Optical diffusion imaging in highly scattering media such as tissue, as an alternative to X-ray tomography, presents significantly lower health risks, and has successfully demonstrated its potential in biomedical applications. Although current reconstruction algorithms have been applied with some success, there are a number of opportunities for improving both the accuracy of the reconstructions and the speed of convergence. Most studies of frequency-resolved diffusion imaging involve casting the diffusion as a Helmholtz equation, which involves the approximation that ∇D = 0. We describe here an analysis of the effects of this approximation on both the generation of synthetic data for simulations, and the effect on reconstructions.
{"title":"Effect of the “∇D” Term in Optical Diffusion Imaging","authors":"J. C. Ye, R. Millane, K. Webb, T. Downar","doi":"10.1364/srs.1998.sthb.2","DOIUrl":"https://doi.org/10.1364/srs.1998.sthb.2","url":null,"abstract":"Optical diffusion imaging in highly scattering media such as tissue, as an alternative to X-ray tomography, presents significantly lower health risks, and has successfully demonstrated its potential in biomedical applications. Although current reconstruction algorithms have been applied with some success, there are a number of opportunities for improving both the accuracy of the reconstructions and the speed of convergence. Most studies of frequency-resolved diffusion imaging involve casting the diffusion as a Helmholtz equation, which involves the approximation that ∇D = 0. We describe here an analysis of the effects of this approximation on both the generation of synthetic data for simulations, and the effect on reconstructions.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132595932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Clarkson, J. Denny, H. Barrett, C. Abbey, B. Gallas
In tomographic and other digital imaging systems the goal is often to reconstruct an object function from a finite amount of noisy data generated by that function through a system operator. One way to determine the reconstructed function is to minimize the distance between the noiseless data vector it would generate via the system operator, and the data vector created through the system by the real object and noise. The former we will call the reconstructed data vector, and the latter the actual data vector. A reasonable constraint to place on this minimization problem is to require that the reconstructed function be non-negative everywhere. Different measures of distance in data space then result in different reconstruction methods. For example, the ordinary Euclidean distance results in a positively constrained least squares reconstruction, while the Kulback-Leibler distance results in a Poisson maximum likelihood reconstruction. In many cases though, if the reconstruction algorithm is continued until it converges, the end result is a reconstructed function that consists of many point-like structures and little else. These are called night-sky reconstructions, and they are usually avoided by stopping the reconstruction algorithm early or using regularization. The expectation-maximization algorithm for Poisson maximum likelihood reconstructions is an example of this situation.
{"title":"Night-sky reconstructions for linear digital imaging systems","authors":"E. Clarkson, J. Denny, H. Barrett, C. Abbey, B. Gallas","doi":"10.1364/srs.1998.sthc.5","DOIUrl":"https://doi.org/10.1364/srs.1998.sthc.5","url":null,"abstract":"In tomographic and other digital imaging systems the goal is often to\u0000 reconstruct an object function from a finite amount of noisy data\u0000 generated by that function through a system operator. One way to\u0000 determine the reconstructed function is to minimize the distance\u0000 between the noiseless data vector it would generate via the system\u0000 operator, and the data vector created through the system by the real\u0000 object and noise. The former we will call the reconstructed data\u0000 vector, and the latter the actual data vector. A reasonable constraint\u0000 to place on this minimization problem is to require that the\u0000 reconstructed function be non-negative everywhere. Different measures\u0000 of distance in data space then result in different reconstruction\u0000 methods. For example, the ordinary Euclidean distance results in a\u0000 positively constrained least squares reconstruction, while the\u0000 Kulback-Leibler distance results in a Poisson maximum likelihood\u0000 reconstruction. In many cases though, if the reconstruction algorithm\u0000 is continued until it converges, the end result is a reconstructed\u0000 function that consists of many point-like structures and little else.\u0000 These are called night-sky reconstructions, and they are usually\u0000 avoided by stopping the reconstruction algorithm early or using\u0000 regularization. The expectation-maximization algorithm for Poisson\u0000 maximum likelihood reconstructions is an example of this\u0000 situation.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131352764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sampling diversity occurs under certain circumstances during multiple-frame imaging of a common object. When an undersampled sensor takes images without repeating the locations of the samples on the object, sampling diversity will occur. The undersampling causes the local phenomenon of aliasing, and small local differences between frames can be seen upon close inspection. Small object features near the sampling limit can exhibit radical changes and may even vanish if at Nyquist. The multiple frames can be combined with a Projection Onto Convex Sets (POCS) approach [1], resulting in significant resolution improvement. Under the assumption of linear transformation of coordinates, we discuss an algorithm that computes the result in FFT-time using the Fast Fractional Fourier Transform [2].
