Blind Reconstruction Method Research Articles

Challenges of reliable AFM-tip shape reconstruction and approximation.

Reliable reconstruction of AFM tip geometry is not an easy task. The shape of the tip can be (partially) reconstructed from the AFM image of a calibration sample using a blind reconstruction method. The result is a range of the tip shapes (from unrealistically sharp to blunt). A criterion for selecting the true shape is proposed. It is based on reconstruction of the calibration relief. Further refining the probe geometry by indenting an elastic polymer is discussed. The choice of the test sample is another problem. In practice, the researcher has a small number of commercially available test gratings. Their limitations are highlighted. An approximation of tip geometry by a body of revolution is required in indentation experiments. A hyperboloid was found to be the closest approximation to the conventional probes. The contact area was obtained for the hyperboloids with different parameters indenting an elastic material. RESEARCH HIGHLIGHTS: Criteria for blind reconstruction algorithm of AFM tip shape. Pros and cons of tip shape calibration samples. Contact area of the elastic indentation by hyperbolic indenter.

Joint blind reconstruction of cyclic codes and self‐synchronous scramblers

AbstractThe inverse analysis of the intercepted signals to reconstruct the communication scheme used by the transmitter is a key problem in the non‐cooperative context. In this paper, the problem of blind reconstruction of cyclic codes and self‐synchronous scramblers is considered. There is no existing solution to this problem. To solve this problem, a joint blind reconstruction method for cyclic codes and self‐synchronous scramblers is proposed in this paper. A lemma is proposed and proved theoretically that the maximum common factor of the inverse polynomial of the polynomial form of the dual vectors of the self‐synchronous scrambled bit matrix is the product of the parity polynomial of the cyclic code and the feedback polynomial of the self‐synchronous scrambler. Using this lemma, the joint blind reconstruction of the cyclic code and the self‐synchronous scrambler is completed. Finally, a Gaussian elimination based on random column exchange and soft information (GERCESI) method is proposed, which can apply the proposed method to a noisy environment. Simulations prove that the fault‐tolerance performance of the GERCESI method proposed in this paper is at least 0.5 dB higher than that of the GJETP method.

End-to-end differentiable blind tip reconstruction for noisy atomic force microscopy images

Observing the structural dynamics of biomolecules is vital to deepening our understanding of biomolecular functions. High-speed (HS) atomic force microscopy (AFM) is a powerful method to measure biomolecular behavior at near physiological conditions. In the AFM, measured image profiles on a molecular surface are distorted by the tip shape through the interactions between the tip and molecule. Once the tip shape is known, AFM images can be approximately deconvolved to reconstruct the surface geometry of the sample molecule. Thus, knowing the correct tip shape is an important issue in the AFM image analysis. The blind tip reconstruction (BTR) method developed by Villarrubia (J Res Natl Inst Stand Technol 102:425, 1997) is an algorithm that estimates tip shape only from AFM images using mathematical morphology operators. While the BTR works perfectly for noise-free AFM images, the algorithm is susceptible to noise. To overcome this issue, we here propose an alternative BTR method, called end-to-end differentiable BTR, based on a modern machine learning approach. In the method, we introduce a loss function including a regularization term to prevent overfitting to noise, and the tip shape is optimized with automatic differentiation and backpropagations developed in deep learning frameworks. Using noisy pseudo-AFM images of myosin V motor domain as test cases, we show that our end-to-end differentiable BTR is robust against noise in AFM images. The method can also detect a double-tip shape and deconvolve doubled molecular images. Finally, application to real HS-AFM data of myosin V walking on an actin filament shows that the method can reconstruct the accurate surface geometry of actomyosin consistent with the structural model. Our method serves as a general post-processing for reconstructing hidden molecular surfaces from any AFM images. Codes are available at https://github.com/matsunagalab/differentiable_BTR.

