Nyquist Limit Research Articles

Ultimate resolution limits of speckle-based compressive imaging.

Compressive imaging using sparsity constraints is a very promising field of microscopy that provides a dramatic enhancement of the spatial resolution beyond the Abbe diffraction limit. Moreover, it simultaneously overcomes the Nyquist limit by reconstructing an N-pixel image from less than N single-point measurements. Here we present fundamental resolution limits of noiseless compressive imaging via sparsity constraints, speckle illumination and single-pixel detection. We addressed the experimental setup that uses randomly generated speckle patterns (in a scattering media or a multimode fiber). The optimal number of measurements, the ultimate spatial resolution limit and the surprisingly important role of discretization are demonstrated by the theoretical analysis and numerical simulations. We show that, in contrast to conventional microscopy, oversampling may decrease the resolution and reconstruction quality of compressive imaging.

Experimental evaluation of super-resolution imaging and magnification choice in single-particle cryo-EM

The resolution of cryo-EM reconstructions is fundamentally limited by the Nyquist frequency, which is half the sampling frequency of the detector and depends upon the magnification used. In principle, super-resolution imaging should enable reconstructions to surpass the physical Nyquist limit by increasing sampling frequency, yet there are few reports of reconstructions that do so. Here we directly examine the contribution of super-resolution information, obtained with the K3 direct electron detector using a 2-condenser microscope, to single-particle cryo-EM reconstructions surpassing the physical Nyquist limit. We also present a comparative analysis of a sample imaged at four different magnifications. This analysis demonstrates that lower magnifications can be beneficial, despite the loss of higher resolution signal, due to the increased number of particle images obtained. To highlight the potential utility of lower magnification data collection, we produced a 3.5 Å reconstruction of jack bean urease with particles from a single micrograph.

Rethinking medical image reconstruction via shape prior, going deeper and faster: Deep joint indirect registration and reconstruction.

Indirect image registration is a promising technique to improve image reconstruction quality by providing a shape prior for the reconstruction task. In this paper, we propose a novel hybrid method that seeks to reconstruct high quality images from few measurements whilst requiring low computational cost. With this purpose, our framework intertwines indirect registration and reconstruction tasks is a single functional. It is based on two major novelties. Firstly, we introduce a model based on deep nets to solve the indirect registration problem, in which the inversion and registration mappings are recurrently connected through a fixed-point interaction based sparse optimisation. Secondly, we introduce specific inversion blocks, that use the explicit physical forward operator, to map the acquired measurements to the image reconstruction. We also introduce registration blocks based deep nets to predict the registration parameters and warp transformation accurately and efficiently. We demonstrate, through extensive numerical and visual experiments, that our framework outperforms significantly classic reconstruction schemes and other bi-task method; this in terms of both image quality and computational time. Finally, we show generalisation capabilities of our approach by demonstrating their performance on fast Magnetic Resonance Imaging (MRI), sparse view computed tomography (CT) and low dose CT with measurements much below the Nyquist limit.

De-aliasing of ultrasonic velocity profiler on bubbly flow beyond the Nyquist limit

De-aliasing of ultrasonic velocity profiler on bubbly flow beyond the Nyquist limit

Effect of Sampling Rate on Photovoltaic Self-Consumption in Load Shifting Simulations

Grid-connected photovoltaic (PV) capacity is increasing and is currently estimated to account for 3.0% of worldwide energy generation. One strategy to balance fluctuating PV power is to incentivize self-consumption by shifting certain loads. The potential improvement in the amount of self-consumption is usually estimated using smart meter and PV production data. Smart meter data are usually available only at sampling frequences far below the Nyquist limit. In this paper we investigate how this insufficient sampling rate affects the estimated self-consumption potential of shiftable household appliances (washing machines, tumble dryers and dishwashers). We base our analyses on measured consumption data from 16 households in the UK and corresponding PV data. We found that the simulated results have a marked dependence on the data sampling rate. The amount of self-consumed energy estimated with data sampled every 10 min was overestimated by 30–40% compared to estimations using data with 1 min sampling rate. We therefore recommend to take this factor into account when making predictions on the impact of appliance load shifting on the rate of self-consumption.

