This paper presents an end-to-end optimized image compression method that combines nonlinear analysis and synthesis transforms with a uniform quantizer. The method uses a three-stage convolutional process with nonlinear activation functions, inspired by biological neurons, to model local gain control. The entire model is optimized using stochastic gradient descent to minimize a weighted sum of rate and distortion, with the rate being lower-bounded by the entropy of the quantized data. The method introduces a continuous proxy for the discontinuous loss function arising from the quantizer, allowing for efficient optimization. The proposed method outperforms standard JPEG and JPEG 2000 compression in terms of rate-distortion performance and visual quality across a range of test images. It achieves better visual quality at all bit rates, as supported by objective quality estimates using MS-SSIM. The method uses a generalized divisive normalization (GDN) joint nonlinearity, which has been shown to be effective in Gaussianizing image densities. The analysis and synthesis transforms are optimized jointly for a weighted sum of rate and distortion, with the parameters of both transforms being optimized using stochastic gradient descent. The method is compared to two standard compression methods: JPEG and JPEG 2000. The proposed method achieves better rate-distortion performance and visual quality, especially at lower bit rates. The results show that the method produces images with less detail but with a more natural appearance, preserving the smoothness of contours and sharpness of edges. The method is also compared to variational autoencoders, and it is shown that the proposed method has a different structure and optimization approach. The method is evaluated on a set of test images, including the Kodak image dataset and a set of standard images used by the compression community. The results show that the proposed method achieves better rate-distortion performance and visual quality than JPEG and JPEG 2000 for most test images, especially at lower bit rates. The method is also compared to other image compression methods, and it is shown that the proposed method has a different structure and optimization approach. The method is also compared to other image compression methods, and it is shown that the proposed method has a different structure and optimization approach.This paper presents an end-to-end optimized image compression method that combines nonlinear analysis and synthesis transforms with a uniform quantizer. The method uses a three-stage convolutional process with nonlinear activation functions, inspired by biological neurons, to model local gain control. The entire model is optimized using stochastic gradient descent to minimize a weighted sum of rate and distortion, with the rate being lower-bounded by the entropy of the quantized data. The method introduces a continuous proxy for the discontinuous loss function arising from the quantizer, allowing for efficient optimization. The proposed method outperforms standard JPEG and JPEG 2000 compression in terms of rate-distortion performance and visual quality across a range of test images. It achieves better visual quality at all bit rates, as supported by objective quality estimates using MS-SSIM. The method uses a generalized divisive normalization (GDN) joint nonlinearity, which has been shown to be effective in Gaussianizing image densities. The analysis and synthesis transforms are optimized jointly for a weighted sum of rate and distortion, with the parameters of both transforms being optimized using stochastic gradient descent. The method is compared to two standard compression methods: JPEG and JPEG 2000. The proposed method achieves better rate-distortion performance and visual quality, especially at lower bit rates. The results show that the method produces images with less detail but with a more natural appearance, preserving the smoothness of contours and sharpness of edges. The method is also compared to variational autoencoders, and it is shown that the proposed method has a different structure and optimization approach. The method is evaluated on a set of test images, including the Kodak image dataset and a set of standard images used by the compression community. The results show that the proposed method achieves better rate-distortion performance and visual quality than JPEG and JPEG 2000 for most test images, especially at lower bit rates. The method is also compared to other image compression methods, and it is shown that the proposed method has a different structure and optimization approach. The method is also compared to other image compression methods, and it is shown that the proposed method has a different structure and optimization approach.