Optimal binary filters with linearly separable preprocessing

An analytic solution for real optimal filters is known, and the special case of optimal binary phase-only filters can be solved by a fast binning algorithm but no analytic solution is known. We establish a geometric solution for the design of optimal binary amplitude filters (OBAF's) and optimal binary phase-only filters (OBPOF's) for any object. The optimal filter is found in terms of maximizing the field strength at the origin in the correlation plane. We found that it is possible to construct a unique convex polygon by using an ordered set of phasors from the filter object's Fourier transform. This process leads eventually to an exact solution for the filter-design problem. We show that the maximum distance across the polygon divides the phasors into two groups: For the OBAF, it determines the group that is passed or blocked; for the OBPOF, it determines which group is passed with a zero or a pi phase shift. The shape of the convex polygon gives qualitative information on the criticalness and the tightness needed in the design process. It provides good insight into the binning-process algorithm and permits us to bound the error in the binning process. Design examples through computer simulation and applications in fingerprint identification are presented.

Optimal binary filters estimate an ideal random set by means of an observed random set. By parameterizing the ideal and observation random sets, one can examine the robustness of filter design relative to parameter states. This paper addresses the question as to which states possess the most robust optimal filters. Based on the prior distribution of the states, a measure of robustness is defined for each state and the state possessing maximal robustness is determined. The paper focuses on sparse noise, for which an analytic formulation of robustness is known. It proposes a parametric model from which to approximate robustness by estimating model parameters from image data.

This paper presents the results obtained in the simulation and implementation of adaptive and matched filters using the new technology of FPAA (Field Programmable Analog Arrays). The proposed filter structures are intended to be used in conditioning of signals from radiation sensors but can be also used in any application that necessitates signal extraction from noise. For the implementation of the filter were used configurable analog blocks (CABs) from Anadigm AN221E04 dynamically reconfigurable chip. The most important advantage of the proposed design is represented by the possibility to reconfigure the filter characteristics in order to meet application specific requirements.

This article presents the design and implementation of a low power FPGA-based optimal multiband filter with Spline function for denoising ECG signals. The proposed multiband filter design utilizes least mean square algorithm to determine the optimal filter coefficients for multiple frequency bands, while the Spline function is used to interpolate the filter coefficients within each band to achieve a smooth transition between adjacent bands. The experimental work is carried out with ECGID database and it shows that the proposed filter outperforms in terms of benchmark performance matrices SNR, MSE, CC and PRD. The filter is implemented on a low power FPGA platform, which allows for real-time processing of ECG signals with low power consumption. The experimental results are analyzed and compared for different architecture using the MATLAB and XILINX VIVADO tools. The serial architecture of proposed filter design is implemented on Artix 7 (XC7A35T) EDGE Board, utilizing 1932 LUT, 5299 FF, 1 DSP block and 0.158 W on-chip power. The experimental results indicate that the proposed filter design approach is efficient, effective, and suitable for implementation in compact biomedical devices.

Use of the Magneto-Optic Spatial Light Modulator (MOSLM) in the filter plane of optical correlatorsis attractive because it is capable of high frame rates. This has led to the design of several differenttypes of Binary Phase-Only Filters (BPOFs) and Ternary Filters matched to a single reference. Tofurther increase the throughput of an optical correlator employing the MOSLM, attempts at designingBinary Phase-Only Composite Filters have been made. In this paper, we introduce a new iterativetechnique to design such Composite Filters in which we simultaneously maximize the peak sharpnessand minimize the deviation of the actual correlation peak intensities from their desired values. 1 Introduction Binary Phase-Only Filters have received much attention in the past ten years [1-9]. Most of this research has focused on the design of filters matched to a single reference image. These filters have beendesigned to optimize many different figures of merit. Among these are Signal-to-Noise Ratio, Peak-to-Correlation Energy and light efficiency. Now, the focus appears to be shifting to the design of Binary Phase-Only Composite Filters (BPOCFs) [10,11]. If we desire real-time implementation, then binary phase-onlycomposite filters, which are used to recognize many distortions of an image, should be considered sincethey require fewer filters.In this paper, we present a new algorithm for designing BPOCFs. The advantage of this new algorithmover the previous ones is that it allows us to not only approach the desired correlation peak value, butit also maximizes the peak sharpness produced by the filter. The remainder of this paper is organized asfollows. Section 2 introduces composite filters or synthetic discriminant functions (SDFs) [12,13] and setsup the notation we use. Section 3 develops the new algorithm for designing BPOCFs. Section 4 presentssome initial results and Section 5 gives our conclusions.

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.

