Synthesis versus analysis in patch-based image priors
This work clarifies foundational concepts in patch-based image processing, addressing a gap for researchers in the field, though it is incremental as it does not introduce a new paradigm or show performance gains.
The paper identifies a new analysis vs synthesis dichotomy in patch-based image priors, showing that existing global priors are analysis-based and proposing a synthesis formulation where images are synthesized from independent patches. It demonstrates computational feasibility for denoising using ADMM, without claiming superiority of either approach.
In global models/priors (for example, using wavelet frames), there is a well known analysis vs synthesis dichotomy in the way signal/image priors are formulated. In patch-based image models/priors, this dichotomy is also present in the choice of how each patch is modeled. This paper shows that there is another analysis vs synthesis dichotomy, in terms of how the whole image is related to the patches, and that all existing patch-based formulations that provide a global image prior belong to the analysis category. We then propose a synthesis formulation, where the image is explicitly modeled as being synthesized by additively combining a collection of independent patches. We formally establish that these analysis and synthesis formulations are not equivalent in general and that both formulations are compatible with analysis and synthesis formulations at the patch level. Finally, we present an instance of the alternating direction method of multipliers (ADMM) that can be used to perform image denoising under the proposed synthesis formulation, showing its computational feasibility. Rather than showing the superiority of the synthesis or analysis formulations, the contributions of this paper is to establish the existence of both alternatives, thus closing the corresponding gap in the field of patch-based image processing.