Denoising with Three Dimensional Fourier Transform for Three Dimensional Images, Including Image Sequences

A method of mitigating noise in source image data representing pixels of a 3-D image. The "3-D image" may be any type of 3-D image, regardless of whether the third dimension is spatial, temporal, or some other parameter. The 3-D image is divided into three-dimensional chunks of pixels. These chunks are apodized and a three-dimensional Fourier transform is performed on each chunk, thereby producing a three-dimensional spectrum of each chunk. The transformed chunks are processed to estimate a noise floor based on spectral values of the pixels within each chunk. A noise threshold is then determined, and the spectrum of each chunk is filtered with a denoising filter based on the noise threshold. The chunks are then inverse transformed, and recombined into a denoised 3-D image

Solar Magnetic Tracking. IV. The Death of Magnetic Features

The removal of magnetic flux from the quiet-sun photosphere is important for maintaining the statistical steady-state of the magnetic field there, for determining the magnetic flux budget of the Sun, and for estimating the rate of energy injected into the upper solar atmosphere. Magnetic feature death is a measurable proxy for the removal of detectable flux. We used the SWAMIS feature tracking code to understand how nearly 20000 detected magnetic features die in an hour-long sequence of Hinode/SOT/NFI magnetograms of a region of quiet Sun. Of the feature deaths that remove visible magnetic flux from the photosphere, the vast majority do so by a process that merely disperses the previously-detected flux so that it is too small and too weak to be detected. The behavior of the ensemble average of these dispersals is not consistent with a model of simple planar diffusion, suggesting that the dispersal is constrained by the evolving photospheric velocity field. We introduce the concept of the partial lifetime of magnetic features, and show that the partial lifetime due to Cancellation of magnetic flux, 22 h, is 3 times slower than previous measurements of the flux turnover time. This indicates that prior feature-based estimates of the flux replacement time may be too short, in contrast with the tendency for this quantity to decrease as resolution and instrumentation have improved. This suggests that dispersal of flux to smaller scales is more important for the replacement of magnetic fields in the quiet Sun than observed bipolar cancellation. We conclude that processes on spatial scales smaller than those visible to Hinode dominate the processes of flux emergence and cancellation, and therefore also the quantity of magnetic flux that threads the photosphere.Comment: Accepted by Ap

Solar Polar Spicules Observed with Hinode

We examine solar polar region spicules using high-cadence Ca II data from the Solar Optical Telescope (SOT) on the Hinode spacecraft. We sharpened the images by convolving them with the inverse-point-spread function of the SOT Ca II filter, and we are able to see some of the spicules originating on the disk just inside the limb. Bright points are frequently at the root of the disk spicules. These "Ca II brightenings" scuttle around at approx.few x 10 km/s, live for approx.100 sec, and may be what are variously known as "H_{2V} grains," "K_{2V} grains," or "K_{2V} bright points." When viewed extending over the limb, some of the spicules appear to expand horizontally or split into two or more components, with the horizontal expansion or splitting velocities reaching approx.50 km/s. This work was funded by NASA's Science Mission Directorate through the Living With a Star Targeted Research and Technology Program, the Supporting Research and Program, the Heliospheric Guest Investigator Program, and the Hinode project

Three-polarizer Treatment of Linear Polarization in Coronagraphs and Heliospheric Imagers

Linearly polarized light has been used to view the solar corona for over 150 years. While the familiar Stokes representation for polarimetry is complete, it is best matched to a laboratory setting and therefore is not the most convenient representation either for coronal instrument design or for coronal data analysis. Over the last 100 years of development of coronagraphs and heliospheric imagers, various representations have been used for both direct measurement and analysis. These systems include famous representations such as the (B, pB) system, which is analogous to the Stokes system in solar observing coordinates, and also internal representations such as in-instrument Stokes parameters with fixed or variable "vertical" direction, and brightness values through a particular polarizing optic or set thereof. Many polarimetric instruments currently use a symmetric three-polarizer measurement and representation system (which we refer to as "(M, Z, P)") to derive the (B, pB) or Stokes parameters. We present a symmetric derivation of (B, pB) and Stokes parameters from (M, Z, P), analyze the noise properties of (M, Z, P) in the context of instrument design, develop (M, Z, P) as a useful intermediate system for data analysis including background subtraction, and draw a helpful analogy between linear polarimetric systems and the large existing body of work on photometric colorimetry. &nbsp;</p

Square Root Compression and Noise Effects in Digitally Transformed Images

We report on a particular example of noise and data representation interacting to introduce systematic error into scientific measurements. Many instruments collect integer digitized values and apply nonlinear coding, in particular square root coding, to compress the data for transfer or downlink; this can introduce surprising systematic errors when they are decoded for analysis. Square root coding and subsequent decoding typically introduces a variable &plusmn;1 count value-dependent systematic bias in the data after reconstitution. This is significant when large numbers of measurements (e.g., image pixels) are averaged together. Using direct modeling of the probability distribution of particular coded values in the presence of instrument noise, one may apply Bayes' theorem to construct a decoding table that reduces this error source to a very small fraction of a digitizer step; in our example, systematic error from square root coding is reduced by a factor of 20 from 0.23 to 0.012 count rms. The method is suitable both for new experiments such as the upcoming PUNCH mission, and also for post facto application to existing data sets&mdash;even if the instrument noise properties are only loosely known. Further, the method does not depend on the specifics of the coding formula, and may be applied to other forms of nonlinear coding or representation of data values. &nbsp;</p

Measurement of Stresses in Fixed-Bridge Restorations Using a Brittle Coating Technique

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67230/2/10.1177_00220345650440042201.pd