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The process of optimizing data storage by removing unnecessary items is best described as purging. Purging involves the systematic deletion of data that is no longer needed, thereby freeing up space and potentially improving data retrieval efficiency. This aligns with the concept of data management, where maintaining relevant and necessary data is crucial for effective operations.

Compression, while related to data storage optimization, refers specifically to reducing the size of data files to save space without necessarily removing any items. It involves techniques to encode data more efficiently. Therefore, it does not specifically involve the elimination of data, which is a key aspect of purging.

Cleaning generally refers to the process of correcting inaccuracies or inconsistencies within a dataset rather than removing items wholesale. It focuses on enhancing data quality rather than optimizing storage by deletion.

Killing is not a standard term used in data storage contexts, making it less relevant to the question.

Thus, purging stands out as the correct answer, specifically indicating the removal of unnecessary data to optimize storage.