Multispectral imaging is an optical modality that can provide real-time in vivo information about tissue characteristics and function through signal sensitivity to chromophores in the tissue. In this paper, we present a deblurring strategy that enables imaging of dynamic tissues at wavelengths where the required acquisition time can cause significant motion blur and obscure the image. We use deconvolution for spatially varying kernels to process multispectral information obtained by using a novel laparoscopic imaging device. The trinocular design of the system allows visible light images provide information about the tissue morphology and motion that we use to construct a per pixel deformation map. We demonstrate that with the proposed method the multispectral image stack can be synthesised into a meaningful signal even in the presence of significant tissue motion. Experiments on synthetic data validate the numerical properties of the method and experiments with ex vivo tissue demonstrate the practical potential of the technique.