2025/02/27 by Li Song, Yu Xia, Li, Song +1
Computer Science · Engineering · #Advanced Image Processing Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2503.03765
openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel \boldsymbolh is convolved with multiple random modulations \\boldsymboldl\l=1L(coded masks) of a signal \boldsymbolx, subject to ℓ2-bounded noise. We introduce a more generalized framework for coded masks, enhancing the versatility of our approach. Our work begins within a constrained least squares framework, where we establish a robust recovery bound for both \boldsymbolh and \boldsymbolx, demonstrating its near-optimality up to a logarithmic factor. Additionally, we present a new recovery scheme that leverages sparsity constraints on \boldsymbolx. This approach significantly reduces the sampling complexity to the order of L=O(log n) when the non-zero elements of \boldsymbolx are sufficiently separated. Furthermore, we demonstrate that incorporating sparsity constraints yields a refined error bound compared to the traditional constrained least squares model. The proposed method results in more robust and precise signal recovery, as evidenced by both theoretical analysis and numerical simulations. These findings contribute to advancing the field of blind deconvolution and offer potential improvements in various applications requiring signal reconstruction from modulated inputs.