Modeling of 3-D elastic waves in nonlinear elastic solids using the iterative nonlinear contrast source method

In nondestructive testing, the generation of higher harmonics and the mixing of elastic waves are used to measure the nonlinearity parameters, which in turn are closely related to the microscopic state of the material. A 3-D numerical tool that can simulate large scale, four-dimensional, nonlinear elastic wavefields would be very useful for the reliable interpretation of experimental results. Here, a method is presented that can efficiently compute the nonlinear displacement fields in a homogeneous, isotropic elastic medium, taking into account its third-order elastic constants (A, B, C). The method is based on the Neumann iterative solution of an integral equation involving a Green's function of the linear `background' medium, and a contrast source representing the nonlinearity of the medium. The integral equation is solved iteratively, and the computations are based on Fast Fourier Transforms using a sampling rate close to the Nyquist limit, i.e., two grid points of the shortest wavelength. The displacement fields are evaluated using the scalar and vector potential functions representing the compressional and shear displacements. In this presentation, the suitability of the INCS method for modeling the harmonics of 3-D nonlinear elastic waves and its validation by comparison with an analytical benchmark solution, will be presented.

Modeling Geoelectric Fields Induced by Geomagnetic Disturbances in 3D Subsurface Geology, an Example From Southeastern Australia

AbstractGeomagnetic storms can cause power grid instabilities and blackouts due to excessive geomagnetically induced currents (GICs) flowing in electric transmission systems. In this study, we assess regional vulnerability to GICs by modeling the geoelectric fields induced by significant historic geomagnetic disturbance events in the presence of 3D subsurface geology using data from the Australian Lithospheric Architecture Magnetotelluric Project (AusLAMP) magnetotelluric array, Australia‐Wide Array of Geomagnetic Stations (AWAGS) magnetometer array, and Geoscience Australia geomagnetic observatory network. We analyze the vertical component of the magnetic field with respect to the horizontal magnetic‐field polarization for two magnetic storms and gain insight into the inductive effects associated with field polarization orientations in the 3D case. We also analyze the telluric field intensity and polarization for a unit geomagnetic field polarized in northerly and easterly directions at AusLAMP sites and find that in the presence of 3D geology the induced field has a very polarization‐sensitive anomaly. We model the geoelectric fields in southeastern Australia for the 1989 “Québec storm.” The induced ground electric fields are typically in the range 1,000–2,000 mV/km with a few sites within 2,000–5,000 mV/km on highly resistive regions and in coastal areas, and below 300 mV/km on inland sedimentary basins. The current study focuses on magnetic‐field variations with periods between 120 and ~20,000 s due to bandwidth limits in our magnetotelluric tensor data and the Nyquist limit for the 60 s sampling of our geomagnetic‐field data. Hence, our modeled maximum values should be considered lower estimates of potential real values.

In-phase sub-Nyquist lenslet arrays encoded onto spatial light modulators.

When encoding diffractive lenses onto a spatial light modulator (SLM), there is a Nyquist limit to the smallest focal length that can be formed. When this limit is surpassed, a two-dimensional array of lenslets is formed. There have been very few discussions on the performance of these lenslets. In this work, we focus on the phase distribution of these lenses in the array. We show that, for certain values of the focal length, the lenslets are all in perfect phase. We show that this situation happens for a total number of N/4 different discrete equidistant sub-Nyquist focal lengths, where N×N is the number of pixels in the SLM. We find other distances in between where the array is composed of two sets of lenslets with a relative π phase among them. Finally, we illustrate these phase distributions in the application to generate an array of vortex producing lenses. We expect that these results might be useful for high-accuracy interferometric or multiple imaging where this phase must be exactly the same for each replica.

Practical Considerations of Using the K3 Camera in CDS Mode for High-resolution and High-throughput Single Particle Cryo-EM

Abstract Detector technology plays a pivotal role in high-resolution and high-throughput cryo-EM structure determination. Compared with the first-generation, single-electron counting direct detection camera (Gatan K2), the latest K3 camera is faster, larger, and now offers a correlated-double sampling mode (CDS). Importantly this results in a higher DQE and improved throughput compared to its predecessor. In this study, we focused on optimizing camera data collection parameters for daily use within a cryo-EM facility and explored the balance between throughput and resolution. In total, eight data sets of murine heavy-chain apoferritin were collected at different dose rates and magnifications, using 9-hole image shift data collection strategies. The performance of the camera was characterized by the quality of the resultant 3D reconstructions. Our results demonstrated that the Gatan K3 operating in CDS mode outperformed standard (nonCDS) mode in terms of reconstruction resolution in all tested conditions with 8 electrons per pixel per second being the optimal dose rate. At low magnification (64kx) we were able to achieve reconstruction resolutions of 149% of the physical Nyquist limit (1.8 A with a 1.346 A physical pixel). Low magnification allows more particles to be collected per image, aiding analysis of heterogeneous samples requiring large data sets. At moderate magnification (105kx, 0.834 A physical pixel size) we achieved a resolution of 1.65 A within 9 hours of data collection, a condition optimal for achieving high-resolution on well behaved samples. Our results also show that for an optimal sample like apoferritin, one can achieve better than 2.5 A resolution with 5 minutes of data collection. Together, our studies validate the most efficient ways of imaging protein complexes using the K3 direct detector and will greatly benefit the cryo-EM community.

