We further develop a modeling and reconstruction framework, based on modelbased compressed sensing, which characterizes a large variety of depth sensing systems. Compressive imaging spectrometers using coded apertures. It places a coded aperture in front of an xray source. A coded aperture compressive imaging array and its visual. The energy of each source is modulated by means of a coded aperture. Coded aperture compressive temporal imaging patrick llull, xuejun liao, xin yuan, jianbo yang, david kittle. Light field compressed sensing over a disparityaware. In contrast, the application of compressive sensing cs to hyperspectral images is an active area of research over the past few years, both in terms of the hardware and the signal processingalgorithms7,wheretheacquisitionofthedatain an already compressed form is involved. This system can visualize the source distribution using the detector pattern from incident radiation, and performs spectroscopy for incoming radiation. A spectral imager provides a 3d data cube in which the spatial information 2d of the image is comple mented by spectral information 1d a bout each spatial location. T, where m is the spatial dimension of such a patch and t is the spectral dimension. We perform coded sampling on these patches and obtain the coded snapshots which may or may not be further jpeg2000 compressed.
Coded aperture imaging seminal work in coded aperture imaging includes the development of masks based on hadamard transform optics 32 and pseudorandom phase masks 33. In this paper we propose a new depth sensing archi tecture that exploits a fixed coded aperture to significantly reduce the number of sensors compared to. Compressive sensing of signals from a gmm with sparse precision matrices. Compressed sensing solves the underdetermined data cube estimation problem by relying on a crucial property of natural scenes, namely, that they tend to be sparse on some multiscale basis.
High spatiotemporal resolution video with compressed sensing roman koller,1 lukas schmid,1 nathan matsuda,2 thomas niederberger,1 leonidas spinoulas,2 oliver cossairt,2. The measurements are manifested as a superposition of the coded wavelength. In this study, in order to improve this tradeoff, we propose a method combining a random coded aperture and compressed sensing image reconstruction. In typical compressive sensing scenarios, the code can be. Coded aperture cameras have traditionally been used for imaging wavelengths beyond the visible spectrum e. This paper proposes an adaptive grayscale coded aperture design which combines the advantages of blue noise and blockunblock coding patterns. In particular, several architectures 4, 5, 6 exploit digital micromirror devices dmd or other spatial light modulators slm to create a coded aperture that can be modi. The sensing matrix structure must facilitate fast reconstruction algorithms. Compressive sensing dictates that the number of measurements must be in excess of slog. Parallel hyperspectral coded aperture for compressive sensing. Parallel hyperspectral coded aperture for compressive.
Coded aperture design by uniform sensing in compressive x. Spatiotemporal compressed sensing with coded apertures. While xray tomography is the canonical example, reference structure tomography rst and coded aperture snapshot spectral imaging cassi are examples of physically unrelated but mathematically equivalent. Golub1, amir averbuch2, menachem nathan1, valery a. However, recent advances in the fields of image reconstruction, inverse problems, and compressed sensing indicate that substantial performance gains may be possible in many contexts via computational methods. Zheludev2, jonathan hauser1, shay gurevitch1, roman malinsky1 and.
Single disperser design for coded aperture snapshot. Coded aperture computed tomography coded aperture computed tomography choi, kerkil 20090820 00. Compressed sensing snapshot spectral imaging by a regular. We then describe how cs leads to a new, optimal coded aperture design, and how these coded apertures can be used in conjunction with subframe superimposition to increase both video resolution and. Contributions the primary contribution of this paper is the design and theoretical characterization of compressive coded aperture keyed exposure cake sensing. Bioucasdias 2 and antonio plaza 1 1 hyperspectral computing laboratory, department of technology of computers and communications. Random gaussian, toeplitz and binary phase coded masks are utilized to obtain the compressive sensing images. The purpose of this work is to introduce and study a novel imaging geometry for xray luminescence. However, applying compressed sensing theory to practical imaging systems poses a key challenge. Assuming the side length of the detector spans an integer number of coded aperture features, the horizontal and vertical spatial superresolution are thus limited by. For the design of highresolution apertures, let us define a 1. Mixing spacetime derivatives for video compressive sensing.
Bioucasdias 2 and antonio plaza 1 1 hyperspectral computing laboratory, department of technology of computers and communications, universityof extremadura, e10071 caceres, spain. Coded aperture compressive temporal imaging semantic scholar. In recent years, coded aperture based systems using compressive sensing principles. We use mechanical translation of a coded aperture for code division multiple access compression of video. On the basis of this approach, it is envisioned that realtime 26 fps thz. Compressive coded aperture imaging compressive coded aperture imaging marcia, roummel f.
