In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation and coding. The proposed PT is able to convert high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality. We believe that the concept explored in this work, designing a nonlinear transform to convert hard-to-compress signals into easy ones, is very useful. We hope this work would motivate more research work along this direction.