For effective human-robot teaming, it is important for the robots to be able to share their visual perception with the human operators. In a harsh remote collaboration setting, however, it is especially challenging to transfer a large amount of sensory data over a low-bandwidth network in realtime, e.g., for the task of 3D shape reconstruction given 2D camera images. To reduce the burden of data transferring, data compression techniques such as autoencoder can be utilized to obtain and transmit the data in terms of latent variables in a compact form. However, due to the low-bandwidth limitation or communication delay, some of the dimensions of latent variables can be lost in transit, degenerating the reconstruction results. Moreover, in order to achieve faster transmission, an intentional over compression can be used where only partial elements of the latent variables are used. To handle these incomplete data cases, we propose a method for imputation of latent variables whose elements are partially lost or manually excluded. To perform imputation with only some dimensions of variables, exploiting prior information of the category-or instance-level is essential. In general, a prior distribution used in variational autoencoders is achieved from all of the training datapoints regardless of their labels. This type of flattened prior makes it difficult to perform imputation from the category-or instancelevel distributions. We overcome this limitation by exploiting a category-specific multi-modal prior distribution in the latent space. By finding a modal in a latent space according to the remaining elements of the latent variables, the missing elements can be sampled. We evaluate the proposed approach on the 3D object reconstruction from a single 2D image task and show that the proposed approach is robust against significant data losses.