5. Application example: denoising, inverse problem

It often happens (indeed, it's the most common situation) that signals acquired from physical measurements are corrupted by measurement noise and/or modified by a device response. In such cases, observations are of the form

where b is additive (unknown) noise and Φ is a transformation reflecting the measurement. Φ is often modeled by a linear operator. The denoising problem assumes that Φ is the identity, and we then seek to restore from observation y a signal as close as possible to x, making assumptions about noise b. In the inverse...