Color correction is one of the most essential camera imaging operations that transforms a camera-specific RGB color space to a standard color space, typically the XYZ or the sRGB color space. Linear color correction (LCC) and polynomial color correction (PCC) are two widely used methods; they perform the color space transformation using a color correction matrix. Owing to the use of high-order terms, PCC generally achieves lower colorimetric errors than LCC. However, PCC amplifies noise more severely than LCC. Consequently, for noisy images, there exists a trade-off between LCC and PCC regarding color fidelity and noise amplification. We propose a color correction framework called tunable color correction (TCC) that enables us to tune the color correction matrix between the LCC and the PCC models. We also derive a mean squared error calculation model of PCC that enables us to select the best trade-off balance in the TCC framework. We experimentally demonstrate that TCC effectively balances the trade-off for noisy images and outperforms LCC and PCC. We also generalize TCC to multispectral cases and demonstrate its effectiveness by taking the color correction for an RGB-near-infrared sensor as an example.