In the research field of digital signal processing

compressive sensing (CS) becomes more and more important because it changes the traditional signal processing method based on Shannon’s sampling theorem.Under the CS framework

signal recovery is a key point to obtain the digital termination product.The basis pursuit (BP) algorithm seems the most fundamental method of CS recovery

which is essentially an L-norm minimization problem.However

BP can not be used for the signals with more than one dimension.Therefore

this paper presents a new high-dimension CS recovery method based on fractal dimension theory.The Minkowski dimension is used to replace the L-norm as an object function in CS recovery.The visualization and SNR of our experimental results show that fractal CS recovery not only inherits the advantage of BP but also improves the dimensional extensive property.