Topic

# Iterative reconstruction

About: Iterative reconstruction is a(n) research topic. Over the lifetime, 41296 publication(s) have been published within this topic receiving 841132 citation(s).

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ETH Zurich

^{1}TL;DR: The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil configurations and k‐space sampling patterns and special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density.

Abstract: The invention relates to a method of parallel imaging for obtaining images by means of magnetic resonance (MR). The method includes the simultaneous measurement of sets of MR singals by an array of receiver coils, and the reconstruction of individual receiver coil images from the sets of MR signals. In order to reduce the acquisition time, the distance between adjacent phase encoding lines in k-space is increased, compared to standard Fourier imaging, by a non-integer factor smaller than the number of receiver coils. This undersampling gives rise to aliasing artifacts in the individual receiver coil images. An unaliased final image with the same field of view as in standard Fourier imaging is formed from a combination of the individual receiver coil images whereby account is taken of the mutually different spatial sensitivities of the receiver coils at the positions of voxels which in the receiver coil images become superimposed by aliasing. This requires the solution of a linear equation by means of the generalised inverse of a sensitivity matrix. The reduction of the number of phase encoding lines by a non-integer factor compared to standard Fourier imaging provides that different numbers of voxels become superimposed (by aliasing) in different regions of the receiver coil images. This effect can be exploited to shift residual aliasing artifacts outside the area of interest.

6,205 citations

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TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.

Abstract: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

4,654 citations

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TL;DR: This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD‐AUTO‐SMASH reconstruction techniques and provides unaliased images from each component coil prior to image combination.

Abstract: In this study, a novel partially parallel acquisition (PPA) method is presented which can be used to accelerate image acquisition using an RF coil array for spatial encoding. This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques. As in those previous methods, a detailed, highly accurate RF field map is not needed prior to reconstruction in GRAPPA. This information is obtained from several k-space lines which are acquired in addition to the normal image acquisition. As in PILS, the GRAPPA reconstruction algorithm provides unaliased images from each component coil prior to image combination. This results in even higher SNR and better image quality since the steps of image reconstruction and image combination are performed in separate steps. After introducing the GRAPPA technique, primary focus is given to issues related to the practical implementation of GRAPPA, including the reconstruction algorithm as well as analysis of SNR in the resulting images. Finally, in vivo GRAPPA images are shown which demonstrate the utility of the technique.

4,463 citations

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TL;DR: Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm, applicable in both single photon (SPECT) and positron emission tomography (PET).

Abstract: The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained. >

3,588 citations

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TL;DR: The goal of this article is to introduce the concept of SR algorithms to readers who are unfamiliar with this area and to provide a review for experts to present the technical review of various existing SR methodologies which are often employed.

Abstract: A new approach toward increasing spatial resolution is required to overcome the limitations of the sensors and optics manufacturing technology. One promising approach is to use signal processing techniques to obtain an high-resolution (HR) image (or sequence) from observed multiple low-resolution (LR) images. Such a resolution enhancement approach has been one of the most active research areas, and it is called super resolution (SR) (or HR) image reconstruction or simply resolution enhancement. In this article, we use the term "SR image reconstruction" to refer to a signal processing approach toward resolution enhancement because the term "super" in "super resolution" represents very well the characteristics of the technique overcoming the inherent resolution limitation of LR imaging systems. The major advantage of the signal processing approach is that it may cost less and the existing LR imaging systems can be still utilized. The SR image reconstruction is proved to be useful in many practical cases where multiple frames of the same scene can be obtained, including medical imaging, satellite imaging, and video applications. The goal of this article is to introduce the concept of SR algorithms to readers who are unfamiliar with this area and to provide a review for experts. To this purpose, we present the technical review of various existing SR methodologies which are often employed. Before presenting the review of existing SR algorithms, we first model the LR image acquisition process.

3,308 citations