The authors introduce a directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information. The passband regions of the component filters are wedge-shaped and thus provide directional information. It is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed. The authors discuss the theory for directional decomposition and reconstruction. In addition, implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered. >

A filter bank for the directional decomposition of images: theory and design

/pdf/two-dimensional-fir-filters-2loqgd3j45.pdf

Two-dimensional FIR filters

Collagen fibers and their component fibrils make up the protenaceous " backbone" of most tissues and provide the majority of their resistance to tensile loading. Spatial orientation of collagen fibrils is an important factor in determining tissue properties. This is particularly true in ligament tissue, since ligaments must be loose enough to allow joints to move but tight enough to prevent joint surfaces from separating. A method is presented here to reproducibly quantify this collagen arrangement, which should be useful in studies on ligament healing and growth.

A Fourier Domain Directional Filterng Method for Analysis of Collagen Alignment in Ligaments

Wavelength filters permit the separation of anomalies of different horizontal extents on magnetic and gravity maps. They can be used equally well for structural and topographic maps or for any other type of data amenable to gridding. Practical filters were developed following two series of cutoff wavelengths. Of special interest is the small size of the filters as compared to the steepness and smoothness of their wavenumber characteristics. Filters for any desired wavelengths can easily be derived from the described coefficient sets. Examples are given for the application of filters which can be used as regional, residual, and band‐pass filters. The resultant maps are in the same units as the original maps. A given map can be divided into several wavelength components, and the sum of the components is equal to the original data. The method is shown to be versatile, and second‐derivative calculations can be approximated by a properly chosen residual filter.

Applications of two-dimensional linear wavelength filtering

Amplitude‐ and frequency‐modulated wave motion constitute the ground‐roll noise in seismic reflection prospecting. Hence, it is possible to eliminate ground roll by applying one‐dimensional, linear frequency‐modulated matched filters. These filters effectively attenuate the ground‐roll energy without damaging the signal wavelet inside or outside the ground roll’s frequency interval. When the frequency bands of seismic reflections and ground roll overlap, the new filters eliminate the ground roll more effectively than conventional frequency and multichannel filters without affecting the vertical resolution of the seismic data.

A method of ground-roll elimination

A new technique has been developed which makes it possible to process a seismic record‐section in such a way that all seismic events with dips in a given range are preserved with no alteration over a wide frequency band, while all seismic events with dips outside the specified range are uniformly and severely attenuated. By applying this process to a noisy record‐section, a record‐section may be obtained which has all events within a specified dip range perfectly preserved, and very high‐velocity noise essentially eliminated, a result which is impossible by simple wave‐number filtering or conventional array usage. In structurally complex areas where several steeply dipping events interfere, the technique may be applied to separate the events with different dips. In areas where a normal‐moveout contrast exists between primaries and multiples, the technique may be used for wide‐band multiple attenuation. By application of a “rotating Pie‐Slice” to micro‐spread noise data, seismic noise may be separated on t...

Wide-band velocity filtering; The Pie-Slice process

The development of a new technique makes it possible to process a seismic record section in such a way that all seismic events with dips in a given range are preserved with no alteration over a wide frequency band, while all seismic events with dips outside the specified range are uniformly and severely attenuated. To state it another way, it is possible to combine the elements of a line array in a manner resulting in a directed beam in which the beam width is independent of frequency, and which has uniformly low side lobes, also essentially independent of frequency. By applying this process to a noisy record section, a record section may be obtained which has all events within a specified dip range perfectly preserved, and very high velocity noise such as the PL mode has been essentially eliminated, a result which is impossible by simple wave-number filtering or conventional array usage. In structurally complex areas, where several steeply dipping events interfere, the technique may be applied to separate the events with different dips. In areas where a normal-moveout contrast exists between primaries and multiples, the technique may be used for wide-band multiple-attenuation. By application of a "rotating pie-slice" to microspread noise data, seismic noise may be separated on the basis of propagation velocity, and a clearer picture of the seismic noise problem obtained. The "rotating pie-slice" also provides a means of uncovering diffractions and other steeply curved events from a record section. The technique is described in terms of its application to synthetic examples. Various examples of its application to actual seismic data illustrate its practical effectiveness. End_of_Article - Last_Page 1769------------

/pdf/wide-band-velocity-filtering-the-pie-slice-process-abstract-456h3haaug.pdf

Wide-Band Velocity Filtering--The Pie Slice Process: ABSTRACT

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Wide-band velocity filtering; The Pie-Slice process

Wide-Band Velocity Filtering--The Pie Slice Process: ABSTRACT