Image　compression　has　always　been　an　important　topic　in　the　last　decades　due　to　the　explosive　increase　of　images.　The　popular　image　compression　formats　are　based　on　different　transforms　which　convert　images　from　the　spatial　domain　into　compact　frequency　domain　to　remove　the　spatial　correlation.　In　this　paper,　we　focus　on　the　exploration　of　data-driven　transform,　Karhunen-Loeve　transform　(KLT),　the　kernels　of　which　are　derived　from　specific　images　via　Principal　Component　Analysis　(PCA),　and　design　a　high　efficient　KLT　based　image　compression　algorithm　with　variable　transform　sizes.　To　explore　the　optimal　compression　performance,　the　multiple　transform　sizes　and　categories　are　utilized　and　determined　adaptively　according　to　their　rate-distortion　(RD)　costs.　Moreover,　comprehensive　analyses　on　the　transform　coefficients　are　provided　and　a　band-adaptive　quantization　scheme　is　proposed　based　on　the　coefficient　RD　performance.　Extensive　experiments　are　performed　on　several　class-specific　images　as　well　as　general　images,　and　the　proposed　method　achieves　significant　coding　gain　over　the　popular　image　compression　standards　including　JPEG,　JPEG　2000,　and　the　state-of-the-art　dictionary　learning　based　methods.