Abstract: Methods and systems for computed tomography provide advances in efficiency. The methods operating within the parallel-beam geometry, rather than a divergent beam geometry, for the majority of the operations. In back projection methods perform digital image coordinate transformations on selected intermediate-images, the parameters of one or more coordinate transformations being chosen such that Fourier spectral support of the intermediate-image is modified so that a region of interest has an increased extent along one or more coordinate direction and the aggregates of the intermediate-images can be represented with a desired accuracy by sparse samples.

Abstract: Methods and systems for computed tomography provide advances in efficiency. The methods operating within the parallel-beam geometry, rather than a divergent beam geometry, for the majority of the operations. In back projection methods perform digital image coordinate transformations on selected intermediate-images, the parameters of one or more coordinate transformations being chosen such that Fourier spectral support of the intermediate-image is modified so that a region of interest has an increased extent along one or more coordinate direction and the aggregates of the intermediate-images can be represented with a desired accuracy by sparse samples.

Abstract: Methods and systems for computed tomography. A subject is imaged with a divergent beam source using a plurality of source positions and a detector array comprising a plurality of detector bins to obtain a representation of the subject including a plurality of image voxels. Contribution of a voxel to a detector bin in a computed forward projection or a detector bin to a voxel in a backprojection is determined by the intensity value assigned to the voxel, or to the detector bin, respectively, multiplied by the product of an area or volume of overlap and an additional weighting factor, and the area or volume of overlap is determined by overlap of the voxel with the area or volume of the image illuminated by a ray-wedge defined by detector bin edge rays.

Abstract: A system executes efficient computational methods for high quality image reconstructions from a relatively small number of noisy (or degraded) sensor imaging measurements or scans. The system includes a processing device and instructions. The processing device executes the instructions to employ transform learning as a regularizer for solving inverse problems when reconstructing an image from the imaging measurements, the instructions executable to: adapt a transform model to a first set of image patches of a first set of images containing at least a first image, to model the first set of image patches as sparse in a transform domain while allowing deviation from perfect sparsity; reconstruct a second image by minimizing an optimization objective comprising a transform-based regularizer that employs the transform model, and a data fidelity term formed using the imaging measurements; and store the second image in the computer-readable medium, the second image displayable on a display device.

Abstract: Methods and systems for computed tomography. A subject is imaged with a divergent beam source using a plurality of source positions and a detector array comprising a plurality of detector bins to obtain a representation of the subject including a plurality of image voxels. Contribution of a voxel to a detector bin in a computed forward projection or a detector bin to a voxel in a backprojection is determined by the intensity value assigned to the voxel, or to the detector bin, respectively, multiplied by the product of an area or volume of overlap and an additional weighting factor, and the area or volume of overlap is determined by overlap of the voxel with the area or volume of the image illuminated by a ray-wedge defined by detector bin edge rays.

Abstract: Methods and systems for iterative computed tomography add an auxiliary variable to the reconstruction process, while retaining all variables in the original formulation, A weighting operator or filter can be applied that causes the Hessian with respect to an image of the cost function to be well-conditioned. An auxiliary sinogram variable distinct from both a set of actual image measurements and from the set of projections computed based on an image can be applied to iteratively update during the statistical iterative image reconstruction, with applied conditions that causes the Hessian with respect to an image of the cost function to be well-conditioned.

Abstract: A system executes efficient computational methods for high quality image reconstructions from a relatively small number of noisy (or degraded) sensor imaging measurements or scans. The system includes a processing device and instructions. The processing device executes the instructions to employ transform learning as a regularizer for solving inverse problems when reconstructing an image from the imaging measurements, the instructions executable to: adapt a transform model to a first set of image patches of a first set of images containing at least a first image, to model the first set of image patches as sparse in a transform domain while allowing deviation from perfect sparsity; reconstruct a second image by minimizing an optimization objective comprising a transform-based regularizer that employs the transform model, and a data fidelity term formed using the imaging measurements; and store the second image in the computer-readable medium, the second image displayable on a display device.