Verification of Sensors for Yaw Rate and Lateral Acceleration in Car ESP System

This study analyzed the possibilities to validate the indications of sensors for yaw rate and lateral acceleration within the scope of extended diagnostic routine of the car ESP system at Vehicle Inspection Stations (SKP). The stand tests were performed using the reference sensors and a standard diagnostic tester. The comparison of the yaw rate and lateral acceleration results obtained from the working sensor under examination, recorded with the V box unit, and the results from the reference sensor demonstrated a good conformity both in quality and quantity. But these tests were demonstrated also a pure conformity (both in quality and quantity) with runs obtained from tester. The Root Mean Square (RMS) was used as factor of qualitative estimation. These inconveniences were caused from in sampling frequency incompatibility and lack of recording synchronization for signals from the tester and from reference sensors. The primary importance question is a firmware modification for selected testers. Such a tester should be able to record signals from a reference sensor and have a set sampling frequency for signals from a working sensor. On the basis of already carried out research analyses the suggested frequency should be no fewer than about of 10 Hz. It resulted from a spectral analysis carried out for possessed runs maintaining the Nyquist limit frequency.

Reconstructing the time evolution of wall-bounded turbulent flows from non-time-resolved PIV measurements

Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on Rapid Distortion Theory (RDT) and Taylor's Hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forwards and backwards in time using the PIV snapshots as initial conditions. The flow field in the intervening period is then reconstructed by taking a weighted sum of the forward and backward estimates. This spatiotemporal weighting function is designed to account for the advective nature of the RDT and TH equations. Reconstruction accuracy is evaluated as a function of spatial resolution and reconstruction time horizon using Direct Numerical Simulation data for turbulent channel flow from the Johns Hopkins Turbulence Database. This method reconstructs single-point turbulence statistics well and resolves velocity spectra at frequencies higher than the temporal Nyquist limit of the acquisition system. Reconstructions obtained using a characteristics-based evolution of the flow field under TH prove to be more accurate compared to reconstructions obtained from numerical integration of the discretized forms of RDT and TH. The effect of measurement noise on reconstruction error is also evaluated.

Endo-microscopy beyond the Abbe and Nyquist limits

For several centuries, far-field optical microscopy has remained a key instrument in many scientific disciplines, including physical, chemical, and biomedical research. Nonetheless, far-field imaging has many limitations: the spatial resolution is controlled by the diffraction of light, and the imaging speed follows the Nyquist–Shannon sampling theorem. The recent development of super-resolution techniques has pushed the limits of spatial resolution. However, these methods typically require complicated setups and long acquisition times and are still not applicable to deep-tissue bioimaging. Here, we report imaging through an ultra-thin fibre probe with a spatial resolution beyond the Abbe limit and a temporal resolution beyond the Nyquist limit simultaneously in a simple and compact setup. We use the random nature of mode coupling in a multimode fibre, the sparsity constraint and compressive sensing reconstruction. The new approach of super-resolution endo-microscopy does not use any specific properties of the fluorescent label, such as depletion or stochastic activation of the molecular fluorescent state, and therefore can be used for label-free imaging. We demonstrate a spatial resolution more than 2 times better than the diffraction limit and an imaging speed 20 times faster than the Nyquist limit. The proposed approach can significantly expand the realm of the application of nanoscopy for bioimaging.