{"title":"Resolution improvement using sampling diversity","authors":"D. Granrath","doi":"10.1364/srs.1998.sthc.6","DOIUrl":"https://doi.org/10.1364/srs.1998.sthc.6","url":null,"abstract":"Sampling diversity occurs under certain circumstances during multiple-frame imaging of a common object. When an undersampled sensor takes images without repeating the locations of the samples on the object, sampling diversity will occur. The undersampling causes the local phenomenon of aliasing, and small local differences between frames can be seen upon close inspection. Small object features near the sampling limit can exhibit radical changes and may even vanish if at Nyquist. The multiple frames can be combined with a Projection Onto Convex Sets (POCS) approach [1], resulting in significant resolution improvement. Under the assumption of linear transformation of coordinates, we discuss an algorithm that computes the result in FFT-time using the Fast Fractional Fourier Transform [2].","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125099680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the past, fixed aberrations in large astronomical telescopes were not considered to be a problem as long as the errors were no worse than the seeing at the telescope sight. Adaptive optics are now allowing researchers to correct for local seeing errors as well as fixed aberrations. In order to better understand the correction capabilities it is important to separate the fixed aberration errors from the seeing errors. The Lockheed Palo Alto Research labs ongoing phase diversity program has addressed this problem by using phase diversity techniques to estimate the fixed aberrations in the 1 meter and 3 meter telescopes at the Lick Observatory. The phase information extracted from the focused and defocused images is also used to enhance images of extended objects such as Jupiter, Saturn and the Earth’s moon.
{"title":"Phase Diversity: Experimental Results from the Lick Observatory","authors":"R. Kendrick","doi":"10.1364/srs.1995.rtue3","DOIUrl":"https://doi.org/10.1364/srs.1995.rtue3","url":null,"abstract":"In the past, fixed aberrations in large astronomical telescopes were not considered to be a problem as long as the errors were no worse than the seeing at the telescope sight. Adaptive optics are now allowing researchers to correct for local seeing errors as well as fixed aberrations. In order to better understand the correction capabilities it is important to separate the fixed aberration errors from the seeing errors. The Lockheed Palo Alto Research labs ongoing phase diversity program has addressed this problem by using phase diversity techniques to estimate the fixed aberrations in the 1 meter and 3 meter telescopes at the Lick Observatory. The phase information extracted from the focused and defocused images is also used to enhance images of extended objects such as Jupiter, Saturn and the Earth’s moon.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114942797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The resolution achieved in space-object imaging is usually limited by turbulence-induced aberrations, which can severely limit the resolution in the images by an order of magnitude or more. The 1.5-meter telescope at the Air Force Research Laboratory Starfire Optical Range (SOR) relies upon an adaptive-optics system to eliminate in real time much of the phase aberration introduced by atmospheric turbulence. Despite the exceptional performance of this system, the correction is never perfect. There are several sources of residual aberrations that degrade the imagery: imperfect wavefront sensing (particularly in low light-level situations), the time lag between sensing and correction (which allows for evolution of the atmosphere and is a particular problem when slewing to track an earth-orbiting space object), and deformable-mirror fitting errors. A post-detection image-reconstruction capability also insures the continuing availability of fine-resolution images, even during adaptive-optics down time owing to routine maintenance or temporary system failure. Therefore, post-detection reconstruction methods provide an important complement to and backup for pre-detection correction.
{"title":"Multi-frame satellite image reconstruction using adaptive-optics compensation","authors":"J. H. Seldin, R. Paxman, B. Ellerbroek, J. Riker","doi":"10.1364/srs.1998.stua.4","DOIUrl":"https://doi.org/10.1364/srs.1998.stua.4","url":null,"abstract":"The resolution achieved in space-object imaging is usually limited by\u0000 turbulence-induced aberrations, which can severely limit the\u0000 resolution in the images by an order of magnitude or more. The\u0000 1.5-meter telescope at the Air Force Research Laboratory Starfire\u0000 Optical Range (SOR) relies upon an adaptive-optics system to eliminate\u0000 in real time much of the phase aberration introduced by atmospheric\u0000 turbulence. Despite the exceptional performance of this system, the\u0000 correction is never perfect. There are several sources of residual\u0000 aberrations that degrade the imagery: imperfect wavefront sensing\u0000 (particularly in low light-level situations), the time lag between\u0000 sensing and correction (which allows for evolution of the atmosphere\u0000 and is a particular problem when slewing to track an earth-orbiting\u0000 space object), and deformable-mirror fitting errors. A post-detection\u0000 image-reconstruction capability also insures the continuing\u0000 availability of fine-resolution images, even during adaptive-optics\u0000 down time owing to routine maintenance or temporary system failure.\u0000 Therefore, post-detection reconstruction methods provide an important\u0000 complement to and backup for pre-detection correction.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116330360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Electromagnetics Technology Division of the Air Force Research Laboratory at Hanscom Air Force Base, Massachusetts has been providing measured and theoretical data to the inverse scattering/imaging community since 1995, via a FTP server. The data is obtained in the course of our work in radar phenomenology and systems analysis, wherein we conduct both theoretical and measurement programs. Since many of our results are obtained from canonical shapes and are not of a sensitive nature we realized that we could do the inverse community a service by providing researchers with real data to exercise their algorithms. We inaugurated the Ipswich data server in late 1994.
