QuIR: Quotient-Informed Recovery Network for Joint Sparse Blind Deconvolution

Jointly sparse blind deconvolution (JSBD) seeks to recover multiple signals and a shared unknown convolution kernel from noisy observations, assuming that the signals have a common sparse support. Existing inverse-filter methods apply a candidate inverse filter to the observations and evaluate the joint sparsity of the resulting signals. This operation can amplify measurement noise at frequencies where the kernel response is weak, degrading recovery under severe ill-conditioning or very low signal-to-noise ratios. We propose Quotient-Informed Recovery Network (QuIR), which predicts a candidate support before inverse-filter estimation to guide signal and kernel recovery. To predict support from a limited number of noisy channels, we train a neural network to estimate normalized counts of cyclic coordinate differences between support locations. The network uses quotient features that do not depend on the unknown kernel in the noiseless model. On the evaluated noise-conditioning grid, QuIR achieves $73.6$ exact support recovery, compared with $13.5$ for inverse-filter JSBD.