Abstract: An optical phase grating produces an interference pattern rich in intensity and spatial-frequency information from the external scene. The grating includes an odd number of repeated sets of adjacent horizontal portions, separated by steps, that fill an area that radiates outward from a central region. At a given distance from the central region and within the area of the phase grating, each of the first horizontal portions is of a first width that differs from a second width of the adjacent second horizontal portions. The interference patterns produced by the grating can be processed to extract images and other information of interest about an imaged scene.

Abstract: An optical phase grating produces an interference pattern rich in intensity and spatial-frequency information from the external scene. The grating includes an odd number of repeated sets of adjacent horizontal portions, separated by steps, that fill an area that radiates outward from a central region. At a given distance from the central region and within the area of the phase grating, each of the first horizontal portions is of a first width that differs from a second width of the adjacent second horizontal portions. The interference patterns produced by the grating can be processed to extract images and other information of interest about an imaged scene.

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 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.