Rate-Distortion Driven Overcomplete Decomposition of Imagery for Compression

This thesis investigates overcomplete decomposition of imagery for the purpose of compression. Overcomplete decomposition isan ill-posed inverse problem. Existing techniques impose prior information to the problem, generally in the form of sparsity orsmoothness constraints, to successfully decompose the original content. For the purpose of compression, it is important that theimposed constraints closely measure the total coding cost of the decomposed components. We propose a rate-distortion (R-D)driven optimization cost function for the problem of decomposition which not only improves the compression performance, butalso provides a meaningful and tractable procedure to separate information. The basic idea comes from the intuition that byincorporating efficient compression models, we are indeed choosing a better prior model for the underlying statistical problem.Applying this concept to the problem of decomposition, our approach penalizes unlikely estimates within a local region which isdifferent from rigid lp norms. We consider the diversity of components to be decomposed and choose distinct and differentsparsifying transforms for each component in the problem formulation. We employ the proposed decomposition approach to twoapplications. First, we develop a framework to decompose low frame rate video sequences into multiplicative illumination fieldsand illumination compensated residuals. We propose an illumination adaptive temporal transform which incorporates illuminationcompensation to lifting-based temporal wavelet transforms. We employ the R-D driven formulation to estimate full resolutionillumination fields, whose complexity is the subject of the optimization process. The R-D driven cost function is not convex but twoapproximations are explored, one being fully convex. A mesh-based illumination model is also developed to provide a point ofcomparison. The proposed method enables a highly scalable coding framework. Comparisons with weighted prediction in nonscala