Radiant energy computation for defocus blurring in single-view catadioptric imaging

In a single-view catadioptric panoramic imaging system, defocus blur is one of the dominant factors leading to image quality degradation. This phenomenon results in the loss of substantial detailed texture information in catadioptric panoramic images and severely reduces the accuracy of subsequent image processing. Therefore, this paper analyzes the inherent radiant energy properties of the imaging system based on geometric optics, and proposes what is believed to be a novel defocus blur model for the catadioptric panoramic image via radiant energy calculation. Furthermore, leveraging the rotational symmetry of the catadioptric mirror, this paper unifies the imaging model and radiant energy formulation within a polar coordinate system, thereby simplifying the proposed defocus blur model. Then, a theoretical derivation is conducted to validate the correctness of this model. Subsequently, this paper proposes a total variation (TV) regularized defocus deblurring algorithm based on radiant energy calculation. The initial parameter values are provided, and the alternating direction method of multipliers (ADMM) is adopted to solve the optimization problem. Finally, simulation and actual experiments verify the correctness and stability of the proposed method. Convergence experiments prove that the algorithm is stable and feasible. In comparative experiments on physically accurate simulation datasets, the restored images achieve competitive quantitative performance, with peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) reaching 30.58 dB and 0.9145, respectively. Subjective visual performance, the restored images exhibit uniform full-field clarity distribution and superior comprehensive performance. The proposed defocus blur model accurately adapts to the geometric characteristics and physical essence of the single-view catadioptric imaging system, providing what is believed to be a novel physical modeling approach for research on defocus deblurring of catadioptric panoramic images.