# Single-Lens Imaging Spectral Restoration Method Based on Gradient Prior Information Optimization
utilized the front lens element of a Canon EF 50 mm F1.8 II lens to construct a single lens and adapted it to use with a Canon 5D Mark II camera [9]. They developed a blind deconvolution image restoration algorithm based on maximum a posteriori probability for blurry images obtained with their single-lens imaging system. They introduced new priors related to the structure of the blur kernel and smooth color transitions in the images, enhancing the accuracy of point spread function (PSF) estimation and, consequently [10; 11], improving the quality of their final image restoration. Utilizing a single-lens imaging system in conjunction with algorithms allows clear images to be obtained. However, two-dimensional image data cannot fully represent certain physical properties of objects. Spectral information can compensate for this limitation. Scholars from various parts of the world have conducted research on whether it is possible to use the straightforward optical structure of single-lens imaging systems in combination with algorithms to acquire spectral information. In 1995, [PERSON], in the United States, proposed a new structure for an imaging spectrometer [12]. This structure primarily utilizes the dispersive properties of a back-ordered erbium (BOE) element, enabling spectral imaging in the visible and near-infrared wavelength ranges. The BOE element can image at different positions, and a charge-coupled device (CCD) scans along the optical axis to obtain image information in the desired spectral bands. A monochromatic CCD is used in this setup. The image received by the CCD consists of an accurately focused image and overlapping images formed by other wavelengths at different defocusing positions. Post-image processing using computer tomography techniques eliminates unwanted blur components, leaving only the images corresponding to each wavelength. [PERSON] et al. designed a visual imaging spectrometer experimental setup that utilizes the axial dispersion of binary optical elements [13]. Its spectral range is from 500 nm to 900 nm, with a spectral resolution of 6.4 nm @ 632.8 nm. The system has an F-number of F/8, a field of view angle of 1.3 degrees, a CCD size of 15 \(\times\) 15 \(\upmu\)m, and a pixel count of 512 \(\times\) 512. The authors used a three-dimensional optical slice microscopy technique for spectral restoration and proposed three deconvolution algorithms suitable for imaging spectrometers with binary optical elements: the nearest-neighbor method, inverse filtering, and constrained iterative deconvolution [14]. [PERSON] and others introduced a simple and fast computational imaging spectrometer system using a single programmable diffractive lens. They also proposed a rapid spectral restoration algorithm based on an alternating direction multiplier for effectively restoring spectral information under different signal-to-noise ratios [15]. Image deblurring is the fundamental element of spectral information recovery based on single-lens imaging. In an imaging system, the process of image formation can be described as the convolution of an ideal image with a blur kernel. Therefore, deconvolution, as the inverse process of convolution, theoretically allows for the restoration of a clear image from a blurred one. For deconvolution-based deblurring algorithms, there is close integration of physical considerations and mathematical principles, so that image quality can be improved without altering the physical design of the system or the imaging environment. Deblurring algorithms can be categorized into non-blind and blind methods based on prior information about the blur kernel. Non-blind methods usually do not consider estimation of the blur kernel, which is typically obtained through direct measurement or simple approximation [16]. With further research, regularization techniques have been introduced to deblur images. One example of this is the total variation (TV) regularization term [17], which is designed on the basis of an understanding of image gradient.