Exploring database tables, small or large, can be challenging if no proper structure and constraints exist. The usual, textbook-based way to impose structure in relational databases is to define functional dependency constraints and apply decomposition theory to achieve smaller, more concise and semantically meaningful relations, without loss of the original information. This procedure requires the existence or definition of functional dependencies, mostly at design time. Consequently, any data instances need to adhere to these constraints. However, functional dependencies are not always available or easy to deduce. In this position paper, we explore a new and novel way to perform decomposition, or reconstruction, of database tables, based on their instances and their information content. We present a technique from Systems Theory, called Reconstructability Analysis, (RA), and discuss how it can be used to decompose relations in a fully unsupervised way and without any pre-existing constraints. RA quantifies the information content of a database relation and searches for sub-relations that retain this information, while they can be described in a more concise fashion than the original one. After defining RA, we show its potential, we discuss advantages and disadvantages and propose problems worth exploring by the database community.