Prior Information and Noise in Three-dimensional Optical Image Reconstruction

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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An Image Reconstruction System Applied to High Voltage Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100115080 ◽

1975 ◽

Vol 33 ◽

pp. 292-293

Author(s):

D. E. Johnson

Keyword(s):

High Voltage ◽

Prior Information ◽

Block Diagram ◽

Three Dimensional ◽

Real Space ◽

Two Dimensional ◽

Efficient Manner ◽

Fourier Methods ◽

Tilt Series ◽

Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

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Three dimensional deblurring of transmitted-light brightfield micrographs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148654 ◽

1993 ◽

Vol 51 ◽

pp. 564-565

Author(s):

Santosh Bhattacharyya

Keyword(s):

Image Reconstruction ◽

Three Dimensional ◽

Transmitted Light ◽

Reconstruction Algorithms ◽

3D Image Reconstruction ◽

Structural Details ◽

Spread Function ◽

Early Testing ◽

Linearized Model ◽

Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

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