# WIG-Net: Wavelet-Based Defocus Deblurring with IFA and GCN
## 1 Introduction  
When an object resides on the focal plane of a lens, the light emitted from a point on the object can be projected onto the image plane as a single point. However, for points that are not positioned on the focal plane, a blurred circle composed of numerous image points is formed, resulting in defocus blur. In real-world applications, errors in the camera's focal length or depth of field settings often lead to image defocus blur, significantly impairing the practical utility of the image. Image deblurring, as a way to improve image quality, is widely used in various fields, such as medical imaging and traffic monitoring. Image defocus deblurring is considered a typical ill-posed problem in image processing, with the aim to recover a corresponding clear image from a defocused blurred image. In recent years, this technology has received widespread attention from the scientific community. Nonetheless, the recovery of a clear image from a real blurred image remains challenging due to the complex and variable nature of the blur kernel in real-world scenarios. In traditional defocus deblurring methods, defocused blurred images are treated as the outcomes of convolving clear images with various blur kernels. Therefore, these methods can restore clear images by predicting these blur kernels and subsequently applying non-blind deconvolution. However, due to the oversight of real-world blur nonlinearity during the process of defocus deblurring, the performance of the traditional approaches in defocus deblurring is suboptimal. Recently, [PERSON] and [PERSON] [1] introduced the first end-to-end learning-based approach, namely DPDNet, which is independent of the specific blur models and directly recovers clear images. By employing an end-to-end learning methodology, DPDNet exhibits superior performance in handling real-world defocused images compared to prior methods. The authors introduced the Dual-Pixel Defocus deblurring (DPDD) dataset. However, their deblurred image frequently exhibited ringing artifacts and remaining blur (Figure 1), primarily due to an excessive loss of original information during the image processingprocedure using straightforward UNet [2] architecture. On the other hand, the network's structure is overly simplistic, hindering both the accurate extraction of image information and the reconstruction of clear images. In this work, an end-to-end network for performing single-image defocus deblurring was proposed. Innovatively, in the encoding phase of the network, the downsampling layers were replaced with wavelet transforms. It was also considered that the lossless image decomposition of images can be achieved using the wavelet transform. Therefore, the size of the feature maps was reduced while ensuring the preservation of image information. Simultaneously, in the decoding phase, wavelet inverse transforms were employed to upsample low-resolution feature maps into high-resolution images, effectively minimizing the image information loss during the process of restoring clear images from feature maps. Additionally, the images exhibiting sparsity in the wavelet domain enabled the network to learn mapping from sparse features to sparse features [3], which significantly enhanced the learning efficiency of the network. Furthermore, to effectively address extensive defocus blur, the Iterative Filter Adaptive module (IFA) [4] and Graph Convolution Network modules (GCN) [5] were utilized. Particularly, IFA, a module proficient in handling spatial variations and significant defocus blur, was used. To address spatial variations, IFA utilizes an adaptive filter prediction scheme. More specifically, IFA does not directly predict pixel values; instead, it adaptively generates per-pixel defocus-deblurring filters and applies them to feature maps. Additionally, the GCN module was employed to exploit the characteristics of graph structures, connecting feature maps and employing graph convolution to recover lost details from the encoded feature maps of different channels.