Mathematical Analysis of SMASH-Based Reconstruction Methods for Parallel MRI

AbstractIn this study, a fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. BASS is applicable when Cartesian fully-sampled k-space measurements of specific anatomy are available for training and the reconstruction method for undersampled measurements is specified; such information is used to define the efficacy of any SP for recovering the values at the non-sampled k-space points. BASS produces a sequence of SPs with the aim of finding one of a specified size with (near) optimal efficacy. BASS was tested with five reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Three datasets were used for testing, two of high-resolution brain images ($$\text {T}_{2}$$ T 2 -weighted images and, respectively, $$\text {T}_{1\rho }$$ T 1 ρ -weighted images) and another of knee images for quantitative mapping of the cartilage. The proposed approach has low computational cost and fast convergence; in the tested cases it obtained SPs up to 50 times faster than the currently best greedy approach. Reconstruction quality increased by up to 45% over that provided by variable density and Poisson disk SPs, for the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Quantitative MRI and prospective accelerated MRI results show improvements. Compared with greedy approaches, BASS rapidly learns effective SPs for various reconstruction methods, using larger SPs and larger datasets; enabling better selection of sampling-reconstruction pairs for specific MRI problems.

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Density waves in disk galaxies

Symposium - International Astronomical Union ◽

10.1017/s0074180900101135 ◽

1967 ◽

Vol 31 ◽

pp. 313-317 ◽

Cited By ~ 8

Author(s):

C. C. Lin ◽

F. H. Shu

Keyword(s):

Mathematical Analysis ◽

Spiral Structure ◽

Stellar System ◽

Collective Modes ◽

Disk Galaxies ◽

Spiral Pattern ◽

Density Waves ◽

The Galaxy ◽

Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

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High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100102158 ◽

1988 ◽

Vol 46 ◽

pp. 14-15

Author(s):

P.J. Lea ◽

M.J. Hollenberg

Keyword(s):

Electron Microscopy ◽

Pigment Epithelium ◽

Retinal Pigment ◽

Rat Hepatocytes ◽

Three Dimensions ◽

Objective Lens ◽

Rat Tissues ◽

Thin Sections ◽

Reconstruction Methods ◽

Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

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3-D reconstruction and analysis of mammalian mitotic spindle structure

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100123295 ◽

1992 ◽

Vol 50 (1) ◽

pp. 578-579

Author(s):

Kent McDonald ◽

David Mastronarde ◽

Rubai Ding ◽

Eileen O'Toole ◽

J. Richard McIntosh

Keyword(s):

Cross Sections ◽

Mitotic Spindle ◽

Experimental Studies ◽

Video Camera ◽

Three Dimensions ◽

Mitotic Spindles ◽

Black And White ◽

Reconstruction Methods ◽

Spindle Structure ◽

Tissue Culture Line

Mammalian spindles are generally large and may contain over a thousand microtubules (MTs). For this reason they are difficult to reconstruct in three dimensions and many researchers have chosen to study the smaller and simpler spindles of lower eukaryotes. Nevertheless, the mammalian spindle is used for many experimental studies and it would be useful to know its detailed structure.We have been using serial cross sections and computer reconstruction methods to analyze MT distributions in mitotic spindles of PtK cells, a mammalian tissue culture line. Images from EM negatives are digtized on a light box by a Dage MTI video camera containing a black and white Saticon tube. The signal is digitized by a Parallax 1280 graphics device in a MicroVax III computer. Microtubules are digitized at a magnification such that each is 10-12 pixels in diameter.

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Computing cell tractions from particle displacements on silicone rubber substrata

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168542 ◽

1994 ◽

Vol 52 ◽

pp. 162-163

Author(s):

Tim Oliver ◽

Akira Ishihara ◽

Ken Jacobsen ◽

Micah Dembo

Keyword(s):

Plane Stress ◽

Linear Elasticity ◽

Silicone Rubber ◽

Mathematical Analysis ◽

Elastic Recovery ◽

Video Images ◽

Cell Traction Forces ◽

Latex Beads ◽

Cell Traction ◽

Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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Structural Studies on the Eukaryotic Ribosome

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180033 ◽

1990 ◽

Vol 48 (1) ◽

pp. 256-257

Author(s):

Adriana Verschoor ◽

Ronald Milligan ◽

Suman Srivastava ◽

Joachim Frank

Keyword(s):

Chick Embryo ◽

3D Reconstruction ◽

Single Particle ◽

Mass Density ◽

Particle Surface ◽

Uranyl Acetate ◽

Electron Microscopic ◽

Eukaryotic Ribosome ◽

Negative Stain ◽

Reconstruction Methods

We have studied the eukaryotic ribosome from two vertebrate species (rabbit reticulocyte and chick embryo ribosomes) in several different electron microscopic preparations (Fig. 1a-d), and we have applied image processing methods to two of the types of images. Reticulocyte ribosomes were examined in both negative stain (0.5% uranyl acetate, in a double-carbon preparation) and frozen hydrated preparation as single-particle specimens. In addition, chick embryo ribosomes in tetrameric and crystalline assemblies in frozen hydrated preparation have been examined. 2D averaging, multivariate statistical analysis, and classification methods have been applied to the negatively stained single-particle micrographs and the frozen hydrated tetramer micrographs to obtain statistically well defined projection images of the ribosome (Fig. 2a,c). 3D reconstruction methods, the random conical reconstruction scheme and weighted back projection, were applied to the negative-stain data, and several closely related reconstructions were obtained. The principal 3D reconstruction (Fig. 2b), which has a resolution of 3.7 nm according to the differential phase residual criterion, can be compared to the images of individual ribosomes in a 2D tetramer average (Fig. 2c) at a similar resolution, and a good agreement of the general morphology and of many of the characteristic features is seen.Both data sets show the ribosome in roughly the same ’view’ or orientation, with respect to the adsorptive surface in the electron microscopic preparation, as judged by the agreement in both the projected form and the distribution of characteristic density features. The negative-stain reconstruction reveals details of the ribosome morphology; the 2D frozen-hydrated average provides projection information on the native mass-density distribution within the structure. The 40S subunit appears to have an elongate core of higher density, while the 60S subunit shows a more complex pattern of dense features, comprising a rather globular core, locally extending close to the particle surface.

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