<p>This study presents an image encryption technique integrating hyperchaotic systems, wavelet transform, and the Burrows–Wheeler transform. The hash value of the plain image determines the initial parameters of the hyperchaotic system, providing unpredictability to the chaotic course. The proposed hyperchaotic system reveals robust performance in chaotic regimes. The encryption process commences with a chaotic stream scrambling the original image. Subsequently, a lifting strategy divides the image into four sub-bands. Each sub-band is confused and diffused by four distinct chaotic streams, followed by altering sub-bands and inverse lifting scheme. Finally, an XOR operation is performed. The Burrows–Wheeler transform scrambles the hash value and generates an index (<i>ind</i>). The scrambled hash value generates a binary string, which is combined with <i>ind</i> to form an important component in decryption. Simulation and comparative analysis show the efficacy of the presented approach in thwarting cryptographic attacks while ensuring robust encryption.</p>