This paper presents a study of multiscale edge detection and its relationship to wavelet transforms. The authors show that multiscale edge detection is equivalent to finding the local maxima of a wavelet transform. They analyze the properties of multiscale edges using wavelet formalism and derive numerical descriptors for edge types. The completeness of a multiscale edge representation is also studied, and an algorithm is proposed to reconstruct one and two-dimensional signals from their multiscale edges. The reconstruction errors are below visual sensitivity, and the authors implement a compact image coding algorithm that compresses images by over 30 times. The paper also discusses the application of multiscale edges in signal processing and image coding. The authors define the concept of modulus maxima and show how they can be used to characterize different types of edges. They also study the reconstruction of signals from multiscale edges and show that it is possible to reconstruct a close approximation of the original signal. The paper concludes with a discussion of the applications of multiscale edges in signal processing and image coding.This paper presents a study of multiscale edge detection and its relationship to wavelet transforms. The authors show that multiscale edge detection is equivalent to finding the local maxima of a wavelet transform. They analyze the properties of multiscale edges using wavelet formalism and derive numerical descriptors for edge types. The completeness of a multiscale edge representation is also studied, and an algorithm is proposed to reconstruct one and two-dimensional signals from their multiscale edges. The reconstruction errors are below visual sensitivity, and the authors implement a compact image coding algorithm that compresses images by over 30 times. The paper also discusses the application of multiscale edges in signal processing and image coding. The authors define the concept of modulus maxima and show how they can be used to characterize different types of edges. They also study the reconstruction of signals from multiscale edges and show that it is possible to reconstruct a close approximation of the original signal. The paper concludes with a discussion of the applications of multiscale edges in signal processing and image coding.