Cassi and cacti share identical mathematical forward models. Coded hyperspectral imaging and blind compressive sensing. Optical systems which measure independent random projections of a scene according to compressed sensing cs theory face a myriad of practical challenges. The coded aperture enables spatial compression on the order of the size of the code feature relative to the detector pixel pitch.
Codedaperture compressed sensing xray luminescence. Mcnppolimi simulation for the compressedsensing based reconstruction in a codedaperture imaging cai extended to partiallycoded fieldofview. Index termscompressive sensing, coded apertures, convex optimization, sparsity, coded exposure, toeplitz matrices. High spatiotemporal resolution video with compressed sensing. Coded aperture computed tomography, proceedings of spie. Highresolution codedaperture design for compressive x. This theory indicates that, when feasible, judicious selection of the type of distortion induced by. Compression is done by employing coded aperture imaging on a given hyperspectral datacube. Gehm duke university fitzpatrick center for photonics, durham, nc, 27708 abstract a spectral imager provides a 3d data cube in which the spatial information 2d of the image is complemented by spectral information 1d a bout each spatial location. The coded aperture snapshot spectral imager cassi,1618 is a popular compressive spectral imager and acquires image data from different wavelengths simultaneously. Compressive coded aperture imaging, proceedings of spie. Highresolution codedaperture design for compressive xray tomography using low resolution detectors. Request pdf codedaperture compressed sensing xray luminescence tomography objective.
These techniques facilitate the analysis of the imaging model based only on geometric optics. First,thenumberofcompressivemeasurements in cassi may not meet the minimum needed for adequate reconstruction. Compressive coded aperture spectral imaging ececis. Interleaving and sparse random coded aperture for lens. A parallel coded aperture compressive imaging system is proposed to reduce the needed high resolution coded mask requirements and facilitate the storage of the projection matrix. Dispersion through a grating or prism shifts spectral planes after coded aperture modulation. Coded aperture compressive 3d lidar kadambi, a boufounos, p. In contrast to traditional imaging, computational imaging systems involve a tight integration of the sensing system and the computation in order to form the images of interest. This approach relies on recentlydeveloped concepts in compressive sensing. Sensors free fulltext a coded aperture compressive. Tr2015028 april 2015 abstract continuous improvement in optical sensing components, as well as recent advances in signal acquisition theory provide a great opportunity to reduce the cost and enhance the capabilities of depth sensing systems. Compressive coded aperture keyed exposure imaging with. This is what gives us a very light and low complexity compression routine.
Blue noise coding patterns are optimal and provide highquality image reconstructions on regions of nonsaturated compressed pixels. Coded aperture compressive temporal imaging duke university. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by. In addition, an iterative reconstruction algorithm based on compressedsensing cs. Coded apertures reconstruction algorithms coded aperture imaging matrices compressed sensing image resolution. Optimal coded aperture design according to the cs theory, the sensing matrix that maps the hsi to the compressive image in cassi plays a crucial role in the reconstruction quality. Onboard hyperspectral image compression using compressed sensing and deep learning. Pdf coded aperture design for compressive spectral subspace. Coded aperture optimization for compressive xray tomosynthesis. Single disperser design for coded aperture snapshot spectral imaging ashwin wagadarikar, renu john, rebecca willett, and david brady.
Feb 05, 2009 compressive coded aperture imaging compressive coded aperture imaging marcia, roummel f. Compressive imaging spectrometers using coded apertures d. In particular, the sinogram form is obtained by rearranging t as 2dimensional array according to the number of detectors. Compressed sensing cs reconstruction algorithms are then used to reconstruct the underlying spectral 3d data cube from an underdetermined system of linear equations. Single disperser design for coded aperture snapshot spectral. Index termscompressive spectral imaging, coded aperture. Compressed sensing, coded aperture, sparse recovery, wavelets. Compressive sensing, coded aperture, sparse recovery, modelbased sparsity, wavelets 1. It places a coded aperture in front of an xray source in order to obtain 2d patterned projections of a threedimensional object onto a detector plane. Computational imaging is the process of indirectly forming images from measurements using algorithms that rely on a significant amount of computing.
In contrast to previous approaches, we aim at designing apertures to be used with lowresolution detectors in order to. Spatial superresolution in coded aperture based optical. We discuss the compressed videos temporal resolution and present experimental results for reconstructions of 10 frames of temporal data per coded snapshot. In 8, a constrained hyperspectral coded aperture chyca method is. Highly compressed measurements structured sensing matrix large signal dimension need fast algorithm. Compressive coded apertures for highresolution imaging roummel f. Multishot coded aperture snapshot spectral imaging cassi systems capture the spectral information of a scene using a small set of coded focal plane array fpa compressive measurements.
