Image fitting using arctan for JPEG AC coefficient prediction

We explore predictive coding for the JPEG baseline sequential algorithm in this article. Our objective is to reduce inter-block redundancy of discrete cosine transform (DCT) blocks. We first present an implementation of image interpolation approach and develop a method for predicting ac coefficients of a block in terms of sum of pixels (or dc coefficients) of some surrounding patches. If we use 2-D quadratic polynomials for interpolation over 24 $\times$ 24 pixel area, our method derives the same equations, which JPEG developed for reducing blocking artifacts. Next, we show that nonpolynomial functions such as $\arctan$ perform better for ac prediction. We develop additional prediction equations considering different configurations of the interpolation area. Finally, we present performance results, which show that for images compressed at the default quality factor of 75, our equations reduce the ac energy of DCT blocks by about 22% and the final code bit size by about 5.5% over the JPEG sequential algorithm. At the quality factor of 90, the code size reduction is 10.8%. We also present an adaptive dc coding method by considering the prediction algorithm of JPEG-LS. It reduces the average JPEG dc residual by over 20% and the dc code bits by 7.75%.