Logarithmic dyadic wavelet transform with its applications in edge detection and reconstruction

•We introduce a logarithmic dyadic wavelet transform.•It can be used in edge detection.•It can be used in 1D signal reconstruction.•It can be used in 2D image reconstruction.

In this paper, based on the logarithmic image processing model and the dyadic wavelet transform (DWT), we introduce a logarithmic DWT (LDWT) that is a mathematical transform. It can be used in image edge detection, signal and image reconstruction. Comparative study of this proposed LDWT-based method is done with the edge detection Canny and Sobel methods using Pratt's Figure of Merit, and the comparative results show that the LDWT-based method is better and more robust in detecting low contrast edges than the other two methods. The gradient maps of images are detected by using the DWT- and LDWT-based methods, and the experimental results demonstrate that the gradient maps obtained by the LDWT-based method are more adequate and precisely located. Finally, we use the DWT- and LDWT-based methods to reconstruct one-dimensional signals and two-dimensional images, and the reconstruction results show that the LDWT-based reconstruction method is more effective.