Optimization of Information Rate Upper and Lower Bounds for Channels with Memory

We consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete-time channels with memory. The channels we consider can have a finite number of states, such as partial response channels, or they can have an infinite state-space, such as time-varying fading channels. We optimize recently-proposed information rate bounds for such channels, which make use of auxiliary finite-state machine channels (FSMCs). Our main contribution in this paper is to provide iterative expectation-maximization (EM) type algorithms to optimize the parameters of the auxiliary FSMC to tighten these bounds. We provide an explicit, iterative algorithm that improves the upper bound at each iteration. We also provide an effective method for iteratively optimizing the lower bound. To demonstrate the effectiveness of our algorithms, we provide several examples of partial response and fading channels, where the proposed optimization techniques significantly tighten the initial upper and lower bounds. Finally, we compare our results with an improved variation of the \emph{simplex} local optimization algorithm, called \emph{Soblex}. This comparison shows that our proposed algorithms are superior to the Soblex method, both in terms of robustness in finding the tightest bounds and in computational efficiency. Interestingly, from a channel coding/decoding perspective, optimizing the lower bound is related to increasing the achievable mismatched information rate, i.e., the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel, and not to the original channel.Comment: Submitted to IEEE Transactions on Information Theory, November 24, 200

Gradient Intensity-Based Registration of Multi-Modal Images of the Brain

We present a fast and accurate framework for registration of multi-modal volumetric images based on decoupled estimation of registration parameters utilizing spatial information in the form of 'gradient intensity'. We introduce gradient intensity as a measure of spatial strength of an image in a given direction and show that it can be used to determine the rotational misalignment independent of translation between the images. The rotation parameters are obtained by maximizing the mutual information of 2D gradient intensity matrices obtained from 3D images, hence reducing the dimensionality of the problem and improving efficiency. The rotation parameters along with estimations of translation are then used to initialize an optimization step over a conventional pixel intensity-based method to achieve sub-voxel accuracy. Our optimization algorithm converges quickly and is less subject to the common problem of misregistration due to local extrema. Experiments show that our method significantly improves the robustness, performance and efficiency of registration compared to conventional pixel intensity-based methods

Gradient Intensity-Based Registration of Multi-Modal Images of the Brain

We present a fast and accurate framework for registra-tion of multi-modal volumetric images based on decoupled estimation of registration parameters utilizing spatial infor-mation in the form of ‘gradient intensity’. We introduce gra-dient intensity as a measure of spatial strength of an image in a given direction and show that it can be used to deter-mine the rotational misalignment independent of transla-tion between the images. The rotation parameters are ob-tained by maximizing the mutual information of 2D gradient intensity matrices obtained from 3D images, hence reduc-ing the dimensionality of the problem and improving effi-ciency. The rotation parameters along with estimations of translation are then used to initialize an optimization step over a conventional pixel intensity-based method to achieve sub-voxel accuracy. Our optimization algorithm converges quickly and is less subject to the common problem of mis-registration due to local extrema. Experiments show that our method significantly improves the robustness, perfor-mance and efficiency of registration compared to conven-tional pixel intensity-based methods. 1