Blind Reconstruction of BCH and RS Codes Using Single-Error Correction

In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments. The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream. However, they need to have sufficiently correct codewords for successful reconstruction. Therefore, the existing methods are highly dependent on the channel conditions because a sufficient number of correct codewords should be available for achieving good reconstruction performance. To overcome such high dependency on channel conditions, the proposed blind reconstruction method performs error correction of single-error codewords through the proposed single-error correction method (SCM). Then, both the correct codewords and the corrected single-error codewords are utilized for blind reconstruction. Specifically, the correct codewords are selected based on the algebraic property of BCH and RS codes that codeword polynomials have consecutive roots. At the same time, the codewords presumably with a single error are selected and corrected based on the fact that the most of BCH and RS codeword polynomials with either a single error or double errors do not have consecutive roots. Based on this fact, SCM is devise, which selects and corrects the codewords with a single error with high probability. Finally, it is verified that the proposed blind reconstruction method shows much better reconstruction performance by using only one-tenth of the received codewords compared to the existing best methods even under harsh channel conditions.

Analysis of Blind Reconstruction of BCH Codes.

In this paper, the theoretical lower-bound on the success probability of blind reconstruction of Bose–Chaudhuri–Hocquenghem (BCH) codes is derived. In particular, the blind reconstruction method of BCH codes based on the consecutive roots of generator polynomials is mainly analyzed because this method shows the best blind reconstruction performance. In order to derive a performance lower-bound, the theoretical analysis of BCH codes on the aspects of blind reconstruction is performed. Furthermore, the analysis results can be applied not only to the binary BCH codes but also to the non-binary BCH codes including Reed–Solomon (RS) codes. By comparing the derived lower-bound with the simulation results, it is confirmed that the success probability of the blind reconstruction of BCH codes based on the consecutive roots of generator polynomials is well bounded by the proposed lower-bound.

Two-photon image-scanning microscopy with SPAD array and blind image reconstruction.

Two-photon excitation (2PE) laser scanning microscopy is the imaging modality of choice when one desires to work with thick biological samples. However, its spatial resolution is poor, below confocal laser scanning microscopy. Here, we propose a straightforward implementation of 2PE image scanning microscopy (2PE-ISM) that, by leveraging our recently introduced single-photon avalanche diode (SPAD) array detector and a novel blind image reconstruction method, is shown to enhance the effective resolution, as well as the overall image quality of 2PE microscopy. With our adaptive pixel reassignment procedure ∼1.6 times resolution increase is maintained deep into thick semi-transparent samples. The integration of Fourier ring correlation based semi-blind deconvolution is shown to further enhance the effective resolution by a factor of ∼2 - and automatic background correction is shown to boost the image quality especially in noisy images. Most importantly, our 2PE-ISM implementation requires no calibration measurements or other input from the user, which is an important aspect in terms of day-to-day usability of the technique.

Asymptotic Analysis of Blind Reconstruction of BCH Codes Based on Consecutive Roots of Generator Polynomials

In the military surveillance and security information systems, correct blind reconstruction of signal parameters from unknown signals is very important. Especially, many blind reconstruction methods of error-correcting codes have been proposed, and their theoretical performance analysis is essential for both the defender who wants to prevent information leakage and the challenger who wants to extract information from the intercepted signals. However, a proper performance analysis of most blind reconstruction methods has not been performed yet. Among many blind reconstruction methods of BCH codes proposed so far, the blind reconstruction method based on consecutive roots of generator polynomials proposed by Jo, Kwon, and Shin, called the JKS method, shows the best performance under the unknown channel information. However, the performance of the JKS method is only evaluated through simulation without performing theoretical analysis. In this paper, the JKS method is asymptotically analyzed under the binary symmetric channel with the cross-over probability $p$ . Since the blind reconstruction performance heavily depends on how many and which received codewords are used even for the same channel environment, sufficiently many codewords are assumed to perform asymptotic analysis. More specifically, an asymptotic threshold on $p$ , up to which blind reconstruction is successful, is derived when the number of received codewords is sufficiently large, which can be used as a new performance metric for blind reconstruction methods. Finally, the validity of the asymptotic analysis is confirmed through simulation.

