Dennis M. Goodman

BACKPROPAGATION LEARNING FOR MULTILAYER FEED-FORWARD NEURAL NETWORKS USING THE CONJUGATE GRADIENT METHOD

In many applications, the number of interconnects or weights in a neural network is so large that the learning time for the conventional backpropagation algorithm can become excessively long. Numerical optimization theory offers a rich and robust set of techniques which can be applied to neural networks to improve learning rates. In particular, the conjugate gradient method is easily adapted to the backpropagation learning problem. This paper describes the conjugate gradient method, its application to the backpropagation learning problem and presents results of numerical tests which compare conventional backpropagation, steepest descent and the conjugate gradient methods. For the parity problem, we find that the conjugate gradient method is an order of magnitude faster than conventional backpropagation with momentum.

Depth profiling of laser-heated chromophores in biological tissues by pulsed photothermal radiometry

A solution method is proposed to the inverse problem of determining the unknown initial temperature distribution in a laser-exposed test material from measurements provided by infrared radiometry. A Fredholm integral equation of the first kind is derived that relates the temporal evolution of the infrared signal amplitude to the unknown initial temperature distribution in the exposed test material. The singular-value decomposition is used to demonstrate the severely ill-posed nature of the derived inverse problem. Three inversion methods are used to estimate solutions for the initial temperature distribution. A nonnegatively constrained conjugate-gradient algorithm using early termination is found superior to unconstrained inversion methods and is applied to image the depth of laser-heated chromophores in human skin.

Depth determination of chromophores in human skin by pulsed photothermal radiometry

We report on the application of pulsed photothermal radiometry (PPTR) to determine the depth of in-vitro and in-vivo subsurface chromophores in biological materials. Measurements provided by PPTR in combination with a nonnegative constrained conjugate-gradient algorithm are used to determine the initial temperature distribution in a biological material immediately following pulsed laser irradiation. Within the experimental error, chromophore depths (50-450 µm) in 55 in-vitro collagen phantoms determined by PPTR and optical low-coherence reflectometry are equivalent. The depths of port-wine-stain blood vessels determined by PPTR correlate very well with their locations found by computer-assisted microscopic observation of histologic sections. The mean blood-vessel depth deduced from PPTR and histologic observation is statistically indistinguishable (p > 0.94).

Imaging laser heated subsurface chromophores in biological materials: determination of lateral physical dimensions

We describe a non-contact method using infrared radiometry to determine lateral physical dimensions of laser heated subsurface chromophores in biological materials. An imaging equation is derived that relates measured radiometric temperature change to the reduced two-dimensional temperature increase of laser heated chromophores. From measured images of radiometric temperature change, the lateral physical dimensions of chromophores positioned in an in vitro model of human skin are determined by deconvolution of the derived imaging equation using a non-negative constrained conjugate gradient algorithm. Conditions for optimum spatial resolution are found by analysis of a derived radiometric transfer function and correspond to superficial chromophores and/or weak infrared absorption in a laser irradiated biological material. Analysis indicates that if the infrared attenuation coefficient is sufficiently small (i.e., less than 10mm-1), infrared radiometry in combination with a deconvolution algorithm allows estimation of lateral physical dimensions of laser heated subsurface chromophores in human skin.

A design technique for circularly symmetric low-pass filters

The design of two-dimensional (2-D) circularly-symmetric low-pass digital filters by cascading several rotated filters (a rotated filter is defined to be one produced by rotating a one-dimensional (1-D) continuous filter into a two-dimensional continuous filter which is in turn bilinearly transformed into a two-dimensional digital filter) is a well-known and useful technique. An alternate approach which is an extension of the above technique is presented. This new method is based on a spectral transformation from the one-dimensional discrete domain into the two-dimensional discrete domain. This approach retains most of the advantages of the original technique while permitting design entirely in the discrete domain, yielding filters with better stability characteristics, and facilitating frequency response optimization via nonlinear programming.

Non-invasive determination of port wine stain anatomy and physiology for optimal laser treatment strategies

The treatment of port wine stains (PWSs) using a flashlamp-pumped pulsed dye laser is often performed using virtually identical irradiation parameters. Although encouraging clinical results have been reported, we propose that lasers will only reach their full potential provided treatment parameters match individual PWS anatomy and physiology. The purpose of this paper is to review the progress made on the technical development and clinical implementation of (i) infrared tomography (IRT), optical reflectance spectroscopy (ORS) and optical low-coherence reflectometry (OLCR) to obtain in vivo diagnostic data on individual PWS anatomy and physiology and (ii) models of light and heat propagation, predicting irreversible vascular injury in human skin, to select optimal laser wavelength, pulse duration, spot size and radiant exposure for complete PWS blanching in the fewest possible treatment sessions. Although non-invasive optical sensing techniques may provide significant diagnostic data, development of a realistic model will require a better understanding of relevant mechanisms for irreversible vascular injury.

Some difficulties with the double bilinear transformation in 2-D recursive filter design

It is shown that the double bilinear transformation approach for designing a 2-D IIR digital transfer function from a predetermined 2-D analog transfer function, may in certain cases lead to unstable solutions.

Ship wake-detection procedure using conjugate gradient trained artificial neural networks

A method has been developed to reduce large two-dimensional images to significantly smaller feature lists. These feature lists overcome the problem of storing and manipulating large amounts of data. A new artificial neural network using conjugate gradient training methods, operating on sets of feature lists, was successfully trained to determine the presence or absence of wakes in synthetic aperture radar images. A comparison has been made between the different conjugate gradient and steepest-descent training methods and has demonstrated the superiority of the former over the latter. >

Non-contact measurement of thermal diffusivity in tissue

We demonstrate the application of an infrared (IR) imaging technique for non-contact determination of thermal diffusivity in biological materials. The proposed method utilizes pulsed laser excitation to produce an initial three-dimensional temperature distribution in tissue, and records IR images of subsequent heat diffusion. The theoretical model assumes that the time-dependent temperature increase following pulsed laser exposure is due to independent heat diffusion in longitudinal and lateral directions. A nonlinear least-squares algorithm is used to compute the lateral thermal point spread function from a pair of recorded IR images and to determine the thermal diffusivity of a test specimen. The recorded time-sequence of IR images is used to compute thermal diffusivity as a function of increasing time interval between two IR emission images. Experimental application of the method was demonstrated using tissue phantoms, ex vivo samples of hydrated cartilage and in vivo epidermis.

Combining two excitation wavelengths for pulsed photothermal profiling of hypervascular lesions in human skin

When pulsed photothermal radiometry (PPTR) is used for depth profiling of hypervascular lesions in human skin, melanin absorption also heats the most superficial skin layer (epidermis). Determination of lesion depth may be difficult when it lies close to the epidermal dermal junction, due to PPTRs limited spatial resolution. To overcome this problem, we have developed an approximation technique, which uses two excitation wavelengths (585 and 600 nm) to separate the vascular and epidermal components of the PPTR signal. This technique permits a noninvasive determination of lesion depth and epidermal thickness in vivo, even when the two layers are in close physical proximity to each other. Such information provides the physician with guidance in selecting the optimal parameters for laser therapy on an individual patient basis.