An adaptive algorithm has been designed to treat interferometric self-mixing signals for weak and moderate laser feedback. With regard to the creation of an embedded displacement sensor, the reconstruction process is inspired from the interpolation feature found in digital-to-analog converters. By using an adaptive filter as the central process, the algorithm presents a high potential of parallelism to meet timing restrictions. A validation for different signal scenarios was carried out. The obtained precision and ease of maintainability enlightens its capabilities to be coupled with other signal processing methods to produce better system reliability.