VayTek's Homepage
VayTek Website Links
VayTek offers Advanced Image Processing Systems, including both hardware and software for:
- Microscopy
- Industrial Inspection
- Medical Imaging
- Quality Control
- Non-Destructive Testing
- Deconvolution of Confocal Images
- 3D Volume Visualization and Measurement
VayTek, Inc.
305 West Lowe Ave.
Fairfield, IA
Tel 641-472-2227
Fax 641-472-8131
Email vaytek@vaytek.com
Science-Related Images for Education: All images on this site may be downloaded and used for educational purposes. Please note that only low resolution, 72 dpi images are presented on our Web site. For higher resolution, larger images that demonstrate VayTek's deconvolution and 3D volume visualization software, please fax or email your requests to our home office.
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VayTek's Homepage
VayTek, Inc.
305 West Lowe Ave.
Fairfield, IA
Tel 641-472-2227
Fax 641-472-8131
Email vaytek@vaytek.com
VayTek's Homepage
Technical Note
Advancements in computer processing power have enabled new three-dimensional image enhancement and visualization techniques. Data storage capacities of a gigabyte or more are affordable and commonplace. The Power Macintosh computers are RISC based processors which perform graphical and computational tasks many times faster than the older 68000 based systems. These new systems are ideal platforms for three-dimensional deconvolution of microscope data sets.
Deconvolution Algorithms
There are basically three different deconvolution methods. All
of them significantly reduce the out of-focus haze in microscope
data sets.
- Single image deconvolution
- Deconvolution using 3 images (nearest neighbor deconvolution)
- Deconvolution using the whole volume.
Single Image deconvolution is used when the acquired image or images are not a volume scan. For example, researchers studying fast events must keep the image at the same focal plane and quickly capture an image. Each image is a snapshot of the specimen at a unique time sample. These images can be deconvolved by a single image deconvolution method to remove some of the out-of-focus haze.
Nearest Neighbor deconvolution is useful when the specimen can be imaged along the optical axis and a series of images captured and stored to disk. The resulting data set is a volume representation of the object. The image can be deconvolved using the nearest neighbor method. In this approach, three consecutive images are used to deconvolve the middle image. The image on the top and bottom of the triplet can be thought of as windows in which out-of-focus haze from all the images above and below the processed image must pass to reach the middle image. This technique produces excellent results when:
- The images are sampled at the proper frequency along the z axis. For large lens NAs of 1.3 or more, sampling should be at 0.25 microns. For a low NA of 0.7, sampling size can be 1.0 microns.
- The scanned volume is thin (50 microns - larger distance if sample is very transmissive)
Constrained Iterative deconvolution is the third method. This method uses a whole volume during deconvolution. The mathematics is as follows:
- Convolve a focused volume with the point spread function (PSF) to create the original acquired volume.
- Compare the difference between the original volume and the blurred focused volume.
- Use the error difference to correct the focused volume.
- Go back to step one and repeat the procedure.
How do you get the first focused volume? Most procedures use the original volume as a first guess. During this iterative procedure one prevents any pixel from being negative - this is the well known positivity constraint. Differences between various constrained iterative algorithms are due to differences in step 3 where the focused volume is corrected and the rate of convergence is determined. All constrained iterative methods decrease the error computed in step 2.
The PSF is a very important factor when using a constrained iterative method. Both theoretical and experimental deconvolution PSF s can be used. However experimental PSF determination is very difficult. Typically very small fluorescent beads about .2 microns in diameter are used to get a direct PSF representation. Accurate imaging of such small beads is difficult and the beads must be implanted in a medium with the same optical characteristics as the specimen for the PSF to be optimal. For experimental PSF s to be used reliably with an iterative method requiring large amounts of processing time, great care must be exercised when measuring the PSF.
Current Software
VayTek has implemented single image, three image and constrained
iterative deconvolution programs for Windows and Power Macintosh
platforms. The single and three image deconvolution is based
on the work of Agard & Sedat, USCD. The constrained iterative
technique uses a Janson-van Cittert correction method originally
developed by van Cittert (van Cittert, 1930) and modified by
Jansson (Jansson, Hunt et al.,1970). All these deconvolution
programs use a theoretical 3D PSF. An experimental PSF module
has also been developed.
VayTek currently sells an SGI based deconvolution program that uses both theoretical and experimental PSF s. This program is call Huygens and was developed by Hans T.M. van der Voort. Huygens has routines for extracting PSF information from circular beads that are 20 microns in diameter, which are brighter and produce accurate 3D PSF information. Deconvolution methods are the Tikhonov-Miller algorithm (Legandijk, 1990) and the maximum Likelihood Estimation (MLE) (Legandijk, 1990, Conchello and Hansen, 1990; Holmes and Liu, 1991; Csiszar, 1991; Snyder et al., 1992). The Huygens program also deconvolves confocal images. Routines to create a 3D PSF based upon the confocal microscope type are included.
