A computer-implemented method for reconstruction of medical image data includes receiving medical measuring data, and minimizing a cost value via gradient descent. Minimizing the cost value includes: reconstructing the medical image data by applying a reconstruction function to the received medical measuring data in accordance with reconstruction parameters; determining a cost value by applying a cost function to the reconstructed medical image data; determining a gradient of the cost function with respect to the reconstruction parameters; adjusting the reconstruction parameters based on the gradient of the cost function with respect to the reconstruction parameters and the previous reconstruction parameters; and providing the adjusted reconstruction parameters. The acts of the minimizing are repeated until a termination condition is met. The reconstructed medical image data is provided.