Temperature and density asymmetry diagnosis is critical to advance inertial confinement fusion (ICF) science. A multi-monochromatic x-ray imager, MMI, records the spectral signature from an ICF implosion core with time resolution, 2D spatial resolution and spectral resolution. While narrow-band images and 2D space-resolved spectra from the MMI data constrain the temperature and the density spatial structure of the core, the accuracy of the images and the spectra highly depends on the quality of the MMI data and the processing tools. Here, we synthetically investigate the criterion for reliable MMI diagnostics and its effects on the accuracy of the reconstructed images. The pinhole array tilt determines the object spatial sampling efficiency and the minimum reconstruction width, $w$. When the spectral width associated with $w$ is significantly narrower than the spectral linewidth, the line images reconstructed from the MMI data become reliable. The MMI setup has to be optimized for every application to meet this criterion for reliable ICF diagnostics.