Assuming the side length of the detector spans an integer number of coded aperture features, the horizontal and vertical spatial super. Osa coded aperture optimization for compressive xray. Random structures for the coded apertures have been proposed before, however they operate poorly in exploiting the inherent projection patterns proper of the system. Applying this method, statistical noise can be suppressed compared with conventional methods using parallel collimators, and it is expected that scan time or radiation exposure is reduced. Parallel hyperspectral coded aperture for compressive sensing on gpus abstract. Spatiotemporal blue noise coded aperture design for multi. Compressed sensing cs reconstruction algorithms are then used to recover the threedimensional data cube. Compressed sensing also known as compressive sensing, compressive sampling, or sparse sampling is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. Because the number of required measurements is greatly reduced from traditional. In this paper we propose a new depth sensing architecture that exploits a fixed coded aperture to significantly reduce the number of sensors compared to conventional systems. Compressed sensing, coded aperture, sparse recovery, wavelets 1. For the other schemes that use compressed sensing such as applying sparsity in total variation of the image 42, frequency domain 5 and codedaperture xray luminescence tomography 2, our. Compressed sensing snapshot spectral imaging by a regular digital camera with an added optical diffuser michael a. This paper demonstrates that compressive coded aperture keyed exposure systems achieve all these objectives.
Gehm duke university fitzpatrick center for photonics, durham, nc, 27708. Relying on compressive sensing, spectral image reconstruction is achieved by. The depth of a scene can then be acquired using a single detector and adc by transmitting multiple. Coded aperture imaging seminal work in coded aperture imaging includes the development of masks based on hadamard transform optics 29 and pseudorandom phase masks 30. Approximate message passing in coded aperture snapshot spectral imaging. The application of compressive sensing cs to hyperspectral images is an active area of research over the past few years, both in terms of the hardware and the signal processing algorithms. Compressed sensing is applied to recover the coded image by coded aperture, and a physical prototype is developed to examine the proposed techniques. Compressive coded apertures for highresolution imaging. Spatiotemporal compressed sensing with coded apertures and. Osa spatiotemporal blue noise coded aperture design for.
A new technique for hyperspectral compressive sensing gabriel mart. A 256 256 cmos image sensor with dsbased singleshot compressed sensing. Approximate message passing in coded aperture snapshot. Highresolution codedaperture design for compressive xray. Parallel hyperspectral coded aperture for compressive sensing on gpus article in ieee journal of selected topics in applied earth observations and remote sensing 92. The measurements are manifested as a superposition of the coded wavelengthdependent data, with the ambient threedimensional hyperspectral datacube mapped to a twodimensional measurement.
For the other schemes that use compressed sensing such as applying sparsity in total variation of the image 42, frequency domain 5 and coded aperture xray luminescence tomography 2, our. Blind compressive sensing cs is considered for reconstruction of hyperspectral data imaged by a coded aperture camera. Compressive sensing image sensorshardware implementation. Similar to other compressive sensing problems, the linear system x af is underdetermined since there are much fewer measurements than unknown variables. The main contributions of this research can be summarized in the following three aspects. Onboard hyperspectral image compression using compressed. Light field compressed sensing over a disparityaware dictionary. Tr2015028 april 2015 abstract continuous improvement in optical sensing components, as well as recent advances in signal acquisition theory provide a great opportunity to reduce the cost and. Traditionally, optical sensors have been designed to collect the most directly interpretable and intuitive measurements possible. To achieve compressive spectral imaging, our group has developed a new class of imagers dubbed the coded aperture snapshot spectral imager cassi. Compressed sensing cs reconstruction algorithms are then used to reconstruct the underlying spectral 3d data cube from an underde. Radiation dose is a concern in xray tomographic imaging.
Katsaggelos2 1 university of applied sciences of eastern switzerland, oberseestrasse 10, ch8640, rapperswil, switzerland. Here we demonstrate coded aperture compressive temporal imaging cacti. Request pdf parallel hyperspectral coded aperture for compressive sensing on gpus the application of compressive sensing cs to hyperspectral images is an active area of research over the. By using different coded apertures in a multiple source system, multiplexed projections can be. Mcnppolimi simulation for the compressedsensing based. Decompression from this kind of sparse acquisition of data is typically. Coded aperture imaging cai, one of the techniques developed for this purpose, was introduced in the fields of xray cameras and space telescopes. A set of directional wavelet transforms are used for the reconstruction to exploit the sparsity in the angular domain. Single disperser design for coded aperture snapshot spectral imaging ashwin wagadarikar, renu john, rebecca willett, and david brady department of electrical and computer engineering, duke university, durham, north carolina 27708, usa. Photoinduced codedaperture imaging picai based on compressed sensing cs at 590 ghz using a wr1. This paper tackles the problem of designing highresolution coded apertures for compressed sensing computed tomography.
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