Patch-based image denoising approaches have gained popularity recently. We propose an image denoising approach using subspaces that are fit using an L1-norm criterion. This new approach is competitive with existing approaches in terms of objective error metrics and visual fidelity, and has the added benefit that it can be implemented in parallel for large-scale applications.
KEYWORDS: Signal processing, Statistical analysis, Machine learning, Compressed sensing, Principal component analysis, Optimization (mathematics), Chemical elements, Matrices, Analytics, Current controlled current source, Matrix multiplication
Fitting affine objects to data is the basis of many tools and methodologies in statistics, machine learning, and signal processing. The L1 norm is often employed to produce subspaces exhibiting a robustness to outliers and faulty observations. The L1-norm best-fit subspace problem is directly formulated as a nonlinear, nonconvex, and nondifferentiable optimization problem. The case when the subspace is a hyperplane can be solved to global optimality efficiently by solving a series of linear programs. The problem of finding the best-fit line has recently been shown to be NP-hard. We present necessary conditions for optimality for the best-fit subspace problem, and use them to characterize properties of optimal solutions.
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