Accurate cell segmentation in pathology images typically requires dense pixel-wise annotations, which are costly and time-consuming to obtain. This challenge is especially important for emerging biological imaging modalities and multiplexed datasets with variable channel configurations, where expert-labeled data are scarce. In this work, we introduce ImPartial, a deep learning framework designed to achieve state-of-the-art segmentation performance in low-annotation regimes using sparse scribbles and limited supervision. ImPartial augments the segmentation objective via self-supervised multi-channel quantized imputation. This approach leverages the observation that perfect pixel-wise reconstruction or denoising of the image is not needed for accurate segmentation, and thus, introduces a self-supervised classification objective that better aligns with the overall segmentation goal. We demonstrate that ImPartial achieves performance at par with fully supervised models while requiring substantially fewer annotations. Extensive experiments on benchmark multiplexed cellular imaging and single-plex clinical brightfield immunohistochemistry datasets show consistent improvements over strong baselines with only partial annotations. All benchmark datasets and code are available via our Github: https://github.com/nadeemlab/ImPartial.