Abstract: Provided is a method and apparatus for support recovery of jointly sparse signals from a plurality of snapshots, thereby enhancing a capability for reconstructing a support in a variety of circumstances, by providing enhanced robustness against noise and perturbation, and/or enhanced computational efficiency. The method may include partial support recovery using a compressed sensing-multiple measurement vector (CS-MMV) scheme; and a complementary support recovery and sparsity level estimation. The complementary support recovery may use subspace information extracted from the plurality of snapshots and partial support information. The total number of elements in the partial support and in the complementary support may be equal to the sparsity level.

Abstract: Pixel images {circumflex over (f)} are created from projections (q1 . . . qp) by backprojecting selected projections to produce intermediate images (Il,m), and performing digital image coordinate transformations and/or resampling on selected intermediate images. The digital image coordinate transformations are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets, and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image {circumflex over (f)}. Digital image coordinate transformation can include rotation, shearing, stretching, contractions. Resampling can include up-sampling, down-sampling, and the like.

Abstract: A method for acquiring MR data from a beating heart during subject respiration includes a prescan phase in which a respiratory compensation table and a k-space sampling schedule are produced. The k-space sampling table is produced using a spatio-temporal model of the beating heart and time sequential sampling theory. During the subsequent scan an imaging pulse sequence which is prospectively compensated for respiratory motion is used to acquire k-space data from the subject. The imaging pulse sequence is repeated to play out the phase encodings in the order listed in the k-space sampling schedule.

Abstract: Pixel images f are created from projections (q1 . . . qp) by backprojecting (100) selected projections to produce intermediate images (I1, m), and performing digital image coordinate transformations (102) and/or resampling (FIG. 31, 186, 192, 196) on selected intermediate images. The digital image coordinate transformations (102) are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets (104), and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image f. Digital image coordinate transformation can include rotation (FIG. 18, 102), shearing (FIG. 10B, 120, 122), stretching, contractions (109), etc. Resampling can include up-sampling (101, 106), down-sampling (109), and the like.

Abstract: Pixel images {circumflex over (f)} are created from projections (q1 . . . qp) by backprojecting selected projections to produce intermediate images (Il,m), and performing digital image coordinate transformations and/or resampling on selected intermediate images. The digital image coordinate transformations are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets, and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image {circumflex over (f)}. Digital image coordinate transformation can include rotation, shearing, stretching, contractions. Resampling can include up-sampling, down-sampling, and the like.

Abstract: A method for acquiring magnetic resonance (MR) data from a dynamic object in which a k-space sampling schedule are produced. The k-space sampling table is produced using a spatio-temporal model of the beating heart, time sequential sampling theory and a known number of parallel receive channels (coils). The imaging pulse sequence is repeated to play out the phase encodings in the order listed in the k-space sampling schedule and the k-space data sets acquired through the parallel receive channels are combined and used to reconstruct a sequence of images. The method is an improved process for dynamic MRI, designed to overcome the limitations of current MRI systems in imaging dynamic phenomena and produces highly accurate motion movies of the structure, function, perfusion and viability of various anatomical regions in MRI subjects such as the beating heart, flow of contrast agents in blood vessels, brain excitation, or joint movement.

Abstract: Pixel images ƒ are created from projections (q1 . . . qp) by backprojecting (100) selected projections to produce intermediate images (I1, m), and performing digital image coordinate transformations (102) and/or resampling (FIG. 31, 186, 192, 196) on selected intermediate images. The digital image coordinate transformations (102) are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets (104), and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image ƒ. Digital image coordinate transformation can include rotation (FIG. 18, 102), shearing (Fig. IOB, 120, 122), stretching, contractions (109), etc. Resampling can include up-sampling (101, 106), down-sampling (109), and the like.

