🤖 AI Summary
This work addresses the challenge of image restoration under spatially varying degradation, particularly non-uniform motion blur, by proposing a singular value decomposition (SVD)-based restoration framework. The method models the degradation process using position-dependent point spread functions and introduces a novel cumulative singular value energy ratio criterion to systematically determine the number of small singular values retained. This strategy effectively balances noise suppression and detail preservation. Experimental results demonstrate that the proposed approach successfully mitigates the ill-posedness of inverse problems across various motion blur models—including bidirectional linear, Gaussian, and harmonic motions—yielding significantly improved recovery of fine image details and reduced blur-related artifacts.
📝 Abstract
Shift-variant image degradation is frequently encountered in practical imaging systems where the point spread function (PSF) varies across the image field due to motion, optical aberrations, atmospheric turbulence, or sensor-related effects. Unlike shift-invariant, shift-variant degradation presents significant challenges for image restoration because the degradation process cannot be represented by a single convolution kernel. This paper proposes a singular value decomposition (SVD)-based framework for restoring images degraded by shift-variant motion blur. The proposed approach determines the contribution of small singular values using a singular-value energy retention criterion. Specifically, the number of small singular values is selected based on a specified percentage of cumulative singular-value energy, providing a systematic approach for controlling noise amplification while preserving useful image information. The degradation model is formulated using a position-dependent PSF represented by a shift-variant imaging operator. Three representative one dimensional shift-variant motion PSFs are considered: bidirectional linear motion, Gaussian motion, and simple harmonic motion. The image degradation process is modeled as a linear system, and SVD is employed to analyze and invert the corresponding degradation operator. The singular-value representation provides insight into the ill-conditioned nature of the restoration problem and enables the development of stable inversion techniques. The proposed SVD-based restoration algorithm is applied to three degraded images. Experimental results demonstrate the effectiveness of the proposed approach in recovering image details and reducing blur artifacts under different motion models.