Short answer
Lost spectral sensitivity in bichromats or monochromats cannot be made up for by technology. The only thing technology can do is to process the visual image and shift its spectral content such that it falls outside the deficient region in the color-deficient spectrum. Likewise, trichromats can never match the spectral sensitivity of a dodecachromatic shrimp simply because we cannot generate visual acuity de novo. Mantis shrimp can detect UV light and additional cones enhance the spectral reslution in the visible spectrum too. This cannot be emulated with a trichromatic system.
Background
Removing colors from RGB images such that it alludes to the way color-vision impaired people perceive the world is trivial, as the image shows in the question and see Figs. 1 & 2.
Trichromats have three cones: red, green and blue cones, inferring normal RGB vision. Cone opsins are responsible for capturing light and they have overlapping sensitivity spectra (Fig. 3). Dichromats have only two types of cones and lack one cone type. People suffering from protanopia are unable to perceive any ‘red’ light, those with deuteranopia are unable to perceive ‘green’ light and those with tritanopia are unable to perceive ‘blue’ light (source: Colour Blind Awareness). However, while they are said to be color blind, they do not lack the ability to see that one color; in fact they cannot perceive a specific section of the normal visible spectrum.
The most accepted way in which we perceive color is the Hering theory of spectral sensitivity. Basically it states that we perceive color through two opponent systems: a red-green and a yellow-blue opponent system. Without going into detail on this (it's another story...), it's important to realize its consequences. Because of the spectral overlap of the red and green cones and the red-green opponent system in Hering's model, the outcome of either missing the red cones or the green cones is pretty similar. Hence the collective term red/green color blindness, because people with red and green deficiencies see the world in a very similar way. Protanopes and deuteranopes both live in a world of murky greens, where blues and yellows stand out. Browns, oranges, shades of red and green are easily confused. Both types will confuse some blues with some purples and both types will struggle to identify pale shades of most colors. For example, a person with deuteranopia sees red as a shade of green and people with deuteranomaly often misclassify brown as red (source: Colour Blind Awareness).
Now - we cannot regenerate that missing cone with image filtering; removing data from an image is simple (Fig. 1). However, adding it back in is impossible. How can a person without red cones perceive red? It's simply impossible.
To draw an analogy here - when a person at old age is missing the sensory cells in the basal end of the cochlea due to the steady degenerative processes of the hair cells and cannot perceive high frequency tones of, e.g., 8 kHz and up (presbyacusis), it's over. We can amplify with everything we got, but the person simply can't hear it. What we can do, however, is a process called frequency compression. Basically what you do is squeeze the higher frequencies at the front end into the lower frequencies and amplify that through a hearing aid. In this case the person still can't perceive the frequencies, but the information is yet contained in the signal.
Back to your question - what Robin Kramer alluded to is the Chroma device: like the hearing aid example above, this device uses signal processing tricks. Basically it can do three things for you; 1) identify colors, 2) enhance contrast 3) detect edges. Identifying colors can help by replacing reds and greens in red/green color blinds with yellows and blues. Enhancing contrast can be done in red/green color blinds by shifting the red/green spectrum towards the blues and the yellows, much like our acoustic-frequency compression scenario in the hearing aid above. Edge detection can help to improve object detection etcetera in murky images in color blinds. But all it can do is optimally use the limited color information available to the color deficient person. It can not restore normal trichromatic vision in any way.
Then to the mantis shrimp. Six of the additional cones are dedicated to UV vision, which is outside the visible spectrum of ours. The other ones add spectral detail. Extra cones within the visible spectrum add spectral detail. They do not add additional colors as such. UV vision cannot be inferred by technology. What you can do, however, is compressing UV wavelengths into the visible wavelengths. But still we would not be able to 'see' it as such. Further, spectral detail cannot be added by technology either.

Fig. 1. color blindness simulated pictures. source: Vision Salud

Fig. 2. Color blindness. source: Tanuwidjaja et al., 2014

Fig.3. Spectra sensitivity of the cones and the rods. source: wikipedia
Reference
- Tanuwidjaja et al., Ubicomp 2014, September 13–17, Seattle, WA, USA