Processing time for deconvolving images with Huygens depends upon the size of the volume. A 32 by 32 by 32 volume takes 40 seconds to process on an Indigo2, 100 MHZ R4000 processor. Thus a 256 by 256 by 256 volume requires about 6 hours of processing time.
Memory Requirements
For all machines, memory is an extremely important factor in
determining how large a volume can be processed. To determine
the required memory, three volumes must be present at one time:
the original blurred volume, the 3D PSF and the deconvolved volume.
For floating point representation, this means that you multiply
the size of the input volume by 24 to calculate total memory
requirements. This leads to the following table:
| Volume Size | Required Memory |
| 512 cubed | 3.2 gigabytes |
| 256 cubed | 402 megabytes |
| 128 cubed | 50 megabytes |
| 64 cubed | 6.3 megabytes |
| 32 cubed | 785 kilobytes |
This means that computers that deconvolve volumes must either have lots of RAM or very efficient file swapping for an effective virtual memory capability. Presently, UNIX machines handle virtual memory better than either Windows or Macintosh operating systems. This explains why UNIX machines are popular for processing large data sets.
We expect RAM cost will decrease and virtual memory efficiency will increase for both Windows and Macintosh based systems. VayTek is currently porting the SGI based routines to both Windows 95, Windows NT and Power Macintosh platforms. We expect this work will be completed by the end of 1996.
In addition to an appropriate computer platform with adequate RAM, a good three dimensional deconvolution/microscope system requires the following components:
- High quality image acquisition equipment. This may include a CCD camera and a high quality microscope. Complete systems are available from VayTek, or researchers can retrofit VayTek components to their existing systems.
- Excellent microscope control for precise z stage movement and optical sectioning; control of excitation shutters to minimize photo bleaching of fluorescent specimens. Control modules are available from VayTek.
The adage garbage in, garbage out applies to all data acquisition, but is particularly apt for 3D deconvolution of microscope data.. Sophisticated mathematical algorithms cannot add what is not in the data. For collection of accurate 3D data, precise techniques must be applied at every step of the image acquisition. The new, more powerful computers with generous amount of RAM and hard disk space can provide the precision and control needed to acquire and deconvolve the quality of images needed to push scientific research forward.
Question: I'm trying to calibrate the deconvolution
software and I get error messages when using the measured PSF
in the Volume Constrained Iterative to remove haze in the bead
data set using the same bead data set.
Answer: When you deconvolve a bead scan with a bead scan, the
theoretical answer is that there will be one pixel with all the
energy and the rest will be perfectly black. This is called a
delta function in math and like unicorns and fairies they exist
in the mind, not in our world. The Constrained Iterative deconvolution
may balk at trying to converge into a delta function. Deconvolution
will also not work on an object that is infinitely thin (a few
pixels wide). Using the Constrained Iterative algorithm for deconvolution
will only work when the object to be deconvolved is much larger
than the Point Spread Function (PSF). And the PSF must be finite
in extent.
Deconvolution
of Images and Spectra
by Peter A. Jansson (Editor)
Hardcover - 514 pages 1st edition (January 15, 1997)
Academic Pr; ISBN: 0123802229 ; Dimensions (in inches): 1.06
x 9.19 x 6.15
Editorial Reviews Book News, Inc.
Provides an overview of the field, along with techniques to successfully
apply signal or image processing to corrupt images. The authors
assume only a working knowledge of calculus, and emphasize applications
over theory, focusing on areas that have been pivotal to the
evolution of effective methods. Topics include linear and nonlinear
methods of deconvolution, specific applications of a proven method,
advances made in restoration of images from cell biology and
astronomy, and new methods, including maximum probability estimation,
Fourier spectrum continuation, and projections onto convex sets.
Each chapter begins with a symbol list, and notation is consistent
throughout. -- Copyright © 1999 Book News, Inc., Portland,
OR All rights reserved
Reviewer: cameron@rowland.org from Cambridge, MA
"This book is an excellent presentation of exactly what
the title says. It starts with a solid mathematical introduction
to the topic and then continues with numerous extensions and
applications. Recommended if the title interests you."
Articles recommended by VayTek that are available on this website:
- Appropriate Light Sources: Advantages of digital haze removal
- Single Image Haze Removal from an Archived File
- Haze Removal from Color Images and Composite Top Views
- A Comparison of Digital Deconvolution and Scanning Confocal Images
- Data Acquisition Issues and Cameras Appropriate for Deconvolution
- Data Acquisition Issues: Image acquisition techniques
- Introduction to Digital Systems for Microscopy: Microscopy fundamentals
- Selected Papers: Limits of depth measurements on stereo pairs
- What cameras are suitable for deconvolution?
- What resolution should I have for my camera?