Blind Deconvolution Meets Blind Demixing: Algorithms and Performance Bounds

Understand

Suppose that we have $r$ sensors and each one intends to send a function $\boldsymbol{g}_i$ (e.g.\ a signal or an image) to a receiver common to all $r$ sensors.

• During transmission, each $\boldsymbol{g}_i$ gets convolved with a function $\boldsymbol{f}_i$.
• The receiver records the function $\boldsymbol{y}$, given by the sum of all these convolved signals.
• When and under which conditions is it possible to recover the individual signals $\boldsymbol{g}_i$ and the blurring functions $\boldsymbol{f}_i$ from just one received signal $\boldsymbol{y}$? This challenging problem, which intertwines blind deconvolution with blind demixing, appears in a variety of applications, such as audio processing, image processing, neuroscience, spectroscopy, and astronomy.