Inverse Hyperbolic Sine
This article is to describe how inverse hyperbolic functions are used as activators in digital replication of ganglion and bipolar retinal cells.
Inverse hyperbolic sine is often used in quantization and of audio signals, and works very good to compress the high frequency imaging signal or highlight bend in cinematography.
Humans see the relative change in the brightness, while the camera image sensors is developed with linear response to the strength of a light source. To compress and map linear image signal from image sensor to the perceptual domain in imaging often gamma function defined by logarithms are used.
But when compressing high frequency signal which is zero centered we the logarithms are not good due to their behavior near zero and we need a function which derivative would behave like y=x near zero, behave similar to log and satisfy y(-x)=-y(x), and inverse hyperbolic sine is very very good for it.
Its always eye opening to see the behavior of this function of a complex argument
To remember about the function behavior its good to see the derivation process
<<Here will be a link to an article which describes the connection of retinal cells to the visual cortex, where the inverse hyperbolic functions were used.>>
