Maximumentropy expectationmaximization algorithm for image processing and sensor networks In this paper, we propose a maximumentropy expectationmaximization algorithm. We use the proposed algorithm for density estimation. The maximumentropy constraint is imposed in order to ensure smoothness of the estimated density function. The exact derivation of the maximumentropy expectationmaximization algorithm requires determination of the covariance matrix combined with the maximum entropy likelihood function, which is difficult to solve directly. We therefore introduce a new lowerbound for the EM algorithm derived by using the CauchySchwartz inequality to obtain a suboptimal solution. We use the proposed algorithm for function interpolation and image segmentation. We propose the use of the EM algorithm for image recovery from randomly sampled data and signal reconstruction from randomly scattered sensors. We further propose to use our approach to maximumentropy expectationmaximization (MEEM) in all of these applications. Computer simulation experiments are used to demonstrate the performance of our algorithm in comparison to existing methods.

Collective Sensing: a FixedPoint Approach in the Metric Space Conventional wisdom in signal processing heavily relies on the concept of inner product defined in the Hilbert space. Despite the popularity of Hilbertspace formulation, we argue it is overlystructured to account for the complexity of signals arising from the realworld. Inspired by the works on fractal image decoding and nonlocal image processing, we propose to view an image as the fixedpoint of some nonexpansive mapping in the metric space in this paper. Recently proposed BM3Dbased denoising and nonlocal TV filtering can be viewed as the special cases of nonexpansive mappings while differ on the choice of clustering techniques. The physical interpretation of clusteringbased nonexpansive mappings is that they convey organizational principles of the dynamical system underlying the signals of interest. There is an interesting analogy between phases of matters in statistical physics and types of structures in image processing. From this perspective, image reconstruction can be solved by a deterministicannealing based global optimization approach which collectively exploits the a priori information about unknown image. The potential of this new paradigm, which we call collective sensing, is demonstrated on the lossy compression application where significant gain over current stateoftheart (SPIHT) coding scheme has been achieved.