Image Compression

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Image Compression by quantization below noise level

To limit the size of images to be transfered by the network, RAW images are compressed by quantization at or just below the noise level. RAW files have integer pixel values between 0 and 16383 (14-bit resolution), but the noise level allows for a smaller number of discrete values at the cost of a higher quantization noise. The quantization noise is set to be equal (or less than) the quadratic sum of readout and photon noise to avoid a significant increase of overall noise. Pixel values x (0 - 16383) are resampled according the the following equation: 
x [ADU] -> f(x)
The resampling function f (integer->integer) is chosen so that the quantization noise is smaller by a factor α than the quadratic sum of readout and photon noise. With g the gain in e-/ADU and RON the readout noise in ADU:
Noise [ADU] = sqrt( RON2 + x/g)
The quantization noise constraint can be written:
df/dx = 1/(αNoise)
with x and Noise in ADU. Integrating this equation leads to :
f(x) = 2α-1 sqrt(g) (sqrt(g RON2 + x) - RON sqrt(g))
The quantization is achieved by replacing the pixel value x by the nearest integer to f(x).

To recover x from f(x), the following equation can be used:
x = (αf(x)/(2sqrt(g)) + RON sqrt(g) )2 - g RON2

f(x) Example

As an example, I consider here an image acquired at ISO 100: 
alpha = 0.5
g = 1.36 e-/ADU
RON = 15.8 ADU
The function f(x) is shown in the following figure. With these parameters, the image can be quantized into just over 500 levels without increasing the overall noise level by more than sqrt(1+0.52)-1 = 12% .
f(x) example. The input values (x axis) can be quantized into a smaller number of values (30x fewer values) with a small (<12%) increase in the overall noise.

Source Code

The source code is part of module image_format in Cfits. The two functions are requant (compress) and dequant (restore). See the example script for use (this scripts is used for the benchmark below): 
 
# param 1: alpha


Cfits << EOF
loadfits IMG_0000.fits im
requant im imq $1 15.8 1.36 1024
save_sh imq "!imq.fits"
quit
EOF
rzip -k imq.fits 
mv imq.fits.rz imq.fits.$1.rz  


# testing

Cfits << EOF
loadfits imq.fits
dequant imq im $1 15.8 1.36 1024
loadfits IMG_0000.fits im00
imdiff=im-im00
save_fl im "!im.fits"
save_fl imdiff "!imdiff.fits"
quit
EOF

Benchmark

Test on a single image, acquired at ISO 100. 
Description                             size      file name
-------------------------------------------------------------------
RAW image:                              19291122  IMG_0000.CR2
RAW image, rzipped:                     18535254  IMG_0000.CR2.rz
RAW image, FITS (single precision):     60641280  IMG_0000.fits
RAW image, short int:                   30323520  imq.fits
alpha = 0.1, rzipped:                   13099237  imq.fits.0.1.rz
alpha = 0.2, rzipped:                   10238906  imq.fits.0.2.rz
alpha = 0.5, rzipped:                    7409063  imq.fits.0.5.rz
alpha = 1.0, rzipped:                    5425962  imq.fits.1.0.rz
alpha = 1.5, rzipped:                    4361783  imq.fits.1.5.rz
alpha = 2.0, rzipped:                    3628414  imq.fits.2.0.rz
With alpha = 0.5, the image size on disk is reduced to 38% of its original size (28% for alpha = 1.0).
Image compression by quantization, with α = 1. Top left: original RAW image. Top right: compressed image after quantization into approximately 150 levels. Bottom left: reconstructed image from the quantized image. Bottom right: difference between the reconstructed image and the original image.

Use

The compress and uncompress commands are part of the main skycam utility. To compress image 4 acquired on 2011-02-26 : 
/skycam/skycam compress 2011-02-26 4
To compress all files from frame numbers 0 to 100 for date 2011-02-26: 
 
seq 0 100| xargs -I {} /skycam/skycam compress 2011-02-26 {}
Page content last updated: 27/06/2023 06:35:52 HST
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