Shift-and-add Research Articles

Impulse response and Modulation Transfer Function analysis for Shift-And-Add and Back Projection image reconstruction algorithms in Digital Breast Tomosynthesis (DBT)

Breast cancer is second only to lung cancer as the leading cause of non-preventable cancer death in women. Digital Breast Tomosynthesis (DBT) is a promising technique to improve early breast cancer detection. In this paper, we present the impulse response and Modulation Transfer Function (MTF) analysis to quantitatively compare Shift-And-Add (SAA) and point-by-point Back Projection (BP) three-dimensional image reconstruction algorithms in DBT. A Filtered Back Projection (FBP) deblurring algorithm based on point-by-point BP was used to demonstrate deblurred tomosynthesis images.

Importance of point‐by‐point back projection correction for isocentric motion in digital breast tomosynthesis: Relevance to morphology of structures such as microcalcifications

Digital breast tomosynthesis is a three-dimensional imaging technique that provides an arbitrary set of reconstruction planes in the breast from a limited-angle series of projection images acquired while the x-ray tube moves. Traditional shift-and-add (SAA) tomosynthesis reconstruction is a common mathematical method to line up each projection image based on its shifting amount to generate reconstruction slices. With parallel-path geometry of tube motion, the path of the tube lies in a plane parallel to the plane of the detector. The traditional SAA algorithm gives shift amounts for each projection image calculated only along the direction of x-ray tube movement. However, with the partial isocentric motion of the x-ray tube in breast tomosynthesis, small objects such as microcalcifications appear blurred (for instance, about 1-4 pixels in blur for a microcalcification in a human breast) in traditional SAA images in the direction perpendicular to the direction of tube motion. Some digital breast tomosynthesis algorithms reported in the literature utilize a traditional one-dimensional SAA method that is not wholly suitable for isocentric motion. In this paper, a point-by-point back projection (BP) method is described and compared with traditional SAA for the important clinical task of evaluating morphology of small objects such as microcalcifications. Impulse responses at different three-dimensional locations with five different combinations of imaging acquisition parameters were investigated. Reconstruction images of microcalcifications in a human subject were also evaluated. Results showed that with traditional SAA and 45 degrees view angle of tube movement with respect to the detector, at the same height above the detector, the in-plane blur artifacts were obvious for objects farther away from x-ray source. In a human subject, the appearance of calcifications was blurred in the direction orthogonal to the tube motion with traditional SAA. With point-by-point BP, the appearance of calcifications was sharper. The point-by-point BP method demonstrated improved rendition of microcalcifications in the direction perpendicular to the tube motion direction. With wide angles or for imaging of larger breasts, this point-by-point BP rather than the traditional SAA should also be considered as the basis of further deblurring algorithms that work in conjunction with the BP method.

SU‐FF‐I‐21: Two‐Dimensional Shift‐And‐Add (SAA) Algorithm for Digital Breast Tomosynthesis Reconstruction

Purpose: To investigate a two‐dimensional Shift‐And‐Add algorithm for three‐dimensional digital breast tomosynthsis reconstruction to correct for defects existing in the traditional Shift‐And‐Add algorithm that calculates only one‐dimensional shift amount along the axis of x‐ray tube's motion. Method and Materials: With the traditional Shift‐And‐Add (SAA) algorithm for breast tomosynthesis reconstruction, shift amounts for each projection plane are calculated only along the axis of x‐ray tube's movement. As a result, small objects such as microcalcifications appear slightly blurred in the direction perpendicular to the direction of tube motion. In this project, a two‐dimensional SAA method was developed to correct for this phenomenon. Shift amounts for every pixel location on each reconstruction plane were computed, taking into account the 2D arc projection location of reconstructed objects in each plane. Bilinear interpolation was used for partial pixel locations. Impulses at different 3‐D locations were simulated and a few human subject tomosynthesis sequences were acquired for investigation. Results: Two‐dimensional SAA demonstrated the improvement in the direction that is perpendicular to the tube motion direction. For human subjects, the appearance of calcifications from 2D SAA was sharper than traditional SAA at the direction orthogonal to the tube motion direction. The out‐of‐plane artifacts of calcifications changed from curved to be straight. Conclusion: Two‐dimensional SAA is an effective method to reconstruct 3D tomosynthesis images of the breast. Compared with the traditional SAA, the new method corrects for 2D shift amounts coming from the isocentric tube motion. This provides more accurate and reliable results compared with other SAA algorithms. Conflict of Interest: Research sponsored in part by a research grant from Siemens Medical Solutions.

Application of self-deconvolution method to shift-and-add solar imaging

A shift-and-add (SAA) operation is conducted to reconstruct a high-spatial-resolution image from atmospherically degraded solar images. The self-deconvolving data reconstruction algorithm is used to augment high-spatial-frequency components in solar speckle images and rectify the background component that results from the SAA operation. Self-deconvolved solar speckle images are shift and added and the resulting image shows high-spatial-resolution features.

Self-deconvolution for shift-and-add imaging

A shift-and-add (SAA) method is used to restore atmospherically degraded images. The operation of the SAA method is simple, but the deconvolution method of SAA images remains to be developed, especially for extended objects. We propose to deconvolve a SAA image of an extended object by use of a self-deconvolving data reconstruction algorithm (SeDDaRA). Computer simulations show the effectiveness of the SeDDaRA to SAA images. It is also shown that use of the SAA method after each data frame is self-deconvolved leads to a better reconstruction.

