This paper introduces a new method for image enhancement using shock filters, which are based on nonlinear time-dependent partial differential equations (PDEs) and their discretizations. The filters evolve an initial image $ u_0(x,y) $ into a steady-state solution $ u_\infty(x,y) $ as $ t \to \infty $, with the filtering process occurring through the evolution of $ u(x,y,t) $ for $ t > 0 $. The PDEs have solutions that satisfy a maximum principle and preserve the total variation of the initial data. The resulting processed image is piecewise smooth, nonoscillatory, and the jumps occur across zeros of an elliptic operator (edge detector). The algorithm is relatively fast and easy to program. The method is particularly effective for images that are only piecewise smooth, as it avoids the issues associated with traditional deconvolution techniques that amplify high-frequency errors. The paper discusses the mathematical foundation of the shock filters, including their ability to preserve total variation and their application to both one- and two-dimensional images. In one dimension, the method is shown to be an exact deconvolution for certain types of data. In two dimensions, the method is applied to real images, demonstrating its effectiveness in enhancing image quality while preserving edges and other important features. The paper also addresses the challenges of deconvolution in the presence of noise and the importance of feature detection in image processing. It highlights the use of nonlinear PDEs to achieve accurate and stable results, even in the presence of discontinuities or high-frequency noise. The method is shown to be efficient and robust, with the ability to handle a wide range of image processing tasks, including noise removal and edge detection. The results demonstrate that the shock filter method produces high-quality images with clear edges and minimal oscillations, making it a valuable tool for image enhancement.This paper introduces a new method for image enhancement using shock filters, which are based on nonlinear time-dependent partial differential equations (PDEs) and their discretizations. The filters evolve an initial image $ u_0(x,y) $ into a steady-state solution $ u_\infty(x,y) $ as $ t \to \infty $, with the filtering process occurring through the evolution of $ u(x,y,t) $ for $ t > 0 $. The PDEs have solutions that satisfy a maximum principle and preserve the total variation of the initial data. The resulting processed image is piecewise smooth, nonoscillatory, and the jumps occur across zeros of an elliptic operator (edge detector). The algorithm is relatively fast and easy to program. The method is particularly effective for images that are only piecewise smooth, as it avoids the issues associated with traditional deconvolution techniques that amplify high-frequency errors. The paper discusses the mathematical foundation of the shock filters, including their ability to preserve total variation and their application to both one- and two-dimensional images. In one dimension, the method is shown to be an exact deconvolution for certain types of data. In two dimensions, the method is applied to real images, demonstrating its effectiveness in enhancing image quality while preserving edges and other important features. The paper also addresses the challenges of deconvolution in the presence of noise and the importance of feature detection in image processing. It highlights the use of nonlinear PDEs to achieve accurate and stable results, even in the presence of discontinuities or high-frequency noise. The method is shown to be efficient and robust, with the ability to handle a wide range of image processing tasks, including noise removal and edge detection. The results demonstrate that the shock filter method produces high-quality images with clear edges and minimal oscillations, making it a valuable tool for image enhancement.