# Single-Lens Imaging Spectral Restoration Method Based on Gradient Prior Information Optimization
TV regularization emphasizes the gradient information of an image: when the regularization weight coefficient is large, it achieves better results in recovering texture details, while a smaller weight produces smoother results. Therefore, TV regularization combines both denoising and texture preservation characteristics. Some researchers, such as [PERSON] et al., have used channel correlation properties in multispectral images to guide spectral information recovery. They obtained guiding images for each blurry image, computed their gradients, and used this as prior information for spectral recovery, resulting in high-quality spectral restoration [18]. The major difference between blind and non-blind methods lies in the blind estimation of blur kernels. Estimating blur kernels is a critical issue in image restoration algorithms, as the accuracy of blur kernel estimation determines the quality of image restoration. Blind deblurring models have more severe drawbacks as their blur kernels are unknown. A representative approach is the variational Bayesian multi-scale blind deconvolution method proposed by [PERSON] and his team. Initially, they used Bayesian methods to iteratively estimate blur kernels based on a maximum a posteriori (MAP) [19; 20] model. This iterative process, going from coarse to fine, takes place within a spatial pyramid scale space. Subsequently, the authors reconstructed a clear image using the Richardson-Lucy (RL) method [21; 22]. However, due to limitations of the standard RL deconvolution algorithm in suppressing ringing artifacts, the image they achieved exhibits noticeable ringing effects, as seen in their paper. [PERSON] and his team proposed an improved variant of blind image restoration based on the effective edge similarity of an image, building upon the method of [PERSON] and others [23]. This method also operates within the maximum a posteriori (MAP) solving framework. Its primary contribution lies in the processes of updating and estimating a blur kernel. It not only takes into account the influence of the blurred image itself on the estimation of a blur kernel, but also considers the impact of the covariance of potential clear images on the estimation process. [PERSON] and his colleagues proposed a unified probabilistic model for both blind and non-blind deconvolution, addressing respective maximum a posteriori (MAP) problems through advanced iterative optimization. This optimization process alternates between refining a blur kernel and restoring an image until convergence to a global optimum is achieved. The algorithm can be initialized with a rough estimate of the blur kernel and ultimately yields results that preserve complex image structures while avoiding ringing artifacts [24]. [PERSON] proposed an algorithm that uses the ratio of L1 and L2 norms as a regularization constraint [25], allowing a blurry image to gradually become clear. The specific computational process involves initially placing this constraint on the loss function. Then, it alternates between estimating a clear image and the blur kernel. Ultimately, a more accurate blur kernel is estimated. After obtaining a blur kernel, the author utilized a super-Laplacian prior model for non-blind image deconvolution, resulting in the final restoration of a clear image. In this study, [PERSON] compared non-blind deblurring using TV regularization with blind deblurring based on the MAP framework [26]. In the visible light wavelength range, when constrained with the TV regularization term utilizing gradient information,it outperformed the MAP method by effectively suppressing ringing artifacts, preserving texture details better, and achieving faster computation. As the single-lens-based spectral acquisition device in this study only contains a single-lens element, the system's point spread function (PSF) can be directly measured, making it more suitable for non-blind methods.