Abstract: A method for acquiring MR data from a beating heart during subject respiration includes a prescan phase in which a respiratory compensation table and a k-space sampling schedule are produced. The k-space sampling table is produced using a spatio-temporal model of the beating heart and time sequential sampling theory. During the subsequent scan an imaging pulse sequence which is prospectively compensated for respiratory motion is used to acquire k-space data from the subject. The imaging pulse sequence is repeated to play out the phase encodings in the order listed in the k-space sampling schedule.

Abstract: A fast method for divergent-beam backprojection is proposed for generating an electronic image from a preprocessed divergent-beam sonogram, the sinogram being a collection of divergent beam projections. The method consists of the following steps: subdividing the sinogram into multiple sub-sinograms; performing a weighted backprojection of said sub-sinograms, to produce multiple corresponding sub-images; and aggregating said sub-images to create the electronic image. The subdivision of the sinogram into sub-sinograms can be performed in a recursive manner. A dual of the proposed method provides a fast means for reprojecting an electronic image, i.e., generating a divergent-beam sinogram from the image. These methods are applicable to fan-beam and cone-beam tomography utilizing a variety of scanning trajectories, including spiral. These methods do not require rebinning, and offer speedups similar to the FFT when compared to conventional backprojection and reprojection algorithms.

Abstract: A fast method for divergent-beam backprojecion is proposed for generating an electronic image from a preprocessed divergent-beam sonogram, the sinogram being a collection of divergent beam projections. The method can include the following steps: subdividing the sinogram into multiple sub-sinograms; performing a weighted backprojection of said sub-sinograms, to produce multiple corresponding sub-images; and aggregating said sub-images to create the electronic image. The subdivision of the sinogram into sub-sinograms can be performed in a recursive manner. A dual of the proposed method provides a fast means for reprojecting an electronic image, i.e., generating a divergent-beam sinogram from the image.

Abstract: A method for reprojecting images into sinograms includes the steps of dividing a two-dimensional image into sub-images as small as one pixel and reprojecting the sub-images at a smaller number of orientations to form subsinograms. These sub-sinograms are then successively aggregated and processed to form a full sinogram. The method uses two algorithms to aggregate the sub-sinograms. In one algorithm, the aggregation is exact, and in the other algorithm, aggregation is an approximation. The first algorithm is accurate, but relatively slow, and the second algorithm is faster, but less accurate. By performing some aggregations with the exact algorithm and some aggregations with the approximate algorithm, switching between the two algorithms in one of a number of suitable ways, an accurate result can be obtained quickly.

Abstract: A method for reprojecting a 3D image into a 3D Radon sinogram includes the steps of dividing a three-dimensional image into sub-images as small as one voxel and reprojecting the sub-images at a smaller number of orientations to form subsinograms. These sub-sinograms are then successively aggregated and processed to form a full sinogram. The method uses two algorithms to aggregate the sub-sinograms. In one algorithm, the aggregation is exact, and in the other algorithm, aggregation is an approximation, and involves increasing the number of orientations by interpolation. The first algorithm is accurate, but relatively slow, and the second algorithm is faster, but less accurate. By performing some aggregations with the exact algorithm and some aggregations with the approximate algorithm, switching between the two algorithms in one of a number of suitable ways, an accurate result can be obtained quickly.

Abstract: Data representing a three-dimensional (3D) sinogram (array of numbers) is backprojected to reconstruct a 3D volume. The transformation requires N3 log2 N operations. An input sinogram is subdivided into a plurality of subsinograms using either an exact or approximate decomposition algorithm. The subsinograms are repeatedly subdivided until they represent volumes as small as one voxel. The smallest subsinograrns are backprojected using the direct approach to form a plurality of subvolumes, and the subvolumes are aggregated to form a final volume. Two subdivision algorithms are used. The first is an exact decomposition algorithm, which is accurate, but slow. The second is an approximate decomposition algorithm which is less accurate, but fast. By using both subdivision algorithms appropriately, high quality backprojections are computed significantly faster than existing techniques.