In order to find a solution to transmission and storage problem of huge hyperspectral image data

this paper proposes a hyperspectral image compression algorithm based on prediction between bands to remove spectral redundancy and rate pre-allocation. Since the allocated rate for each predicted band determines the definition of that band

which will be the predicting band of the next band and determines the definition of the next band and its subsequent band as well

it is important to propose an algorithm to allocate the rate of each band reasonably. At first

the standard error of residual image of each band is computed by DPCM

and then the rate for SPIHT coding of each band is allocated by the value of the standard error. At last

each band is linear predicted based on minimal square error

and coded via SPIHT algorithm according to the pre-allocated rate. This algorithm uses the optimal linear prediction

so it can remove the correlation between bands efficiently. Meanwhile

the rate pre-allocation algorithm is reasonable for its taking advantage of both the account of information of each band and the correlation between neighboring bands. Experiments show the average PSNR of this algorithm is 0.9～2.5db higher than 3D-SPIHT algorithm. It is suitable for hyperspectral image lossy compression.