Shift-and-add reconstruction of solar granulation images

To restore an atmospherically degraded image of solar granulation the shift-and-add (SAA) method is applied to its specklegrams. It is the first time, to the best of our knowledge, that such a technique has been used for image reconstruction of solar granulation, a largely extended target. SAA, therefore, enables us to monitor restored images of solar granulation in a simple and fast way.

Shift-and-Add Method with Optically Pre-Processed Stellar Specklegrams

We propose a simple optical approach for the convolutional pre-processing of stellar specklegrams in the shift-and-add (SAA) method. It uses an incoherent optical processing, where a speckle pattern on a displaying device is re-imaged and a point-spread-function of the re-imaging system is used as the convolution kernel. This approach is suitable for use in the real-time SAA-system recently proposed. Experimental results using observational stellar specklegrams displayed on a cathode-ray-tube-monitor are reported to demonstrate that the optical pre-processing improves the signal-to-noise ratio of the final image.

Stellar spectral reconstruction from speckle spectroscopic data, 2

In the previous paper, we described speckle spectroscopic instrumentation and presented some observational results with data acquired by our speckle spectrometer. The shift-and-add (SAA) method was used for the data reduction in the previous paper. We have revised the speckle spectrometer to augment the performance. The cross-correlation method is newly introduced for data reduction. The spectra of single stars gamma Cas and alpha Per reconstructed in nearly diffraction-limited angular resolution with the resolved H alpha emission and absorption lines, respectively. It is shown that the cross-correlation method is superior to the shift-and-add method in the narrow bandwidth region. The results of alpha Per are compared with the photometric measurement of Procyon's spectrum which has the similar spectral type as alpha Per and they are shown to be fairly consistent. The new system exhibits a sufficient performance to enable us to make the quantitative spectral analysis and the cross-correlation method produces the higher SNR results.

Stellar spectra reconstruction from speckle spectroscopic data

view Abstract Citations (18) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stellar Spectra Reconstruction From Speckle Spectroscopic Data Kuwamura, Susumu ; Baba, Naoshi ; Miura, Noriaki ; Hege, E. K. Abstract We describe a method to reconstruct stellar spectra from dispersed speckle data with diffraction-limited angular resolution. A shift-and-add (SAA) method is applied on many short exposure frames, each of which contains a dispersed speckle image and a corresponding nondispersed speckle image as a reference. The spectra of the binary star ADS 16836 were reconstructed in wideband and low dispersion mode from the data taken with the Hokudai speckle spectroscopic camera system using the Okayama 188 cm telescope. The result shows the well-separated spectra of the primary and the secondary stars, which are otherwise too close to be distinguishable due to atmospheric turbulence. These results also demonstrate high spatial resolution spectroscopy for a binary star and for a resolvable hypergiant using our SAA speckle method. Publication: The Astronomical Journal Pub Date: February 1993 DOI: 10.1086/116465 Bibcode: 1993AJ....105..665K Keywords: Data Processing; Diffraction Limited Cameras; Speckle Patterns; Spectroscopic Analysis; Stellar Spectra; Angular Resolution; Atmospheric Turbulence; Binary Stars; H Beta Line; Astronomy; TECHNIQUES: SPECTROSCOPIC full text sources ADS | data products SIMBAD (5)

IMAGE QUALITY, TIP-TILT CORRECTION, AND SHIFT-AND-ADD INFRARED IMAGING

ABSTRACT The image quality obtainable with shift-and-add (SAA) imaging for the recovery of diffraction-limited information is quantitatively investigated using data simulating an 8-m aperture at a site with near-IR seeing conditions as found on Mauna Kea. This is compared to the image quality obtainable from image centroiding and wavefront tip-tilt correction. For good seeing conditions, image centroiding and SAA, which tracks the image peak, show similar performance containing about 30 percent of the image power in a diffraction-limited component. However, as the seeing degrades, SAA consistently yields improved resolution maintaining significantly greater diffraction-limited information. This enhances the detection threshold by about 2 magnitudes over the seeing-limited case for the seeing range studied. By comparison, the gain due to image centroiding decreases to less than 1 magnitude at the same poor seeing limit.

Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method

The shift-and-add (SAA) method is used to estimate the magnitude difference of binary star components. A simple procedure based on the SAA method enables an accurate estimation of the magnitude difference. Some computer simulations confirm this. The use of this procedure in stellar speckle interferograms is also demonstrated.

Image restoration by the shift-and-add algorithm

A new method for image restoration based on the shift-and-add (SAA) algorithm is presented, the main advantages of which appear to be speed and simplicity. The SAA pattern produced by an object is given by the object correlated by a nonlinear replica of itself whose intensity distribution is strongly weighted toward the brighter pixels. A method of successive substitutions analogous to Fienup's algorithm can then be used to decorrelate the SAA pattern and recover the object. The method is applied to the case of the extended chromosphere of Betelgeuse.

Effect of nonisoplanaticity on the shift-and-add algorithm

Analysis of the shift-and-add (SAA) algorithm in double-star speckle interferometry has been extended to include the case of partial nonisoplanaticity. It was found that the intensity ratio of the ghost to the principal spots produced by SAA is essentially constant, regardless of the degree of nonisoplanaticity, but that the ratio of either outer spot to the center spot declines in a manner similar to that of the autocorrelation.