The effects of using spectral correlation in a maximum-likelihood estimator (MLE) for backscattered energy corresponding to coherent reflectors embedded in media of microstructure scatterers is considered. The spectral autocorrelation (SAC) function is analyzed for various scatterer configurations based on the regularity of the interspacing distance between scatterers. It is shown that increased regularity gives rise to significant spectral correlation, whereas uniform distribution of scatters throughout a resolution cell results in no significant correlation between spectral components. This implies that when a true uniform distribution for the effective scatterers exists, the power spectral density (PSD) is sufficient to characterize their echoes. However, as the microstructure scatterer distribution becomes more regular, SAC terms become more significant. MLE results for 15 A-scans from stainless steel specimens with three different grain sizes indicate an average 6-dB signal-to-noise ratio (SNR) improvement in the coherent scatterer (flat-bottom hole) echo intensities for estimators using the SAC characterization as opposed to the PSD characterization.

INTRODUCTIONThis paper presents a model for RF broadband ultrasonic A-scans obtained from materials composed of microstructures, in which isolated flaws or impurities may exist. The model incorporates both the RF phase and magnitude differences between the microstructure and coherent flaw echo spectra. An adaptive implementation of the maximumlikelihood estimator (MLE) is presented for estimating A-scan amplitudes associated with coherent scatterers embedded in grain echoes. The adaptive implelllentation is motivated by the nonstationary behavior of the back-scattered energy received over the duration of the A-scan [1]. This nonstationarity results from the frequency dependent absorption, scattering, and diffraction that occurs as the pulse propagates through the material [2,3].The experimental results indicate that the model's covariance matrix characterizes phase information related to the microstructures in the material. While no experiments have been performed to directly demonstrate this conjecture, the MLE performance is compared for cases when the phase elements of the covariance matrix are and are not included in the MLE computation. Significant performance increases are demonstrated for cases where the MLE uses the phase elements of the covariance matrix. Experimental A-scans, obtained from stainless-steel cylinders with flat-bottom holes, are used in the performance comparisons. COHERENT GRAIN-ECHO MODELThis section constructs a statistical model for the discrete Fourier transform (DFT) components corresponding to an A-scan segment received from a volume of scatterers. The A-scan segment length used in this model corresponds to the volume illuminated by the pulse at a single instant of time. This volume will be referred to as aresolution celloThe ultrasonic cross-section (UCS), or reflectivity of the scatterer characterizes the relationship between the scattering center and its back-scattered energy measured at the transducer. The UCS is defined as the ratio of ultrasonic energy received at the transducer, over the incident energy illuminating the scattering center. The UCS value for a given target is dependent on the size and acoustic impedance of the target relative to the surrounding scatterers.Consider an A-scan received from a broadband uItrasonic pulse. Let the strength and position of scatterers within a single resolution cell be modeled by a train of scaled and delayed Dirac Delta functions:(1)where Vk and Sk in the summation represent the UCS and delay associated with each of the Kn unresolvable scattering centers (corresponding to the microstructures), and 0. and 't represent the UCS and delay associated with a coherent target scatterer. In cells where no target scatterer exits, 0. is zero.Let an A-scan segment that corresponds to aresolution cell, be modeled by the an impulse response convolved with the scatterer model:where hs(t, 1..) is the impulse response of the pulse-echo system for the unresolvable scatterers located in the neighborhood corresponding to t. This impulse response depends...

located x,y on the Cartesian image grid is reconstructed by [2]:m m f f In the process of reconstructing an image through digital computer tomography (CT), error is introduced through truncation and sampling of the data used in the algorithm. In this paper a nonlinear digital filtering technique (median filtering) is suggested for processing the projections in order to reduce error without the distortion introduced by linear filtering. The rationale for the application of these filters is discussed. To compare the effectiveness of linear filtering and median filtering computer simulations and further experiments are suggested. It is expected that median filters have potential to improve image quality beyond that of linear filtering, particularly for edge reproduction. NOISE AND BACK-PROJECTION ALGORITHMSThe reconstruction of accurate cross-sectional images from a set of one-dimensional projections is the objective of digital computer tomography (CT). Two major sources of degradation in images reconstructed by back-projection algorithms are noise (from both measurement inaccuracies and truncation error due to digital representation) and aliasing errors (due to finite bandwidth restrictions). Conventional solutions to these problems typically involve some form of low-pass filtering to eliminate frequency components involved in aliasing or to attenuate high frequency components where the signal-to-noise ratio is lower. While these techniques are successful in reducing noise and aliasing error, they also reduce image resolution, since the attenuated high frequency components contain information for resolving boundaries. To maintain the highest resolution allowable by the bandwidth of the projection signal, a set of nonlinear processors known as order statistic (OS) filters [I] are proposed for noise suppression.The sample data for the reconstruction of a two-dimensional image from a three-dimensional object is obtained by passing parallel X-ray beams though the image plane of the object anti measuring the attenuation of the beams at discrete intervals along a detector array (in this paper only parallel-beam projections are considered). The series of values obtained from the detector array are the samples of the projection function. The angle of the projections is incremented and new projection samples are taken. This process continues until the projection data spans 180 degrees around the object. A particular sample at position ti along the projection taken at angle ek is represented by p(ek,tn). p(ek,tn) is called the projection function.Two popular reconstruction algorithms are the filtered-back projection algorithm and the convolution-back projection algorithm. For both of these algorithms the discrete image pixel where K is the total number of projections taken at uniform angular increments, and Q(ek,tn) is the filtered-back projection given by:where s(8k,om) is the discrete Fourier transform (Dm) of p(ek,tn), N is the total number of samples taken at increments of length 7 along the projection axis, and 0, = n/(...