In a previous work, we proposed a source-type formulation to the
electrical resistance tomography (ERT) problem. Specifically, we
showed that inhomogeneities in the medium can be viewed as secondary
sources embedded in the homogeneous background medium and located at
positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.
JPEG2000 is the new ISO/IEC image compression standard. It is a full coding system targeted for various imaging applications. Besides offering the state-of-the-art in still image compression, it provides new features such as scalability in quality and in resolution, random access and region of interest (ROI) coding. Motion JPEG2000 is an inherited video compression standard based on intra-farme coding using JPEG2000. JPIP (the JPEG2000 Interactive Protocol), is a developing protocol for the access and transmission of JPEG2000 coded data and related metadata in a networked environment. In this paper, we present various applications of JPEG2000, Motion JPEG2000 and JPIP, geared specially towards the wireless mobile environment. We present an Image Surfing system for surfing JPEG2000 images on mobile terminals over a wireless network. We also present a scheme for tracking and coding Regions-Of-Interest (ROI) over a Motion JPEG2000 sequence. Finally, we present a Partial Coding scheme for use in Motion JPEG2000 sequences that gives coding gains for certain types of video sequences.
In this paper, we propose a "source-type" solution to the problem of electrical resistance tomography (ERT). The goal of ERT is to develop a map of the electrical properties in a region of space based on observations of voltages collected at the boundary in response to input DC currents also at the boundary. As with many inverse problems, ERT is both nonlinear and poorly posed. Source-type inverse methods have been proposed in the inverse scattering context as a way of quasi-linearizing the problem. Specifically, inhomogeneities in the
medium are viewed as secondary sources embedded in a homogeneous medium. One can solve a linear inverse source problem to localize these sources (i.e. determine their geometry); however resolving their spatial contrasts quantitatively is not possible under this method. In a sense, the nonlinearity of the original problem is buried
in the amplitude. Our work here is motivated by thefact that use of a source-type formulation has not been considered for ERT to the best of our knowledge. We shall show that the secondary sources for ERT are defined by the inner product of the gradients of true
conductivity and electrical potential. Using this equivalence, the inverse problem is easily transformed into a multi-source inversion. Given the ill-posedness of the ERT problem arising from the inherent low sensitivity of the observed data to changes in the internal conductivity of the medium, the proposed transformation provides
a better description of the effect of inhomogeneities and therefore leads to more efficient inversion techniques. We introduce and discuss one step as well as iterative methods, especially for piecewise constant media. In the iterative method, we make use of a level set formulation and we replace the update of the steepest descent approach by the correlation coefficient between the residual vector and the response of a specified source. Using the same measure, i.e. the correlation coefficient, we introduce a simple single step imaging method. Results of both methods using simulated data are presented.