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Classical techniques for solving linear inverse problems have been presented. Our aim was to show how these classical techniques are applied in current state-of-the-art imaging systems. Moreover, we have provided a classification of the techniques into four families: FT-based, direct reconstruction, indirect reconstruction, and interpolation. We hope that this classification will guide the curious reader into a discipline with a rich bibliography and sometimes sophisticated mathematics. In this survey, we skipped complicated methods to solve inverse problems. Through our examples, we have tried to emphasize the large variety of applications of linear inverse problems in imaging. Two main examples have been examined more deeply in this survey. We hope they have helped the reader to understand the application of the general techniques in two interesting contexts: multispectral imaging and magnetic resonance imaging.