesis, super-resolution has been demonstrated using reconstruction planes parallel to the detector. Super-resolution allows for subpixel resolution relative to the detector. The purpose of this work is to develop an analytical model that generalizes super-resolution to oblique reconstruction planes.In a digital tomosynthesis system, a sinusoidal test object is modeled along oblique angles (i.e., "pitches") relative to the plane of the detector in a 3D divergent-beam acquisition geometry. To investigate the potential for super-resolution, the input frequency is specified to be greater than the alias frequency of the detector. Reconstructions are evaluated in an oblique plane along the extent of the object using simple backprojection (SBP) and filtered backprojection (FBP). By comparing the amplitude of the reconstruction against the attenuation coefficient of the object at various frequencies, the modulation transfer function (MTF) is calculated to determine whether modulation is within detectable limits for super-resolution. For experimental validation of super-resolution, a goniometry stand was used to orient a bar pattern phantom along various pitches relative to the breast support in a commercial digital breast tomosynthesis system.Using theoretical modeling, it is shown that a single projection image cannot resolve a sine input whose frequency exceeds the detector alias frequency. The high frequency input is correctly visualized in SBP or FBP reconstruction using a slice along the pitch of the object. The Fourier transform of this reconstructed slice is maximized at the input frequency as proof that the object is resolved. Consistent with the theoretical results, experimental images of a bar pattern phantom showed super-resolution in oblique reconstructions. At various pitches, the highest frequency with detectable modulation was determined by visual inspection of the bar patterns. The dependency of the highest detectable frequency on pitch followed the same trend as the analytical model. It was demonstrated that super-resolution is not achievable if the pitch of the object approaches 90°, corresponding to the case in which the test frequency is perpendicular to the breast support. Only low frequency objects are detectable at pitches close to 90°.This work provides a platform for investigating super-resolution in oblique reconstructions for tomosynthesis. In breast imaging, this study should have applications in visualizing microcalcifications and other subtle signs of cancer.

SUBMITTER: Acciavatti RJ

PROVIDER: S-EPMC3808432 | biostudies-other | 2013 Nov

REPOSITORIES: biostudies-other

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Project description:By convention, slices in a tomosynthesis reconstruction are created on planes parallel to the detector. It has not yet been demonstrated that slices can be generated along oblique directions through the same volume, analogous to multiplanar reconstructions in computed tomography (CT). The purpose of this work is to give a proof-of-principle justification for oblique reconstructions in tomosynthesis, which acquires projection images over a smaller angular range than CT.To investigate the visibility of individual frequencies in an oblique reconstruction, a theoretical framework is developed in which the reconstruction of a sinusoidal input is calculated. The test frequency is pitched at an angle in a 2D parallel-beam acquisition geometry. Reconstructions are evaluated along the pitch of the object. The modulation transfer function (MTF) is calculated from the relative signal at various test frequencies. The MTF determines whether modulation is within detectable limits in oblique reconstructions. In the previous linear systems (LS) model [B. Zhao and W. Zhao, "Three-dimensional linear system analysis for breast tomosynthesis," Med. Phys. 35(12), 5219-5232 (2008)], the MTF was calculated only in reconstructed slices parallel to the detector. This paper generalizes the MTF calculation to reconstructed slices at all possible pitches. Unlike the previous LS model, this paper also analyzes the effect of object thickness on the MTF. A second test object that is considered is a rod whose long axis is pitched similar to the sinusoidal input. The rod is used to assess whether the length of an object can be correctly estimated in oblique reconstructions.To simulate the conventional display of the reconstruction, slices are first created along a 0° pitch. This direction is perpendicular to the rays of the central projection. The authors show that the input frequency of a pitched sinusoidal object cannot be determined using these slices. By changing the pitch of the slice to match the object, it is shown that the input frequency is properly resolved. To prove that modulation is preserved in pitched slices, the MTF is also calculated. Modulation is within detectable limits over a broad range of pitches if the object is thin, but is detectable over a narrower range of pitches if the object is thick. Turning next to the second test object, it is shown that the length of a pitched rod can be correctly determined in oblique reconstructions. Concordant with the behavior of the MTF, the length estimate is accurate over a broad range of pitches if the object is thin, but is correct over a narrower range of pitches if the object is thick.This work justifies the feasibility of oblique reconstructions in tomosynthesis. It is demonstrated that pitched test objects are most easily visualized with oblique reconstructions instead of conventional reconstructions. In order to achieve high image quality over a broad range of pitches, the object must be thin. By analyzing the effect of reconstruction pitch and object thickness on image quality, this paper generalizes the previous LS model for tomosynthesis.