Properties of syndrome distribution for blind reconstruction of cyclic codes

In the problem of blind reconstruction of channel codes, the receiver does not have the knowledge of the channel code used at the transmitter and the aim is to identify this unknown code from the received data. For the case of cyclic codes, typical blind reconstruction methods make use of some elementary properties of syndromes (remainders) of the received polynomials. The main aim of this paper is to provide a detailed analysis of the properties of the syndromes that could be useful to design more efficient blind reconstruction methods. Specifically, we prove that the syndrome distribution of the noise-free sequence can be either degenerate or uniform or restricted uniform. We also provide necessary and sufficient conditions for the syndrome distribution to be of a given type. For the noise-affected received sequence we identify additional structural properties exhibited by the syndrome distribution. Finally, we apply these results to analyze the performance of the existing blind reconstruction methods.

Efficient Blind Signal Reconstruction With Wavelet Transforms Regularization for Educational Robot Infrared Vision Sensing

Fourier transform infrared (FTIR) imaging spectrometers are often corrupted by the problems of band overlap and random noise during the infrared spectrum acquisition process. Such noise would degrade the quality of the acquired infrared spectrum, limiting the precision of the subsequent processing. In this paper, we present a novel blind reconstruction method with wavelet transform regularizations for infrared spectrum obtained from the aging instrument. Inspired by the finding that the wavelet coefficient distribution of the clean spectrum is sparser than that of the degraded spectrum, a blind reconstruction model for infrared spectrum is proposed in this paper to regularize the distribution of the degraded spectrum by total variation regularization. This method outperforms when suppressing random noise and preserving the spectral structure details. In addition, an effective optimization scheme is introduced in overcoming the issue of formulated optimization. The instrument response function and latent spectrum can be simultaneously estimated through the proposed method that can efficiently mitigate the effects caused by instrument degradation. Finally, extensive experiments on simulated and real noisy infrared spectra are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones. Thus, the reconstructed spectrum will better serve the feature extraction and educational robot infrared vision sensing in industrial applications.

Self-Adaptive Grinding for Blind Tip Reconstruction of AFM Diamond Probe

Blind tip reconstruction (BTR) method is one of the favorable methods to estimate the atomic force microscopy (AFM) probe shape. The exact shape of the characterizer is not required for BTR, while the geometry of the sample may affect the reconstruction significantly. A cone-shaped array sample was chosen as a characterizer to be evaluated. The target AFM probe to be reconstructed was a diamond triangular pyramid probe with two feature angles, namely front angle (FA) and back angle (BA). Four conical structures with different semi-angles were dilated by the pyramid probe. Simulation of scanning process demonstrates that it is easy to judge from the images of the isolated rotary structure, cone-shaped, the suitability of the sample to be a tip characterizer for a pyramid probe. The cone-shaped array sample was repeatedly scanned 50 times by the diamond probe using an AFM. The series of scanning images shrank gradually and more information of the probe was exhibited in the images, indicating that the characterizer has been more suitable for BTR. The feature angle FA of the characterizer increasingly reduces during the scanning process. A self-adaptive grinding between the probe and the characterizer contributes to BTR of the diamond pyramid probe.

Blind Reconstruction of BCH Codes Based on Consecutive Roots of Generator Polynomials

In this letter, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed, which uses the property that all the codeword polynomials of a $t$ -error correcting BCH code have the same $2t$ consecutive roots over Galois field. The proposed method inherently eliminates most of the erroneous codewords from the received codewords by utilizing the information about the starting position and length of consecutive roots of each received codeword. Therefore, the blind reconstruction performance is substantially improved and the simulation results confirm that the proposed method outperforms other blind reconstruction methods.

Double regularization medical CT image blind restoration reconstruction based on proximal alternating direction method of multipliers

To solve the problem of CT image degradation, a double regularization CT image blind restoration reconstruction method was proposed. The objective function including both a clear image and point spread function was established. To avoid the over-smoothing phenomenon and protect the detail, the objective function includes two constraint regularization terms. They are total variation (TV) and wavelet sparsity respectively. The objective function was solved by the alternating direction multiplier method (ADMM), and the optimal solution was obtained. Firstly, the CT image blind restoration reconstruction was decomposed into two sub-problems: reconstructed image estimation and point spread function estimation. Furthermore, each sub-problem can be solved by the proximal alternating direction method of multipliers. Finally, the CT image blind restoration reconstruction was realized. The experimental results show that the proposed algorithm takes into account the degradation effect of projection data, and the proposed algorithm is superior to other existing algorithms in the subjective visual effect. At the same time, in the aspect of objective evaluation, the proposed algorithm improves the objective image quality metrics such as peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and universal image quality index (UIQI).

Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion

Full waveform inversion (FWI) reconstructs the underground velocity structures by minimizing the data residual between calculated wavefields and observed wavefileds. The conventional FWI usually uses some local optimization algorithms which lead to a strong dependency on initial velocity model. The objective function corresponding to low-frequency data components has less local minima. Reconstructing low-frequency information from recorded seismic data and using it in FWI can reduce cycle-skipping and thus weaken the dependency of inversion process on initial model. In this paper, based on the conventional frequency down-shifting method, we propose a sparse blind deconvolution-convolution low-frequency data reconstruction method, which can simultaneously update the wavelet and reconstruct the low-frequency components. First, we extract the subsurface reflection impulse responses (SRIR) by solving a L1 norm sparse constraint problem using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Then we test the accuracy of our algorithm, and discuss the effect of wavelet error and noises on the reconstruction result.When the wavelet is inaccurate, we update the amplitude of wavelet by alternately inverting L1 norm constraint and Tikhonov regularization problems, and correct the time-shift error by cross-correlating the direct waves. After that we can get the accurate wavelet and SRIR simultaneously. Then using the reconstructed data successively as observed data, combining it with dynamic random sources and layer-stripping methods, we propose a new strategy for the fast multiscale FWI. We test our method by numerical examples in several cases including blended acquisition cases. The results show that it has good anti-noise property and it can reconstruct valid low-frequency components when the observed data lacking low-frequency information. The example using inaccurate wavelet shows that the blind deconvolution-convolution algorithm is able to obtain accurate wavelet and low-frequency data simultaneously.

Controlled tip wear on high roughness surfaces yields gradual broadening and rounding of cantilever tips.

Tip size in atomic force microscopy (AFM) has a major impact on the resolution of images and on the results of nanoindentation experiments. Tip wear is therefore a key limitation in the application of AFM. Here we show, however, how wear can be turned into an advantage as it allows for directed tip shaping. We studied tip wear on high roughness polycrystalline titanium and diamond surfaces and show that tip wear on these surfaces leads to an increased tip size with a rounded shape of the apex. Next, we fitted single peaks from AFM images in order to track the changes in tip radius over time. This method is in excellent agreement with the conventional blind tip reconstruction method with the additional advantage that we could use it to demonstrate that the increase in tip size is gradual. Moreover, with our approach we can shape and control the tip size, while retaining identical chemical and cantilever properties. This significantly expands the reproducibility of AFM force spectroscopy data and is therefore expected to find a wide applicability.

Discrete blind reconstruction method for multi‐coset sampling

Multi-coset sampling is a compressed sampling strategy for the acquisition of spectrally sparse signal. In previous discrete blind recovery methods, either the sensing matrix is really huge, or the sampled sequences are interpolated to the Nyquist rate at the first step, both leading to a high computational complexity. A new discrete blind reconstruction method is proposed in this study to reconstruct a multiband signal from its multi-coset samples. In the proposed method, the fractional delay is implemented at sub-Nyquist rate, so that the sampled sequences do not need to be interpolated to the Nyquist rate until the final step of the reconstruction process. Hence, the computational complexity of the reconstruction method is reduced. Moreover, a windowing procedure is employed in this method to avoid the spectral spreading effect. Numerical experiments are presented to demonstrate that the authors’ method outperforms previous methods in terms of computational complexity and accuracy.

