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Image compression has a wide range of application since it leads to reduction in storage space and easy transmission. Piecewise smooth image consists of sharp edge boundaries and smooth interior surfaces. This paper deals with compression of Piecewise smooth images using Graph Fourier Transform and Discrete Cosine Transform. In order to obtain better quality of reconstructed image blocks contains edge boundaries are transformed using DCT and smooth regions are transformed using both weighted GFT and unweighted GFT. In order to reduce the computational complexity, low pass filter and down sample a high resolution pixel block to obtain a low resolution one at the encoder, so that LR-GFT can be employed. At the decoder upsampling and interpolation are performed so that sharp edge boundaries can be preserved.

Anomalies are patterns that lack normal behavior. Anomaly detection process can be used to predict changes in input patterns and can prevent different malicious activities. Kernel Principal Component Analysis is an effective, anomaly detection technique. This is an effective technique for nonlinear data set. In this, kernel Eigenspace splitting and merging approach is used for predicting the anomalies effectively. Kernel splitting process, can extract smaller KES from larger KES. Here a QR decomposition technique can be used for, KES splitting. This is done to remove the data patterns that no longer fit to the current data distribution.KES splitting is combined with KES update. An adaptive update takes an appropriate sliding window size into consideration and reduces the number of updates required, when a change in the data distribution occurs. Thus an adaptive split-merge KES with QR decomposition, shows a superior performance in predicting anomalies that have a non-linear behavior. General Terms Anomaly detection, KPCA, Non-linear, QR decomposition