A method to approximate using a processor an image having a first dynamic range in terms of an image having a second dynamic range, the method comprising; receiving a first image and a second image, wherein the second image has a different dynamic range than the first image; selecting a multi-channel, multiple-regression prediction model from one or more MMR models; determining values of prediction parameters of the selected MMR model; computing an output image approximating the first image based on the second image and the determined values of the prediction parameters of the selected MMR prediction model, wherein pixel values of at least one color component in the output image are computed based on a combination of pixel values of all color components in the second image; and outputting the determined values of the prediction parameters and the computed output image, wherein the selected MMR prediction model is at least one of: a first order with cross-product MMR model that incorporates, for each pixel, cross-multiplications between the color components of that pixel, a second order with cross-product MMR model that further incorporates, for each pixel, cross-multiplications between second powers of the color components of that pixel, or a third order with cross-product MMR model that yet further incorporates, for each pixel, cross-multiplications between third powers of the color components of that pixel, and wherein any of the MMR models for predicting a pixel of the output image further comprises prediction parameters related to neighbor pixels of a corresponding pixel in the second image such that the pixel values of said at least one color component of a predicted pixel in the output image depend on a combination of pixel values of all color components of the corresponding pixel in the second image and further on pixel values of said at least one color component of neighbor pixels of the corresponding pixel in the second image. receiving a first image and a second image, wherein the second image has a different dynamic range than the first image; selecting a multi-channel, multiple-regression prediction model from one or more MMR models; determining values of prediction parameters of the selected MMR model; computing an output image approximating the first image based on the second image and the determined values of the prediction parameters of the selected MMR prediction model, wherein pixel values of at least one color component in the output image are computed based on a combination of pixel values of all color components in the second image; and outputting the determined values of the prediction parameters and the computed output image, wherein the selected MMR prediction model is at least one of: a first order with cross-product MMR model that incorporates, for each pixel, cross-multiplications between the color components of that pixel, a second order with cross-product MMR model that further incorporates, for each pixel, cross-multiplications between second powers of the color components of that pixel, or a third order with cross-product MMR model that yet further incorporates, for each pixel, cross-multiplications between third powers of the color components of that pixel, and wherein any of the MMR models for predicting a pixel of the output image further comprises prediction parameters related to neighbor pixels of a corresponding pixel in the second image such that the pixel values of said at least one color component of a predicted pixel in the output image depend on a combination of pixel values of all color components of the corresponding pixel in the second image and further on pixel values of said at least one color component of neighbor pixels of the corresponding pixel in the second image.