Up: Astronomical image compression
Subsections
Numerical image information is simply coded as an array of
intensity values,
reproducing the geometry of the detectors used for the
observation or the densitometer used for plate digitization.
The object signal will be stored with noise, background
variations, and so on.
The relevant information depends on the application domain, and represents what
the astronomer wants to study. The information of relevance
reflects the limits of the observing instrument
and of the digitization process.
Reducing the amount of data to be coded will require that the
relevant information be selected in the image and that the coding
process be reorganized so that
we emphasize the relevant information and drop noise and non-meaningful
data.
For this, we can focus on the region of interest, filter out noise, and
quantize coarsely to take into account the limits of our human visual
system if the images are only used for browsing.
Furthermore, the usual pixel array representation associated with
images stores a lot of redundant information due
to correlation of intensity values between nearby pixels and between different
scales for large image structures or slowly varying background.
A good compression scheme should aim at concentrating on the meaningful
information in
relation to the scientific purpose of the imaging (survey) project and code it
efficiently, thereby limiting as much as possible the redundancy.
For this study, we examined the major available image compression
packages, and
compared their strategies with respect to these goals.
Methods used in astronomy include HCOMPRESS
(White et al. 1992),
FITSPRESS (Press 1992),
and JPEG (Furht 1995). These are all based on linear
transforms, which in principle help to reduce the redundancy of pixel
values in a block and decorrelate spatial
frequencies or scales.
Two other methods have also been proposed for astronomical image
compression: one using mathematical morphology, and
another based on the pyramidal median transform (a nonlinear transform).
A specific decompression method has also been
developed in
Bijaoui et al. (1996) in order to reduce artifacts
relative to the HCOMPRESS method.
In the signal processing domain, two other recent approaches are worthy of
mention. The first is based
on fractals, and the second uses a bi-orthogonal wavelet transform.
We first briefly review all of these methods, and then compare them in the
framework of astronomical images.
HCOMPRESS (White et al. 1992) was developped at Space Telescope
Science Institute (STScI, Baltimore), and is commonly
used to distribute archive images from the Digital Sky Survey
DSS1 and DSS2. It
is based on the Haar wavelet transform. The algorithm consists of
- 1.
- applying a Haar wavelet transform to the data,
- 2.
- quantizing the wavelet coefficients linearly as integer values,
- 3.
- applying a quadtree to the quantified value, and
- 4.
- using a Huffman coder.
Sources are available at
http://www.stsci.edu/software/hcompress.html
Iterative decompression was proposed in
Bijaoui et al. (1996)
to decompress files which
were compressed using HCOMPRESS. The idea is to consider the decompression
problem as a restoration problem, and to add constraints on the solution in
order to reduce the artifacts.
FITSPRESS (Press 1992) uses a threshold on very bright
pixels and applies a linear wavelet
transform using the Daubechies-4 filters. The wavelet coefficients are
thresholded according to a noise threshold, quantized linearly and
runlength encoded.
This was developed at the Center for Astrophysics, Harvard.
Sources are available at
ftp://cfata4.harvard.edu/pub/fitspress08.tar.Z.
JPEG is the standard video compression software
for single frame images (Furht 1995).
It decorrelates pixel coefficients within 8
8 pixel blocks
using the discrete cosine
transform (DCT) and uniform quantization.
Various wavelet packages exist which support image compression,
leading to more sophisticated compression methods. The wavelet transform
we used
is based on a bi-orthogonal wavelet transform (using Antonini-Daubechies
7/9 coefficients) with non-uniform coding
(Taubman & Zakhor 1994),
and arithmetic encoding.
Source code is available at http://www.cs.dartmouth.edu/
gdavis
The image is decomposed into blocks, and each block is represented
by a fractal.
See Fisher (1994) for more explanation.
This method
(Starck et al. 1998), denoted MathMorph in this work,
is based on mathematical morphology (erosion and dilation).
It consists of detecting structures above a given level, the level being
equal to the background plus three times the noise standard deviation.
Then, all structures are compressed by using erosion and dilation, followed by
quadtree and Huffman coding. This method relies on a first step of object
detection, and leads to high compression ratios if the image does not contain
a lot of information, as is often the case in astronomy.
The principle of this compression method
(Starck et al. 1996;
Starck et al. 1998),
denoted PMT here,
is to select the information
we want to keep,
by using the pyramidal median transform, and to code this information without
any loss. Thus
the first phase searches for the minimum set of quantized multiresolution
coefficients which produce an image of "high quality''. The quality is
evidently subjective, and we will define by this term an image such as
the following:
- there is no visual artifact in the decompressed image; and
- the residual (original image - decompressed image) does not
contain any structure.