BER performance of finite in time optimal FTN signals for the Viterbi algorithm

In this article, we consider the faster than Nyquist (FTN) technology in aspects of the application of the Viterbi algorithm (VA). Finite in time optimal FTN signals are used to provide a symbol rate higher than the “Nyquist barrier” without any encoding. These signals are obtained as the solutions of the corresponding optimization problem. Optimal signals are characterized by intersymbol interference (ISI). This fact leads to significant bit error rate (BER) performance degradation for “classical” forms of signals. However, ISI can be controlled by the restriction of the optimization problem. So we can use optimal signals in conditions of increased duration and an increased symbol rate without significant energy losses. The additional symbol rate increase leads to the increase of the reception algorithm complexity. We consider the application of VA for optimal FTN signals reception. The application of VA for receiving optimal FTN signals with increased duration provides close to the potential performance of BER, while the symbol rate is twice above the Nyquist limit.

A High-Performance 2.5 μm Charge Domain Global Shutter Pixel and Near Infrared Enhancement with Light Pipe Technology.

We developed a new 2.5 μm global shutter (GS) pixel using a 65 nm process with an advanced light pipe (LP) structure. This is the world’s smallest charge domain GS pixel reported so far. This new developed pixel platform is a key enabler for ultra-high resolution sensors, industrial cameras with wide aperture lenses, and low form factors optical modules for mobile applications. The 2.5 μm GS pixel showed excellent optical performances: 68% quantum efficiency (QE) at 530 nm, ±12.5 degrees angular response (AR), and quite low parasitic light sensitivity (PLS)—10,400 1/PLS with the F#2.8 lens. In addition, we achieved an extremely low memory node (MN) dark current 13 e−/s at 60 °C by fully pinned MN. Furthermore, we studied how the LP technology contributes to the improvement of the modulation transfer function (MTF) in near infrared (NIR) enhanced GS pixel. The 2.8 μm GS pixel using a p-substrate showed 109 lp/mm MTF@50% at 940 nm, which is 1.6 times better than that without an LP. The MTF can be more enhanced by the combination of the LP and the deep photodiode (PD) electrically isolated from the substrate. We demonstrated the advantage of using LP technology and our advanced stacked deep photodiode (SDP) technology together. This unique combination showed an improvement of more than 100% in NIR QE while maintaining an MTF that is close to the theoretical Nyquist limit (MTF @50% = 156 lp/mm).

Single-Pixel Imaging Authentication Using Sparse Hadamard Spectrum Coefficients

We experimentally present optical authentication using a small number of Hadamard spectrum coefficients in single-pixel imaging (SPI). A method is applied to generate sparse Hadamard spectrum coefficients in the SPI. By randomly selecting and using a small number of Hadamard spectrum coefficients (e.g., less than 8.0% of Nyquist limit), information of an object (i.e., plaintext) can be effectively hidden in the decrypted object. Although the decrypted object cannot visually render information about the plaintext, it can be effectively authenticated. Optical experiment is conducted to verify feasibility and effectiveness of the proposed optical authentication method. It is expected that the proposed method can provide a promising insight for single-pixel optical authentication.

Direct Under-Sampling Compressive Sensing Method for Underwater Echo Signals and Physical Implementation

Compressive sensing can guarantee the recovery accuracy of suitably constrained signals by using sampling rates much lower than the Nyquist limit. This is a leap from signal sampling to information sampling. The measurement matrix is key to implementation but limited in the acquisition systems. This article presents the critical elements of the direct under-sampling—compressive sensing (DUS–CS) method, constructing the under-sampling measurement matrix, combined with a priori information sparse representation and reconstruction, and we show how it can be physically implemented using dedicated hardware. To go beyond the Nyquist constraints, we show how to design and adjust the sampling time of the A/D circuit and how to achieve low-speed random non-uniform direct under-sampling. We applied our method to data measured with different compression ratios (volume ratios of collected data to original data). It is shown that DUS-CS works well when the SNR is 3 dB, 0 dB, −3 dB, and −5 dB and the compression ratio is 50%, 20%, and 10%, and this is validated with both simulation and actual measurements. The method we propose provides an effective way for compressed sensing theory to move toward practical field applications that use underwater echo signals.

Bi-frequency 3D ghost imaging with Haar wavelet transform.

