Methods and apparatus are provided for video encoding and decoding with learned transform and compressive sensing. An apparatus includes a video encoder for encoding an image block in a picture by determining from a training data set an adaptive transform for transforming a signal capable of representing the image block into zero coefficients and non-zero coefficients, reconstructing the image block in a pixel domain to obtain a reconstructed version of the image block by minimizing a number of the non-zero coefficients in a transform domain corresponding to the transform responsive to information of the signal and a prediction of the image block, and incorporating the reconstructed version of the image block into a coding mode that is absent from any video coding standards and video coding recommendations.