Project description:Digital breast tomosynthesis (DBT) is a 3D x-ray imaging modality in which tomographic sections of the breast are generated from a limited range of tube angles. Because oblique x-ray incidence shifts the image of an object in subpixel detector element increments with each increasing projection angle, it is demonstrated that DBT is capable of super-resolution (i.e., subpixel resolution).By convention, DBT reconstructions are performed on planes parallel to the breast support at various depths of the breast volume. In order for resolution in each reconstructed slice to be comparable to the detector, the pixel size should match that of the detector elements; hence, the highest frequency that can be resolved in the plane of reconstruction is the alias frequency of the detector. This study considers reconstruction grids with much smaller pixelation to visualize higher frequencies. For analytical proof of super-resolution, a theoretical framework is developed in which the reconstruction of a high frequency sinusoidal input is calculated using both simple backprojection (SBP) and filtered backprojection. To study the frequency spectrum of the reconstruction, its Fourier transform is also determined. The experimental feasibility of super-resolution was investigated by acquiring images of a bar pattern phantom with frequencies higher than the detector alias frequency.Using analytical modeling, it is shown that the central projection cannot resolve frequencies exceeding the detector alias frequency. The Fourier transform of the central projection is maximized at a lower frequency than the input as evidence of aliasing. By contrast, SBP reconstruction can resolve the input, and its Fourier transform is correctly maximized at the input frequency. Incorporating filters into the reconstruction smoothens pixelation artifacts in the spatial domain and reduces spectral leakage in the Fourier domain. It is also demonstrated that the existence of super-resolution is dependent on position in the reconstruction and on the directionality of the input frequency. Consistent with the analytical results, experimental reconstructions of bar patterns showed visibility of frequencies greater than the detector alias frequency. Super-resolution was present at positions predicted from analytical modeling.This work demonstrates the existence of super-resolution in DBT. Super-resolution has the potential to impact the visualization of fine structural details in the breast, such as microcalcifications and other subtle signs of cancer.

Project description:We developed a novel dual-energy (DE) virtual monochromatic (VM) very-deep super-resolution (VDSR) method with an unsharp masking reconstruction algorithm (DE-VM-VDSR) that uses projection data to improve the nodule contrast and reduce ripple artifacts during chest digital tomosynthesis (DT). For estimating the residual errors from high-resolution and multiscale VM images from the projection space, the DE-VM-VDSR algorithm employs a training network (mini-batch stochastic gradient-descent algorithm with momentum) and a hybrid super-resolution (SR) image [simultaneous algebraic reconstruction technique (SART) total-variation (TV) first-iterative shrinkage-thresholding algorithm (FISTA); SART-TV-FISTA] that involves subjective reconstruction with bilateral filtering (BF) [DE-VM-VDSR with BF]. DE-DT imaging was accomplished by pulsed X-ray exposures rapidly switched between low (60 kV, 37 projection) and high (120 kV, 37 projection) tube-potential kVp by employing a 40° swing angle. This was followed by comparison of images obtained employing the conventional polychromatic filtered backprojection (FBP), SART, SART-TV-FISTA, and DE-VM-SART-TV-FISTA algorithms. The improvements in contrast, ripple artifacts, and resolution were compared using the signal-difference-to-noise ratio (SDNR), Gumbel distribution of the largest variations, radial modulation transfer function (radial MTF) for a chest phantom with simulated ground-glass opacity (GGO) nodules, and noise power spectrum (NPS) for uniform water phantom. The novel DE-VM-VDSR with BF improved the overall performance in terms of SDNR (DE-VM-VDSR with BF: 0.1603, without BF: 0.1517; FBP: 0.0521; SART: 0.0645; SART-TV-FISTA: 0.0984; and DE-VM-SART-TV-FISTA: 0.1004), obtained a Gumbel distribution that yielded good images showing the type of simulated GGO nodules used in the chest phantom, and reduced the ripple artifacts. The NPS of DE-VM-VDSR with BF showed the lowest noise characteristics in the high-frequency region (~0.8 cycles/mm). The DE-VM-VDSR without BF yielded an improved resolution relative to that of the conventional reconstruction algorithms for radial MTF analysis (0.2-0.3 cycles/mm). Finally, based on the overall image quality, DE-VM-VDSR with BF improved the contrast and reduced the high-frequency ripple artifacts and noise.

Project description:X-ray diffraction plays a pivotal role in the understanding of biological systems by revealing atomic structures of proteins, nucleic acids and their complexes, with much recent interest in very large assemblies like the ribosome. As crystals of such large assemblies often diffract weakly (resolution worse than 4 A), we need methods that work at such low resolution. In macromolecular assemblies, some of the components may be known at high resolution, whereas others are unknown: current refinement methods fail as they require a high-resolution starting structure for the entire complex. Determining the structure of such complexes, which are often of key biological importance, should be possible in principle as the number of independent diffraction intensities at a resolution better than 5 A generally exceeds the number of degrees of freedom. Here we introduce a method that adds specific information from known homologous structures but allows global and local deformations of these homology models. Our approach uses the observation that local protein structure tends to be conserved as sequence and function evolve. Cross-validation with R(free) (the free R-factor) determines the optimum deformation and influence of the homology model. For test cases at 3.5-5 A resolution with known structures at high resolution, our method gives significant improvements over conventional refinement in the model as monitored by coordinate accuracy, the definition of secondary structure and the quality of electron density maps. For re-refinements of a representative set of 19 low-resolution crystal structures from the Protein Data Bank, we find similar improvements. Thus, a structure derived from low-resolution diffraction data can have quality similar to a high-resolution structure. Our method is applicable to the study of weakly diffracting crystals using X-ray micro-diffraction as well as data from new X-ray light sources. Use of homology information is not restricted to X-ray crystallography and cryo-electron microscopy: as optical imaging advances to subnanometre resolution, it can use similar tools.

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Oblique reconstructions in tomosynthesis. II. Super-resolution.

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