K-MP compressed sensing rapid reconstruction method

The invention discloses a K-MP (Matching Pursuit) compressed sensing rapid reconstruction method. During compressed sensing, a sparse signal is reconstructed from an underdetermined linear system y=phix+e, wherein (x is an element of a set R) is a signal which has only K nonzero values (K is less than n); (y is an element of a set R) is an observation signal; (phi is an element of a set R (m is to be shifted to the left of n) is a sensing matrix; and (e is an element of a set R is quantizing noise. Common compressed sensing reconstruction algorithms comprise Basis Pursuit, Orthogonal Matching Pursuit and the like. The K-MP algorithm provided by the invention does not need any iteration process of an orthogonal matching pursuit algorithm, does not need to be converted into a complex high-dimensional model, and is simple in process and high in speed. The finite equidistant distribution of the method is proved theoretically, and the converging speed of the method is explained through a numerical value experiment