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We consider the bilinear inverse problem of recovering two vectors, x and w,  RL from their entrywise product. For the case where the vectors have known signs and belong to known subspaces. An immediate formulation of the inverse problem leads to a non-convex optimization program. We use a geometrical insight to formulate a convex relaxation BranchHull, which is posed in the natural parameter space that does not require&

Imaging inverse problems arise in a myriad of applications in signal processing, and computer vision. In particular, image dehazing, and deblurring is required in astronomy to recover sharp images from blurred, hazy, observed galaxy images; image retrieval and denoising from partial measurements for MRI or CT scan in medical imaging; image super resolution, and inpainting for human face recognition from blurred out, low resolution, and corrupted images&