Recently, ghost imaging has been attracting attention because its mechanism could lead to many applications inaccessible to conventional imaging methods. However, it is challenging for high-contrast and high-resolution imaging, due to its low signal-to-noise ratio (SNR) and the demand of high sampling rate in detection. To circumvent these challenges, we propose a ghost imaging scheme that exploits Haar wavelets as illuminating patterns with a bi-frequency light projecting system and frequency-selecting single-pixel detectors. This method provides a theoretically 100% image contrast and high-detection SNR, which reduces the requirement of high dynamic range of detectors, enabling high-resolution ghost imaging. Moreover, it can highly reduce the sampling rate (far below Nyquist limit) for a sparse object by adaptively abandoning unnecessary patterns during the measurement. These characteristics are experimentally verified with a resolution of 512×512 and a sampling rate lower than 5%. A high-resolution (1000×1000×1000) 3D reconstruction of an object is also achieved from multi-angle images.

Ultrahigh resolution and color gamut with scattering-reducing transmissive pixels

While plasmonic designs have dominated recent trends in structural color, schemes using localized surface plasmon resonances and surface plasmon polaritons that simultaneously achieve high color vibrancy at ultrahigh resolution have been elusive because of tradeoffs between size and performance. Herein we demonstrate vibrant and size-invariant transmissive type multicolor pixels composed of hybrid TiOx-Ag core-shell nanowires based on reduced scattering at their electric dipolar Mie resonances. This principle permits the hybrid nanoresonator to achieve the widest color gamut (~74% sRGB area coverage), linear color mixing, and the highest reported single color dots-per-inch (58,000~141,000) in transmission mode. Exploiting such features, we further show that an assembly of distinct nanoresonators can constitute a multicolor pixel for use in multispectral imaging, with a size that is ~10-folds below the Nyquist limit using a typical high NA objective lens.

P3728Impact of residual leaks and device-associated thrombus after left atrial appendage occlusion: long-term transesophageal follow-up and clinical outcome

Abstract Background Standardized transesophageal echocardiography (TEE) data regarding peri-device leaks and thrombus formation after left atrial appendage occlusion (LAAO) are sparse. Criteria to quantify residual leaks seem to appear highly arbitrarily. We therefore examined patients by long-term TEE follow-up after LAAO in a standardized Echo protocol. Methods Our patients were prospectively examined by questionnaires and TEE 6 weeks post-procedurally and ≥12 months after LAAO. TEE was performed according to the Munich consensus document, including multiple TEE views (2D and 3D) and an adequate, lower Nyquist limit (20–30cm/s) to detect low velocity flow. The severity of the leaks were graded as follows: >5mm severe, 3–5mm moderate and 1–2mm mild. Antithrombotic regime was administered according to the PROTECT-AF protocol for the Watchman device in the first 60 patients, and dual antiplatelet therapy for 1–3 months thereafter as well as for the Amplatzer device. Results In total, 107 LAAO were performed in our institution in patients with a mean age of 77 years. Mean CHA2DS2-VASc score was 4.3±1.3, mean HAS-BLED score 2.7±0.9. Mean clinical follow-up duration was 52.8 months, mean TEE follow-up 43.1 months. The overall annual stroke rate was 1.49%. None of the patients with a post-procedural stroke showed an intracardial thrombus by TEE after six weeks, during the event and in long-term FU. In long-term TEE follow-up 46% (n=18/39) had a mild to moderate residual leak and 2.6% (n=1/39) a severe leak >5mm.Two of the patients with a permanently existing leak sustained an ischemic stroke: in the first patient with a peri-device leak of 3mm the stroke occurred 80 months post-procedurally, in the second one with a growing leak from 3 to 6,5mm 25 months post-procedurally, both classified most likely as a cardioembolic stroke. One patient without a leak in long-term TEE FU suffered a stroke 5 years after LAAO (p=0.61). In all three patients antithrombotic regime during the event consisted of ASS alone.Device-associated thrombus was observed in 1.9% (n=2/107) six weeks after the procedure and increased to 15.4% (n=6 out of 39 TEE studies) in long-term FU, all appeared immobile. None of those patients suffered a thromboembolic event. Conclusions In long-term follow up, residual, mostly mild to moderate leaks and device-associated thrombi after LAAO seem to occur occasionally. However, patients with a residual leak or immobile thrombus do not appear to have a higher risk for thromboembolism so far.

Encoding lenses with focal lengths lower than the Nyquist limit using high phase-modulation displays.

Liquid crystal displays allow the easy implementation of diffractive optical elements. However, the shortest focal lengths for lenses are limited by Nyquist conditions. In this work, we show that focal lengths much lower than this Nyquist limit can be encoded onto devices having a large phase-dynamic range. Experimental results are included with a display showing 10π phase modulation reducing the Nyquist limit by a factor of about 1/10.