Lost information cannot be recovered, so if we do not accept any loss,
we have to compress what we take as
noise too, and the compression ratio will be low (3 or 4 only).
The pyramidal median transform (PMT) is similar to the mathematical
morphology
(MathMorph) method in the sense that
both try to understand what is represented in the image, and to compress
only what is
considered as significant.
The PMT uses a multiresolution approach, which allows more
powerful separation of signal and noise.
The latter two methods are both implemented in the MR/1 package
(see http://ourworld.compuserve.com/homepages/multires).
Table 1:
Description and comparison of the different steps in the
compression packages tested
![\begin{tabular}[t]
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\hline
Sof...
.... Morph. & Dilation &Noise estimation & -- & bitplanes & \\ \hline\end{tabular}](/articles/aas/full/1999/09/ds1667/img4.gif) |
Each of these methods belongs to a general scheme where the following
steps can be distinguished:
- 1.
- Decorrelation of pixel values inside a block, between wavelength,
scales or shape, using orthogonal or nonlinear
transforms.
- 2.
- Selection and quantization of relevant coefficients.
- 3.
- Coding improvement: geometrical redundancy reduction of the
coefficients,
using the fact that pixels are contiguous in an array.
- 4.
- Reducing the statistical redundancy of the code.
How each method realizes these different steps is indicated in Table 1.
Clearly these methods combine many strategies to reduce
geometrical and
statistical redundancy. The best results are obtained if appropriate
selection of relevant information has been performed before applying these
schemes.
For astronomical images, bright or extended objects are sought, as well as
faint structures, all showing good spatial correlation of pixel values and
within a wide range of greylevels. Noise background, on the contrary, shows no
spatial correlation and fewer greylevels.
The removal of noisy background helps in regard to data compression of
course. This can be
done with filtering, greylevel thresholding, or coarse quantization of
background pixels.
This is used by FITSPRESS, PMT and MathMorph which divide information
into a noise part, estimated
as a Gaussian process, and a highly correlated signal part.
MathMorph simply thresholds the background noise estimated by a
3-sigma clipping,
and quantizes the signal as a multiple of sigma
(Huang & Bijaoui 1991).
FITSPRESS thresholds background pixels and allows for
coarse background reconstruction,
but also keeps the highest pixel values in a separate list.
PMT uses a multiscale noise filtering and selection approach based on
noise standard deviation
estimation.
JPEG and HCOMPRESS do not carry out noise separation before the transform stage.
Apart from signal-to-noise discrimination, information losses may
appear after the
transforms at two steps: coefficient selection and coefficient quantization.
The interpretable resolution of the decompressed images clearly depends upon
these two steps.
If the spectral bandwidth is limited, then the more it is shortened,
the better the
compression rate. The coefficients generally associated with
the high spatial
frequencies related to small structures (point objects) may be suppressed
and lost.
Quantization also introduces information loss, but can be optimized using a
Lloyd-Max quantizer for example
(Proakis 1995).
All other steps, shown in
Table 1, such as reorganizing
the quantized coefficients, hierarchical and statistical redundancy coding,
and so on,
will not compromise data integrity. This statement can be made
for all packages.
The main improvement clearly comes from an appropriate noise/signal
discrimination
and the choice of a transform appropriate to the objects' signal properties.
Following the kind of images and the application needs, different strategies
can be used:
- 1.
- Lossy compression: in this case the compression ratio is relatively
low (< 5).
- 2.
- Compression without visual loss. This means that one cannot see the
difference between the original image and the decompressed one. Generally,
compression ratios between 10 and 20 can be obtained.
- 3.
- Good quality compression: the decompressed image does not contain any
artifact, but some information is lost. Compression ratios up to 40 can be
obtained in this case.
- 4.
- Fixed compression ratio: for some technical reasons, one may decide to
compress all images with a compression ratio higher than a given value,
whatever the effect on the decompressed image quality.
- 5.
- Signal-to-noise separation: if noise is present in the data, noise
modelling can allow very high compression ratios just by including some type
of filtering in the wavelet space during the compression.
Following the image types, and the selected strategy, the optimal compression
method may vary. The main
interest in using a multiresolution framework is to avail of
progressive information transfer and visualization.
Up: Astronomical image compression
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