Changes between Initial Version and Version 1 of asinh_compression

Timestamp:

Mar 28, 2016, 5:22:04 PM (10 years ago)

Author:

watersc1

Comment:

--

asinh_compression

@@ +1 @@
+= Short version =
+
+If you have a asinh compressed stack (C):
+{{{
+ L = BOFFSET + BSOFTEN * (exp(C / alpha) - exp(-C / alpha))
+}}}
+where BOFFSET and BSOFTEN are supplied in the header, and alpha = log10(exp(2.5)) = 1.0857362.
+
+If you want to compress something (L) with asinh compression:
+{{{
+  BOFFSET = mean(L)
+  BSOFTEN = sqrt(alpha) * stddev(L)
+  C = alpha * asinh( (L - BOFFSET) / (2.0 * BSOFTEN) )
+}}}
+
+
+= Long version =
+
+Due to the expected large range of data values in the final stacked
+image, saving them as compressed 16-bit integer images with linear
+BSCALE and BZERO scaling values is likely to offer poor
+reconstructions of the stacked image.  This will lead either to
+truncation of the extrema of the image, or quantized values that are
+poorly spaced for the image histogram.  Saving the images as 32-bit
+floating point values would alleviate this quantization issue, at the
+cost of a large increase in the disk space required for the stacked
+images.
+
+Transforming the data prior to writing to disk by taking the logarithm
+of the pixel values can resolve this, with the complication that all
+data values must first be made positive, which then sets the highest
+quantization sampling near the lowest values in the image.  Following
+techniques used by SDSS, we have instead opted to use the
+inverse hyperbolic sine function to transform the data.  This domain
+of this function allows any input value to be converted.  In addition,
+the quantization sampling can be tuned by placing the zero of the
+inverse hyperbolic sine function at the most interesting pixel values.
+
+Formally, prior to being written to disk, the pixel values are
+transformed by C = alpha asinh( (L - BOFFSET) / (2.0 \cdot   
+BSOFTEN) ), where L is the linear input pixel
+values, C the transformed values, alpha = 2.5 log10(e), and
+BOFFSET = \langle L \rangle and BSOFTEN =                                                                                                        
+sqrt(alpha) * sigma_{L} are saved to the header as the scaling
+parameters used.  The image is then passed to the standard BSCALE and
+BZERO calculation and saved to disk.
+
+To reverse this process (on subsequent reads of the image, for example
+in warp-stack difference calculations), the BOFFSET and BSOFTEN
+parameters are read from the header and the transformation inverted,
+such that: L = BOFFSET + BSOFTEN * (exp(C                                                                                                
+/ alpha) - exp(-C / alpha) ).