QC 351 A7 no. 65 / The significance of signal-dependent noise is discussed. Particular emphasis is placed on the type of multiplicative noise present in the density variations in a photographic emulsion. A theoretical treatment of the effect of multiplicative noise on signal detection and signal discrimination problems is presented. Optimum test statistics are derived for processing a sampled message to detect the presence of a known signal. Multiplicative noise described by Poisson and Gaussian statistics is considered. The expressions are extended to include the two-signal discrimination problem. Two-dimensional signal fields in the presence of multiplicative noise are simulated in a computer and processed for optimum signal detection according to the two derived methods. These results are compared to the results of processing based on the assumption of stationary noise statistics. This comparison reveals that modest improvements (20% to 30% reduction in false alarm rate) are obtained when the signal-dependent nature of the noise statistics is considered. The effects of signal-to-noise ratio, signal structure, and changing background level are also investigated. An example of optimum signal discrimination using circles and squares as signals in multiplicative noise is reported. An improvement in the percentage of correctly identified signals is again observed when the proper test statistic is used. Two examples of signal filtering in the presence of signal-dependent noise are included. The first concerns the processing of a real star field to determine the location of weak stars. The second is an illustration of the signal information contained in the noise spectrum of a message recorded on a common photographic film.

Early detection, diagnosis, and suitable treatment are known to significantly improve the chance of survival for breast cancer (BC) patients. To date, the most cost effective method for screening and early detection is screen-film mammography, which is also the only tool that has demonstrated its ability to reduce BC mortality. Full-field digital mammography (FFDM) is an extension of screen-film mammography that eliminates the need for film-processing because the images are detected electronically from their inception. Tomosynthesis is an emerging technology in digital mammography built on the FFDM framework, which offers an alternative to conventional two-dimensional mammography. Tomosynthesis produces three-dimensional (volumetric) images of the breast that may be superior to planar imaging due to improved visualization. In this work preliminary tomosynthesis data derived from cadaver breasts are analyzed, which includes volume data acquired from various reconstruction techniques as well as the planar projection data. The noise and power spectra characteristics analyses are the focus of this study. Understanding the noise characteristics is significant in the study of radiological images and in the evaluation of the imaging system, so that its degrading effect on the image can be minimized, if possible and lead to better diagnosis and optimal computer aided diagnosis schemes. Likewise, the power spectra behavior of the data are analyzed, so that statistical methods developed for digitized film images or FFDM images may be applied directly or modified accordingly for tomosynthesis applications. The work shows that, in general, the power spectra for three of the reconstruction techniques are very similar to the spectra of planar FFDM data as well as digitized film; projection data analysis follows the same trend. To a good approximation the Fourier power spectra obey an inverse power law, which indicates a degree of self-similarity. The noise analysis indicates that the noise and signal are dependent and the dependency is a function of the reconstruction technique. New approaches for the analysis of signal dependent noise were developed specifically for this work based on both the linear wavelet expansion and on nonlinear order statistics. These methods were tested on simulated data that closely follow the statistics of mammograms prior to the real-data applications. The noise analysis methods are general and have applications beyond mammography.

abstract: I propose a new communications scheme where signature signals are used to carry digital data by suitably modulating the signal parameters with information bits. One possible application for the proposed scheme is in underwater acoustic (UWA) communications; with this motivation, I demonstrate how it can be applied in UWA communications. In order to do that, I exploit existing parameterized models for mammalian sounds by using them as signature signals. Digital data is transmitted by mapping vectors of information bits to a carefully designed set of parameters with values obtained from the biomimetic signal models. To complete the overall system design, I develop appropriate receivers taking into account the specific UWA channel models. I present some numerical results from the analysis of data recorded during the Kauai Acomms MURI 2011 (KAM11) UWA communications experiment. It is shown that the proposed communication scheme results in approximate channel models with amplitude-limited inputs and signal-dependent additive noise. Motivated by this observation, I study capacity of amplitude-limited channels under different transmission scenarios. Specifically, I consider fading channels, signal-dependent additive Gaussian noise channels, multiple-input multiple-output (MIMO) systems and parallel Gaussian channels under peak power constraints. I also consider practical channel coding problems for channels with signal-dependent noise. I consider two specific models; signal-dependent additive Gaussian noise channels and Z-channels which serve as binary-input binary-output approximations to the Gaussian case. I propose a new upper bound on the probability of error, and utilize it for design of codes. I illustrate the tightness of the derived bounds and the performance of the designed codes via examples. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015