Malicious manipulation of digital images cannot be ignored in certain critical application like telemedicine, where medical records of the patients (mostly in the form of diagnostic images of brain, chest, heart, lungs, etc.) need to be securely transmitted over the internet for various life-saving consultation and treatments. Watermarking is used to protect such documents from being manipulated and helps detect the authenticity of the image received. A robust and blind image watermarking technique based on discrete wavelet transform is proposed in this paper. For embedding purpose, suitable coefficients are found out using the Set Partitioning in Hierarchical Trees algorithm. Level of security is further enhanced by scrambling the watermark using Arnold transform and by making the set of embedding locations random using a secret key. Noise Visibility Function is used to compute the minimum allowable distortion for each coefficient before embedding to achieve better image fidelity. Experimental results show that the proposed scheme is robust against certain standard image processing attacks and outperforms the prior existing similar types of watermarking schemes.