AFM tip characterization by using FFT filtered images of step structures

The measurement resolution of an atomic force microscope (AFM) is largely dependent on the radius of the tip. Meanwhile, when using AFM to study nanoscale surface properties, the value of the tip radius is needed in calculations. As such, estimation of the tip radius is important for analyzing results taken using an AFM. In this study, a geometrical model created by scanning a step structure with an AFM tip was developed. The tip was assumed to have a hemispherical cone shape. Profiles simulated by tips with different scanning radii were calculated by fast Fourier transform (FFT). By analyzing the influence of tip radius variation on the spectra of simulated profiles, it was found that low-frequency harmonics were more susceptible, and that the relationship between the tip radius and the low-frequency harmonic amplitude of the step structure varied monotonically. Based on this regularity, we developed a new method to characterize the radius of the hemispherical tip. The tip radii estimated with this approach were comparable to the results obtained using scanning electron microscope imaging and blind reconstruction methods.

Blind spectrum reconstruction algorithm with L0-sparse representation

Raman spectrum often suffers from band overlap and Poisson noise. This paper presents a new blind Poissonian Raman spectrum reconstruction method, which incorporates the L0-sparse prior together with the total variation constraint into the maximum a posteriori framework. Furthermore, the greedy analysis pursuit algorithm is adopted to solve the L0-based minimization problem. Simulated and real spectrum experimental results show that the proposed method can effectively preserve spectral structure and suppress noise. The reconstructed Raman spectra are easily used for interpreting unknown chemical mixtures.

Blind reconstruction of linear scrambler

An algorithm based on eigenanalysis technique and Walsh-Hadamard transform (WHT) is proposed. The algorithm contains two steps. Firstly, the received sequence is divided into temporal windows, and a covariance matrix is computed. The linear feedback shift register (LFSR) sequence is reconstructed from the first eigenvector of this matrix. Secondly, equations according to the recovered LFSR sequence are constructed, and the Walsh spectrum corresponding to the equations is computed. The feedback polynomial of LFSR is estimated from the Walsh spectrum. The validity of the algorithm is verified by the simulation result. Finally, case studies are presented to illustrate the performance of the blind reconstruction method.

Blind Single-Image Super Resolution Reconstruction with Gaussian Blur and Pepper & Salt Noise

To improve the spatial resolution of low resolution image with Gaussian blur and Pepper & salt noise, a blind single-image super resolution reconstruction method is proposed. In the low resolution imaging model, the Gaussian blur, down-sampling, as well as Pepper & Salt noise are all considered. Firstly, the Pepper & Salt noise in the low resolution image is reduced through median filtering method. Then, the Gaussian blur of the de-noised image is estimated through error-parameter analysis method. Finally, super resolution reconstruction is carried out through iterative back projection algorithm. Experimental results show that the Gaussian blur is estimated with high accuracy, and the Pepper & Salt noise are removed effectively. The visual effect and peak signal to noise ratio (PSNR) of the super resolution reconstructed image is improved. In addition, the importance of Gaussian blur in single-image super resolution reconstruction is justified in an experimental way.

Towards easy and reliable AFM tip shape determination using blind tip reconstruction.

Quantitative determination of the geometry of an atomic force microscope (AFM) probe tip is critical for robust measurements of the nanoscale properties of surfaces, including accurate measurement of sample features and quantification of tribological characteristics. Blind tip reconstruction, which determines tip shape from an AFM image scan without knowledge of tip or sample shape, was established most notably by Villarrubia [J. Res. Natl. Inst. Stand. Tech. 102 (1997)] and has been further developed since that time. Nevertheless, the implementation of blind tip reconstruction for the general user to produce reliable and consistent estimates of tip shape has been hindered due to ambiguity about how to choose the key input parameters, such as tip matrix size and threshold value, which strongly impact the results of the tip reconstruction. These key parameters are investigated here via Villarrubia's blind tip reconstruction algorithms in which we have added the capability for users to systematically vary the key tip reconstruction parameters, evaluate the set of possible tip reconstructions, and determine the optimal tip reconstruction for a given sample. We demonstrate the capabilities of these algorithms through analysis of a set of simulated AFM images and provide practical guidelines for users of the blind tip reconstruction method. We present a reliable method to choose the threshold parameter corresponding to an optimal reconstructed tip shape for a given image. Specifically, we show that the trend in how the reconstructed tip shape varies with threshold number is so regular that the optimal, or Goldilocks, threshold value corresponds with the peak in the derivative of the RMS difference with respect to the zero threshold curve vs. threshold number.