We present a systematic procedure for the design of filters intended for multirate systems. This procedure Is motivated by viewing the equiripple design of filters in linear time-invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals. The philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems, which are not time-invariant. We develop a generalized Fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design. Using such criteria yields optimum minimax multirate filters for the input signal class. The utility of our method is demonstrated by using it to analyze several multirate systems. We give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design. Our numerical analysis is based upon a new formulation of the design as a semi-infinite linear programming problem. >

Optimizing the optical field distribution of near-field SIL optical storage system using five-zone binary phase filters

This paper presents an alternative approach for the design of linear phase digital high pass FIR filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA). FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, PSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency characteristic. In this paper, for the given problem, the realization of the optimal FIR high pass filters of different orders has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithm such as genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Detecting changes in remote sensing images taken at different times is challenging when images' data come from different sensors. The performance of change detection algorithms based on radiometric values alone is not satisfactory and need the fusion of other features. Local similarity measures such as Mutual Information, Kullback-Leibler Divergence, and Cluster Reward Algorithm can be used for enhancing change detection. In the paper, we propose an improved local similarity measure using weighted local histogram. Each pixel contributes to the calculation of the histogram according to its weight only. The weight assigned to each pixel in the histogram estimation window follows an exponential function of its distance from the center of the window and the corresponding pixel value in an initial change map image which is derived from other micro-structure or radiometric information. The proposed improved similarity measure benefits from the good detection ability of small estimation window and the good estimation accuracy of large estimation window; hence it can replace the time-consuming multi-scale selection approaches for statistics based similarity measures in remote sensing. The efficiency of this useful improvement has been validated on change detection in remote sensing image series.

An optimal binary-image filter estimates an ideal random set by means of an observed random set. A fundamental and practically important question regards the robustness of a designed filter: to what extent does performance degrade when the filter is applied to a different model than the one for which it has been designed? By parameterizing the ideal and observation random sets, one can analyze the robustness of filter design relative to parameter states. Based on a prior distribution for the states, a robustness mesure is defined for each state in terms of how well its optimal filter performs on models for different states. Not only is filter performance on other states taken into account, but so too is the contribution of other states in terms of their mass relative to the prior state distribution. This paper characterizes maximally robust states, derives performance bounds, treats mean robustness (as opposed to robustness by state), introduces a global filter that is applied across all states, particularizes the entire analysis to a sparse noise model for which there are analytic robustness expressions, and proposes a simplified model for determination of robust states from data. Sufficient conditions are given under which the global filter is uniformly more robust than all state-specific optimal filters.

An existing multi-scale residual network (MSRN) has demonstrated its success on conducting the single image super-resolution (SISR) task. The MSRN consists of a number of multi-scale residual blocks (MSRBs), and each MSRB performs convolutions by exploiting two different sizes of windows for conducting multi-scale feature extraction. The smaller window is used to extract image features at a low scale, while the larger one is used for a high scale. To significantly reduce the number of parameters involved in the MSRB, a new feature extraction module, called the asynchronous multi-scale block (AMB), is proposed in this paper. It is based on the fact that the larger window used in the MSRB can be replaced by two smaller windows without affecting the original MSRB's function. Consequently, by replacing each MSRB with our AMB, an asynchronous multi-scale network (AMNet) is then constructed, which can yield a significant reduction on computational complexity. This means that more AMBs can be used in our AMNet to deliver superior SISR performance, while maintaining the same or comparable computational complexity to that of the MSRN. To consolidate all image features generated from all scales, a new fusion scheme, called the adaptive feature fusion block (AFFB), is proposed that weights the extracted features according to their importance for further increasing SISR's performance. Extensive experimental results have clearly shown the superiority of our proposed AMNet when compared with multiple state-of-the-arts.

In this paper, synthesis and design of hybrid-shaped cavity filters using substrate integrated waveguide (SIW) technique is proposed. Both triangular - and rectangular SIW cavities are combined for the first time in the design of band pass filter. Cross-coupling structures are realized in both proposed filters via two or three propagation paths. Measured results are presented and compared to those simulated by Ansoft's High Frequency Structure Simulator (HFSS) software package. A good agreement between the simulated and measured results is observed, which has also validated the proposed filtering structure with hybrid-shaped SIW cavities.

In this paper, an optimal multilevel stack filtering algorithm (the stack filters used at each level are designed to be optimal) is introduced. Optimal multilevel stack filter is capable of considering a larger window mask than an optimal stack filter. Multilevel unidirectional stack filters and multilevel bidirectional stack filters are studied in particular. Design of an optimal multilevel stack filter is similar to the design of an optimal stack filter where the compare-and- select algorithm can be used. However, the design procedure needs to be adapted to operation on more than one level. Several design examples are presented showing the good performance of the proposed method.

An EMI filter design procedure for power converters is proposed. Based on a given noise spectrum, information about the converter noise source impedance and design constraints, the design space of the input filter is defined. The design is based on component databases and detailed models of the filter components, including high frequency parasitics, losses, weight, volume, etc.. The design space is mapped onto a performance space in which different filter implementations are evaluated and compared. A multi-objective optimization approach is used to obtain optimal designs w.r.t. a given performance function.