Multi-Band Image raster to RGB

If I get it right then the answer is YES but just for clarification this is how I see it:

You got 4 bands intensities and you need RGB color value from it. Last number is not related to color in any way so ignore it.

1. What you need to know

   if the intensity is linear or not and if nonlinear how to convert it to linear scale. You need to know wavelength or RGB color for each band used

2. how to convert

   take each RGB of band and multiply it by its linear intensity then sum all of them together.

   color_rgb = band0_rgb*band0_intensity+...+band3_rgb*band3_intensity
   

3. how to get usable RGB of band from wavelength

   obtain color of light of wavelength by RGB values of visible spectrum and rescale the color so if you add all the bands together with same intensity you get white color.

I am using evenly distributed bands through visible spectrum for multi spectral rendering and this is how I do it in C++:

//---------------------------------------------------------------------------
//--- multi band rendering --------------------------------------------------
//---------------------------------------------------------------------------
const int _Bands=10;                            // number of bands used
double _Band_RGB[_Bands][3];                    // RGB of each band with white bias correction
double _Band_Wavelength[_Bands];                // wavelength of each band
//---------------------------------------------------------------------------
void wavelength2RGB(double *rgb,double lambda)  // RGB <0,1> <- lambda <400e-9,700e-9> [m]
    {
    double r=0.0,g=0.0,b=0.0,t;
         if ((lambda>=400.0e-9)&&(lambda<410.0e-9)) { t=(lambda-400.0e-9)/(410.0e-9-400.0e-9); r=    +(0.33*t)-(0.20*t*t); }
    else if ((lambda>=410.0e-9)&&(lambda<475.0e-9)) { t=(lambda-410.0e-9)/(475.0e-9-410.0e-9); r=0.14         -(0.13*t*t); }
    else if ((lambda>=545.0e-9)&&(lambda<595.0e-9)) { t=(lambda-545.0e-9)/(595.0e-9-545.0e-9); r=    +(1.98*t)-(     t*t); }
    else if ((lambda>=595.0e-9)&&(lambda<650.0e-9)) { t=(lambda-595.0e-9)/(650.0e-9-595.0e-9); r=0.98+(0.06*t)-(0.40*t*t); }
    else if ((lambda>=650.0e-9)&&(lambda<700.0e-9)) { t=(lambda-650.0e-9)/(700.0e-9-650.0e-9); r=0.65-(0.84*t)+(0.20*t*t); }
         if ((lambda>=415.0e-9)&&(lambda<475.0e-9)) { t=(lambda-415.0e-9)/(475.0e-9-415.0e-9); g=             +(0.80*t*t); }
    else if ((lambda>=475.0e-9)&&(lambda<590.0e-9)) { t=(lambda-475.0e-9)/(590.0e-9-475.0e-9); g=0.8 +(0.76*t)-(0.80*t*t); }
    else if ((lambda>=585.0e-9)&&(lambda<639.0e-9)) { t=(lambda-585.0e-9)/(639.0e-9-585.0e-9); g=0.84-(0.84*t)           ; }
         if ((lambda>=400.0e-9)&&(lambda<475.0e-9)) { t=(lambda-400.0e-9)/(475.0e-9-400.0e-9); b=    +(2.20*t)-(1.50*t*t); }
    else if ((lambda>=475.0e-9)&&(lambda<560.0e-9)) { t=(lambda-475.0e-9)/(560.0e-9-475.0e-9); b=0.7 -(     t)+(0.30*t*t); }
    rgb[0]=r;
    rgb[1]=g;
    rgb[2]=b;
    }
//---------------------------------------------------------------------------
double wavelength2int(double lambda)                // white bias correction intensity <0,1+> <- lambda <400e-9,700e-9> [m]
    {                                               // this is mine empirically deduced equation and works for evenly distributed bands
    const double a0=  8.50/double(_swColorWavelengths);// for 3-5 bands low bias, >5 almost no visible bias present
    const double a1=-27.37/double(_swColorWavelengths);
    const double a2=+26.35/double(_swColorWavelengths);
    double t=divide(lambda-400e-9,700e-9-400e-9);
    return (a0)+(a1*t)+(a2*t*t);
    }
//---------------------------------------------------------------------------
void init_multiband_colors()                    // init evenly distributed bands through visible spectrum range
    {
    double l,dl; int ix;
    l=405e-9; dl=695e-9; dl=divide(dl-l,_Bands); l+=0.5*dl;
    for (ix=_Bands-1;ix>=0;ix--,l+=dl)          // init colors and wavelengths (multispectral rendering)
        {
        _Band_Wavelength[ix]=l;
        wavelength2RGB(_Band_RGB[ix],l);
        _Band_RGB[ix][0]*=wavelength2int(l);    // white bias removal
        _Band_RGB[ix][1]*=wavelength2int(l);
        _Band_RGB[ix][2]*=wavelength2int(l);
        }
    }
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------

This is how it looks like:

first line shows number and color of used bands the second is part of rendered image in white color using multi spectral rendering. As you can see a small white bias is there. I make that formula to be as close to white as it can be for any number of bands used (>=3). The idea is that if you have white noise (all frequencies with same intensity) then you got a white color. So when add all bands colors used you should have white color. So I empirically experimented with scaling colors by function of wavelength and that is what I came up with …

if your bands are not evenly distributed

Then you need to integrate all evenly distributed bands they cover so for example:

1. set colors for 100 bands
2. divide them by your 4 bands to groups
3. integrate each group to obtain band color
4. scale the integrated band colors to common usable scale like /=100
5. check white bias