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We study the question of reconstructing a sequence of {fi, gi}i=1s from the sum of their convolution, i.e., y = ∑i=1s fi * gi. This problem is closely related to both blind deconvolution and blind demixing problem. Our goal is to find all {fi, gi}i=1s by jointly demixing each component fi * gi and performing deconvolution procedure. While the convex program is able to solve this problem effectively...
Suppose that we have $r$ sensors and each one intends to send a function ${g}_{i}$ (e.g., a signal or an image) to a receiver common to all $r$ sensors. During transmission, each ${g}_{i}$ gets convolved with a function ${f}_{i}$ . The receiver records the function ${y}$ , given by the sum of all these convolved signals. When and under which conditions is it possible to recover the individual...
Suppose that one receives the superposition of r signals and each of them passes through an unknown channel, can we correctly recover the signals and their corresponding channels simultaneously from only one received signal? This problem, which intertwines blind deconvolution with blind demixing, appears in many fields of science and engineering such as wireless communication, imaging sciences, audio...
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