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Register a new userA Compressed Sensing-based Image Reconstruction Algorithm for Solar Flare X-Ray Observations
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One way of imaging X-ray emission from solar flares is to measure Fourier components of the spatial X-ray source distribution. We present a new Compressed Sensing-based algorithm named VIS_CS, which reconstructs the spatial distribution from such Fourier components. We demonstrate the application of the algorithm on synthetic and observed solar flare X-ray data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite and compare its performance with existing algorithms. VIS_CS produces competitive results with accurate photometry and morphology, without requiring any algorithm- and X-ray source-specific parameter tuning. Its robustness and performance make this algorithm ideally suited for generation of quicklook images or large image cubes without user intervention, such as for imaging spectroscopy analysis.
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We describe two inversion methods for the reconstruction of hard X-ray solar images. The methods are tested against experimental visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and synthetic visibilities based on the design of the Spectrometer/Telescope for Imaging X-rays (STIX).
We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurements of the string signal, which exhibits sparse or compressible magnitude of the gradient due to the Kaiser-Stebbins (KS) effect. In this context the versatile framework of compressed sensing naturally applies for solving the corresponding inverse problem. Our algorithm notably takes advantage of a model of the prior statistical distribution of the signal fitted on the basis of realistic simulations. Enhanced performance relative to the standard CLEAN algorithm is demonstrated by simulated observations under noise conditions including primary and secondary CMB anisotropies.
We present an analysis of soft X-ray (SXR) and extreme-ultraviolet (EUV) observations of solar flares with an approximate C8 GOES class. Our constraint on peak GOES SXR flux allows for the investigation of correlations between various flare parameters. We show that the the duration of the decay phase of a flare is proportional to the duration of its rise phase. Additionally, we show significant correlations between the radiation emitted in the flare rise and decay phases. These results suggest that the total radiated energy of a given flare is proportional to the energy radiated during the rise phase alone. This partitioning of radiated energy between the rise and decay phases is observed in both SXR and EUV wavelengths. Though observations from the EVE show significant variation in the behavior of individual EUV spectral lines during different C8 events, this work suggests that broadband EUV emission is well constrained. Furthermore, GOES and AIA data, allow us to determine several thermal parameters (e.g. temperature, volume, density, and emission measure) for the flares within our sample. Analysis of these parameters demonstrate that, within this constrained GOES class, the longer duration solar flares are cooler events with larger volumes capable of emitting vast amounts of radiation. The shortest C8 flares are typically the hottest events, smaller in physical size, and have lower associated total energies. These relationships are directly comparable with several scaling laws and flare loop models.
Modern image and video compression codes employ elaborate structures existing in such signals to encode them into few number of bits. Compressed sensing recovery algorithms on the other hand use such signals structures to recover them from few linear observations. Despite the steady progress in the field of compressed sensing, structures that are often used for signal recovery are still much simpler than those employed by state-of-the-art compression codes. The main goal of this paper is to bridge this gap through answering the following question: Can one employ a given compression code to build an efficient (polynomial time) compressed sensing recovery algorithm? In response to this question, the compression-based gradient descent (C-GD) algorithm is proposed. C-GD, which is a low-complexity iterative algorithm, is able to employ a generic compression code for compressed sensing and therefore elevates the scope of structures used in compressed sensing to those used by compression codes. The convergence performance of C-GD and its required number of measurements in terms of the rate-distortion performance of the compression code are theoretically analyzed. It is also shown that C-GD is robust to additive white Gaussian noise. Finally, the presented simulation results show that combining C-GD with commercial image compression codes such as JPEG2000 yields state-of-the-art performance in imaging applications.
This paper shows that compressed sensing realized by means of regularized deconvolution and the Finite Isotropic Wavelet Transform is effective and reliable in hard X-ray solar imaging. The method utilizes the Finite Isotropic Wavelet Transform with Meyer function as the mother wavelet. Further, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. The method is applied against both synthetic data mimicking the Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are compared with the results provided by standard visibility-based reconstruction methods. The results show that the application of the sparsity constraint and the use of a continuous, isotropic framework for the wavelet transform provide a notable spatial accuracy and significantly reduce the ringing effects due to the instrument point spread functions.
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