{"title":"Inverting Real Data: The Ipswich Experience","authors":"R. McGahan","doi":"10.1364/srs.1998.sthd.1","DOIUrl":"https://doi.org/10.1364/srs.1998.sthd.1","url":null,"abstract":"The Electromagnetics Technology Division of the Air Force Research Laboratory at Hanscom Air Force Base, Massachusetts has been providing measured and theoretical data to the inverse scattering/imaging community since 1995, via a FTP server. The data is obtained in the course of our work in radar phenomenology and systems analysis, wherein we conduct both theoretical and measurement programs. Since many of our results are obtained from canonical shapes and are not of a sensitive nature we realized that we could do the inverse community a service by providing researchers with real data to exercise their algorithms. We inaugurated the Ipswich data server in late 1994.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125498251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Previous research has demonstrated the success of using a cubic phase mask in optical systems to perform wavefront coding which, along with digital post-processing can extend the depth of focus of standard optical imaging systems [1, 2]. Experimental images have demonstrated an increase of six to eight times the depth of focus of standard systems when using the extended depth of focus technology. This technology is now being extended to high magnification or light microscope systems. Several challenges have arisen due to the special nature of light microscope systems but extended depth of focus (EDF) technology is still found to be useful in such systems.
{"title":"Applications of extended depth of focus technology to light microscope systems","authors":"S. Bradburn, W. Cathey, E. Dowski","doi":"10.1364/srs.1998.stue.3","DOIUrl":"https://doi.org/10.1364/srs.1998.stue.3","url":null,"abstract":"Previous research has demonstrated the success of using a cubic phase mask in optical systems to perform wavefront coding which, along with digital post-processing can extend the depth of focus of standard optical imaging systems [1, 2]. Experimental images have demonstrated an increase of six to eight times the depth of focus of standard systems when using the extended depth of focus technology. This technology is now being extended to high magnification or light microscope systems. Several challenges have arisen due to the special nature of light microscope systems but extended depth of focus (EDF) technology is still found to be useful in such systems.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129510365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we describe several signal reconstruction problems that arise during the determination of the 3D structure of so-called spherical viruses. Spherical viruses are viruses with a shell of protein (the capsid) surrounding an inner core of nucleic acid. The capsid is “crystalline” in the sense that it is constructed from many repetitions of the same polypeptides and the entire capsid is invariant under some rotational symmetry, often the rotational symmetry of the icosahedron which is the case we focus on. The icosahedron is constructed from 20 equilateral triangles and has 60 rotational symmetries: a 5-fold axis where 5 triangles meet, a 3-fold axis through the center of each triangle, and a 2-fold axis at the midpoint of each edge between two triangles. A typical outer radius of the capsid is in the range 102-103Å.
{"title":"3D reconstruction problems for cryo electron microscopy of viruses","authors":"Wen Gao, P. Doerschuk","doi":"10.1364/srs.1998.swa.4","DOIUrl":"https://doi.org/10.1364/srs.1998.swa.4","url":null,"abstract":"In this paper we describe several signal reconstruction problems that arise during the determination of the 3D structure of so-called spherical viruses. Spherical viruses are viruses with a shell of protein (the capsid) surrounding an inner core of nucleic acid. The capsid is “crystalline” in the sense that it is constructed from many repetitions of the same polypeptides and the entire capsid is invariant under some rotational symmetry, often the rotational symmetry of the icosahedron which is the case we focus on. The icosahedron is constructed from 20 equilateral triangles and has 60 rotational symmetries: a 5-fold axis where 5 triangles meet, a 3-fold axis through the center of each triangle, and a 2-fold axis at the midpoint of each edge between two triangles. A typical outer radius of the capsid is in the range 102-103Å.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133556928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
“A wave is something that obeys the wave equation”. In the spirit of this statement, the triple correlation is indeed a wave. We will derive now this wave Then we will study the properties of triple correlation waves, and finally we will contemplate about application.
{"title":"Triple Correlation Waves","authors":"A. Lohmann, D. Mendlovic, G. Shabtay","doi":"10.1364/srs.1998.swb.5","DOIUrl":"https://doi.org/10.1364/srs.1998.swb.5","url":null,"abstract":"“A wave is something that obeys the wave equation”. In the spirit of this statement, the triple correlation is indeed a wave. We will derive now this wave Then we will study the properties of triple correlation waves, and finally we will contemplate about application.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130869075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the seismic tomography problem, the subsurface slowness distribution is estimated from the travel-times computed along generally curved rays. For a dense and uniform set of rays, the slowness distribution will be correctly reconstructed. However, for an uneven distribution of rays, the estimated slowness distribution may be influenced by the ray configuration.
{"title":"Variable damping in seismic tomography based on ray coverage","authors":"R. Nowack","doi":"10.1364/srs.1998.stha.2","DOIUrl":"https://doi.org/10.1364/srs.1998.stha.2","url":null,"abstract":"In the seismic tomography problem, the subsurface slowness distribution is estimated from the travel-times computed along generally curved rays. For a dense and uniform set of rays, the slowness distribution will be correctly reconstructed. However, for an uneven distribution of rays, the estimated slowness distribution may be influenced by the ray configuration.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126654366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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