Distributed Video Coding (DVC) is rapidly gaining popularity as a low cost, robust video coding solution, that reduces video encoding complexity. DVC is built on Distributed Source Coding (DSC) principles where correlation between sources to be compressed is exploited at the decoder side. In the case of DVC, a current frame available only at the encoder is estimated at the decoder with side information (SI) generated from other frames available at the decoder. The inter-frame correlation in DVC is then explored at the decoder based on the received syndromes of Wyner-Ziv (WZ) frame and SI frame. However, the ultimate decoding performances of DVC are based on the assumption that the perfect knowledge of correlation statistic between WZ and SI frames should be available at decoder. Therefore, the ability of obtaining a good statistical correlation estimate is becoming increasingly important in practical DVC implementations.

Generally, the existing correlation estimation methods in DVC can be classified into two main types: online estimation where estimation starts before decoding and on-the-fly (OTF) estimation where estimation can be refined iteratively during decoding. As potential changes between frames might be unpredictable or dynamical, OTF estimation methods usually outperforms online estimation techniques with the cost of increased decoding complexity.

In order to exploit the robustness of DVC code designs, I integrate particle filtering with standard belief propagation decoding for inference on one joint factor graph to estimate correlation among source and side information. Correlation estimation is performed OTF as it is carried out jointly with decoding of the graph-based DSC code. Moreover, I demonstrate our proposed scheme within state-of-the-art DVC systems, which are transform-domain based with a feedback channel for rate adaptation. Experimental results show that our proposed system gives a significant performance improvement compared to the benchmark state-of-the-art DISCOVER codec (including correlation estimation) and the case without dynamic particle filtering tracking, due to improved knowledge of timely correlation statistics via the combination of joint bit-plane decoding and particle-based BP tracking.

Although sampling (e.g., particle filtering) based OTF correlation advances performances of DVC, it also introduces significant computational overhead and results in the decoding delay of DVC. Therefore, I tackle this difficulty through a low complexity adaptive DVC scheme using the deterministic approximate inference, where correlation estimation is also performed OTF as it is carried out jointly with decoding of the factor graph-based DVC code but with much lower complexity. The proposed adaptive DVC scheme is based on expectation propagation (EP), which generally offers better tradeoff between accuracy and complexity among different deterministic approximate inference methods. Experimental results show that our proposed scheme outperforms the benchmark state-of-the-art DISCOVER codec and other cases without correlation tracking, and achieves comparable decoding performance but with significantly low complexity comparing with sampling method.

Finally, I extend the concept of DVC (i.e., exploring inter-frames correlation at the decoder side) to the compression of biomedical imaging data (e.g., CT sequence) in a lossless setup, where each slide of a CT sequence is analogous to a frame of video sequence. Besides compression efficiency, another important concern of biomedical imaging data is the privacy and security. Ideally, biomedical data should be kept in a secure manner (i.e. encrypted).

An intuitive way is to compress the encrypted biomedical data directly. Unfortunately, traditional compression algorithms (removing redundancy through exploiting the structure of data) fail to handle encrypted data. The reason is that encrypted data appear to be random and lack the structure in the original data. The "best" practice has been compressing the data before encryption, however, this is not appropriate for privacy related scenarios (e.g., biomedical application), where one wants to process data while keeping them encrypted and safe. In this dissertation, I develop a Secure Privacy-presERving Medical Image CompRessiOn (SUPERMICRO) framework based on DSC, which makes the compression of the encrypted data possible without compromising security and compression efficiency. Our approach guarantees the data transmission and storage in a privacy-preserving manner. I tested our proposed framework on two CT image sequences and compared it with the state-of-the-art JPEG 2000 lossless compression. Experimental results demonstrated that the SUPERMICRO framework provides enhanced security and privacy protection, as well as high compression performance.