The invention discloses a sparse sampling and
signal compressive sensing
reconstruction method. The method comprises: establishing a
signal sampling interval of each time, sampling point number, and the number of points recovering, establishing random sparse sampling lower than a Nyquist sampling theorem value; and designing a measurement matrix by random sampling timing sequence values, designing a
transformation matrix of a sparse expression domain of signals, determining a compressive sensing matrix, and separated compressive sensing optimizing
signal reconstruction in a nonlinear manner. The method is based on rationality of objective world rules, and makes full use of signal sparsity, uses transformation space to describe the signals, and establishes theoretical framework of new signal description and
processing, so under the condition that information is not lost is ensured, signals are sampled by speed much lower than required speed of a Shannon's sampling theorem. Simultaneously, signals can be recovered completely, that is, sampling of signals is converted into sampling of information. The invention provides a whole set of
complete method. The method can be used in one-dimensional and multidimensional signals, and can process
audio frequency, videos,
nuclear magnetic resonance, and other signals.