How to decode color mapping in matplotlib's Colormap?

I know how to map a number to a color from this post: Map values to colors in matplotlib

But I don't know how to decode the mapping to get my original color, assuming this is a one-to-one mapping, which it must be I figure.

I am encoding an image for visualization purposes, but I need to be able to decode it and read the original data values.

For reference, here are the Colormap docs: http://matplotlib.org/api/cm_api.html

Here's my try to the main answer below, which still isn't working right.

from PIL import Image
import numpy as np
import matplotlib
import matplotlib.cm as cm
values = [670, 894, 582, 103, 786, 348, 972, 718, 356, 692]
minima = 103
maxima = 972
norm = matplotlib.colors.Normalize(vmin=minima, vmax=maxima, clip=True)
mapper = cm.ScalarMappable(norm=norm, cmap=cm.gist_rainbow_r)
c = []
for i in range(10):
    c.append(mapper.to_rgba(values[i], bytes=True))
print(c) # [(75, 255, 0, 255), (255, 77, 0, 255), (0, 255, 64, 255), (255, 0, 191, 255), (255, 250, 0, 255), (0, 72, 255, 255), (255, 0, 40, 255), (151, 255, 0, 255), (0, 83, 255, 255), (108, 255, 0, 255)]

def get_value_from_cm(color, cmap, colrange):
    # color = matplotlib.colors.to_rgba(color)
    r = np.linspace(colrange[0], colrange[1], 10) # there are 10 values
    norm = matplotlib.colors.Normalize(colrange[0], colrange[1])
    mapvals = cmap(norm(r))[:, :4] # there are 4 channels: r,g,b,a
    distance = np.sum((mapvals - color) ** 2, axis=1)
    return r[np.argmin(distance)]

decoded_colors = []
for i in range(10):
    decoded_colors.append(get_value_from_cm(c[i], cm.gist_rainbow_r, colrange=[minima, maxima]))
print(decoded_colors) # [778.88888888888891, 778.88888888888891, 489.22222222222223, 103.0, 778.88888888888891, 392.66666666666669, 103.0, 778.88888888888891, 392.66666666666669, 778.88888888888891]