Aliasing irreversibly transforms frequencies above the Nyquist limit to appear as frequencies below the limit. Almost no mathematical algorithms are effective compared with a physical anti aliasing filter in front of the sensor.
However, if the sampling frequency of the sensor itself is higher than the numerical aperture of the lens, it may not need the low pass anti aliasing filter any more since lens itself would serve as a low pass filter.
Regarding the color filter, I think it depends on your application. If you are try to image fluorescence, it is possible without a color filter if the emission spectrum is distinguishable with excitation spectrum. Background subtraction operations will recover the pixel information on the fluorescence. Even if several emission spectra are multiplexed, there is still possibility to differentiate them by solving a linear matrix equation under the assumption that the sensor system is a linear system with different wavelengths.
But color correction filters in digital photography may still needed to get more uniform exposure in the desired channels. Otherwise, the denoising process, though maybe possible through some image processing algorithms, is still challenging in complete noise removal without the prior knowledge of the noise distribution.