University of Illinois

Instarecon

Yoram Bresler

Samit Basu

Jeffrey Brokish

Ashvin K George

Luke A Pfister

Nitin Aggarwal

Amir Boag

Behzad Sharif

Shu Xiao

Saiprasad Ravishankar

Saptarshi Bandyopadhyay

David C Munson, Jr

Eric Michielssen

Samit c/o University Of Ilinois Basu

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. Forward projection methods perform digital image coordinate transformations on an input image to produce multiple intermediate-images, the parameters of one or more coordinate transformations being chosen such that Fourier spectral support of an intermediate-image being produced is modified so that a region of interest has a reduced extent along one or more coordinate direction and the intermediate-images can be represented with a desired accuracy by sparse samples.

Method and system for fast reprojection

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.

Method and system for reprojection and backprojection for tomography reconstruction

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.

Highly accelerated imaging and image reconstruction using adaptive sparsifying transforms

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.

Method and system for iterative computed tomography reconstruction

Pixel images {circumflex over (f)} are created from projections (q. . . q) by backprojecting selected projections to produce intermediate images (I), 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. Projections can be created from a pixel image ({circumflex over (f)}), by performing digital image coordinate transformation and/or resampling and/or decimation re-projecting the final intermediate image.

Fast hierachical tomography methods and apparatus

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.

Adaptive acquisition and reconstruction of dynamic MR images

Pixel images f are created from projections (q. . . q) by backprojecting () selected projections to produce intermediate images (I, m), and performing digital image coordinate transformations () and/or resampling (FIG.) 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 f. Digital image coordinate transformation can include rotation (FIG.), shearing (,), stretching, contractions (), etc. Resampling can include up-sampling (), down-sampling (), and the like. Projections (FIG., p&#x3b8;. . . p&#x3b8;) can be created from a pixel image (f), by performing digital image coordinate transformation () and/or resampling () and/or decimation (FIG.; FIG.) re-projecting the final intermediate image ().

Fast hierarchical tomography methods and apparatus

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.

Adaptive parallel acquisition and reconstruction of dynamic MR images

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. Substantial computational savings are obtained without perceptible degradation or significant loss of numerical accuracy.

Methods and apparatus for fast divergent beam tomography

Fast hierarchical reprojection algorithm for tomography

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.

Fast hierarchical reprojection algorithms for 3D radon transforms

Data representing a three-dimensional (3D) sinogram (array of numbers) is backprojected to reconstruct a 3D volume. The transformation requires N,log,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.

Fast hierarchical backprojection for 3D Radon transform

A process for backprojecting a sinogram to a tomographic image includes the steps of subdividing the sinogram into a plurality of subsinograms, preferably in a recursive manner, until each subsinogram represents an image as small as one pixel in size. Each of the final subsinograms is backprojected to produce a plurality of corresponding subimages, and the subimages are aggregated to create the image. Two algorithms can be used in the decomposition process. An exact decomposition algorithm is accurate, but relatively slow. An approximation decomposition algorithm is less accurate, but fast. By switching between the two algorithms, accurate decomposition is realized in a short time, speeding up the backprojection process considerably.

Fast hierarchical backprojection method for imaging

The present method is a process for reprojecting, or computing tomographic projections of an image, based on multilevel image domain decomposition. The method includes decomposing an image into one or more sub-images, followed by reprojection of the sub-images into sinograms, appropriate scaling of the sinograms, and aggregation of the sub-image sinograms into a single sinogram of the entire image. The multilevel process attains image quality comparable to that of direct reprojection methods, while requiring much less computation, and therefore being much faster.

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Urbana, IL, United States of America

Yoram Bresler