Discrete cosine transform (DCT) has been applied extensively to the area of image compressing; in order to improve image encoding

this paper introduces a class of orthogonal complete piecewise k-degree polynomials in L［0

1］ (so-called U-system). Firstly

a class of new U-orthogonal transform is constructed using U-orthogonal basis

and an algorithm of image coding based on U-orthogonal transform is presented by investigating 3-degree U-orthogonal transform (so-called U3). Secondly

two methods of calculating discrete U-orthogonal transform matrices are established

and the fast U-transform is derived from symmetrical characteristic of U-transform matrices. Thirdly

coding gain and de-correlation efficiency of U3 are studied

and then JPEG algorithm is realized using U3 instead of DCT. The experiments show coding gain and de-correlation efficiency of U3 are close to that of DCT

and the computational complexity of U-transform is approximate to that of DCT which computed using fast Fourier transform algorithm. Moreover the effect of reconstructed image from our scheme is comparable to that of decoded image from baseline JEPG. So it is effective to apply U-transform

which may be used extensively in the application of video coding

to the field of image compression.