A biorthogonal transform with overlapping and non-overlapping basis functions for image coding

he paper presents a novel design method of a biorthogonal lapped transform that consists of long (overlapping) and short (nonoverlapping) basis functions (VLLBT, variable-length function lapped biorthogonal transform), which can reduce annoying blocking artifacts and ringing. We formulate the VLLBT by extending conventional lapped transforms. Then, we provide the theory of the Karhunen-Loeve transform in a subspace (SKLT). Using the theory of the SKLT, we show that given the biorthogonal long basis functions of the VLLBT, the optimal short basis functions in the energy compaction sense are derived by solving an eigenvalue problem without iterative searching techniques. This leads to a desirable feature from a parameter optimization point of view since the degree of freedom for the VLLBT can be theoretically reduced by means of the SKLT. Moreover, the SKLT easily enables us to construct a two-dimensional (2D) VLLBT with nonseparable short basis functions. Experimental results show that, compared to the case where all parameters are optimized, the reduction of free parameters by using the SKLT causes no decline in coding gain for the AR(1) process, and the proposed transform provides promising performance in the efficiency of image coding.