This letter introduces a novel regression model structure for the inflated Rayleigh distribution, which effectively models high dynamic amplitude pixel values in synthetic aperture radar (SAR) images. The proposed model estimates the mean of inflated Rayleigh distribution signals by a structure that includes a set of regressors and a link function. The inflated Rayleigh distribution combines the Rayleigh and a degenerate distribution, assigning nonnull probability specifically for observed values equal to zero. Null pixel values in amplitude SAR images can be randomly distributed within the image, especially in low-intensity areas; a model capable of incorporating these values is essential to avoid changes in image statistics. Extensive evaluations are conducted using simulated and real SAR images to validate the proposed model, specifically focusing on ground-type detection in high dynamic amplitude pixel values scenarios. The performance of the proposed inflated Rayleigh regression model is compared with traditional Gaussian-based regression models, excelling in terms of ground-type detection in an SAR image obtained from the ICEYE radar.

This letter introduces the Rayleigh generalized autoregressive score (Ray-GAS) model, a dynamic model useful for synthetic aperture radar (SAR) data interpretation. It is derived from the generalized autoregressive score (GAS) framework, assuming that the Rayleigh conditional mean is an index-varying parameter. We discuss estimation, diagnostic, and prediction tools. Additionally, we perform numerical experiments with simulated and measured single-look amplitude SAR data for forest and lake region data. The results show the Ray-GAS model’s benefits in understanding stochastic behavior and filtering SAR amplitude returns.

Multitemporal satellite images can be represented as a three-dimensional cube. This remote sensing data type require modeling techniques comprising spatial and temporal dependence altogether. This work aims at developing a hybrid framework combining the three-dimensional autoregressive (3D-AR) statistical model and machine learning algorithms to accommodate spatial and temporal correlations in a stack of temporal synthetic aperture radar (SAR) images. We propose using the 3D-AR to model the linear dependence among the voxels and one among artificial neural networks (ANN), support vector regression (SVR), and random forest (RF) for modeling the nonlinear component. The resulting models, labeled as 3D-AR-ANN, 3D-AR-SVR, and 3D-AR-RF hybrid models, respectively, can help to predict missing voxels or to forecast a one-step-ahead image of a remote sensing data sequence in the presence of linear and nonlinear patterns. The procedure is validate by applying the proposed hybridization approach to predict different parts of a SAR image stack from the urban area of Cordoba, Argentina. The results show the usefulness of our approach in predicting multitemporal SAR data, being more accurate than the state-of-the-art 3D-AR model.

This article introduces a continuous probability distribution as an approximation to the${\mathcal {G}}^{0}_{A}$distribution for amplitude synthetic aperture radar (SAR) imagery modeling. Called${\mathcal {L}}_{A}$distribution, it is an empirical model and an analytically more tractable alternative than${\mathcal {G}}^{0}_{A}$model, with the same number of parameters and no special functions in its formulation. It also has a closed form for the quantile function, making it easier to calculate quantiles and generate pseudorandom numbers and obtain closed-form expressions for skewness and kurtosis coefficients. Useful properties of the${\mathcal {L}}_{A}$distribution are introduced, and the maximum likelihood method is considered for parameter estimation. Based on the Kullback–Leibler divergence (KLD), it is shown that the average information missed when using the${\mathcal {L}}_{A}$instead of${\mathcal {G}}^{0}_{A}$distribution is negligible. Numerical studies in simulated and measured SAR images obtained by different systems and representing different land-use regions are conducted to compare the performances of the${\mathcal {G}}^{0}_{A}$and${\mathcal {L}}_{A}$distributions. The simulation results suggest that the parameter estimation performances of both distributions are similar. Applications to real data show that the images were best fit with the${\mathcal {L}}_{A}$distribution in all considered cases and figure-of-metrics.

Synthetic aperture radars (SAR) data plays an important role in remote sensing applications. It is common knowledge that SAR image amplitude pixels can be approximately modeled by the Rayleigh distribution. However, this model is contin-uous and does not accommodate points with non-zero prob-ability, such as a null pixel amplitude value. Thus, in this paper, we propose an inflated Rayleigh distribution for SAR image modeling that is based on a mixed continuous-discrete distribution and can be used to fit signals with observed values on$[0,\ \infty)$. The maximum likelihood approach is considered to estimate the parameters of the proposed distribution. An empirical experiment with a SAR image is also presented and discussed.

The Rayleigh regression model was recently proposed for modeling amplitude values of synthetic aperture radar (SAR) image pixels. However, inferences from such model are based on the maximum-likelihood estimators, which can be biased for small-signal lengths. The Rayleigh regression model for SAR images often considers small pixel windows, which may lead to inaccurate results. In this letter, we introduce bias-adjusted estimators tailored for the Rayleigh regression model based on: 1) Cox and Snell’s method; 2) Firth’s scheme; and 3) the parametric bootstrap method. We present numerical experiments considering synthetic and actual SAR data sets. The bias-adjusted estimators yield nearly unbiased estimates and accurate modeling results.

The ever increasing technological demand for the DFT computation poses several challenges both to theory and hardware realization. The design of usual fast Fourier transform (FFT) algorithms seems to have reached a stage of diminishing returns in terms of performance. Alternatively, approximate transform methods have been demonstrated to provide substantial gains in terms of energy-efficiency and performance by tolerating small inaccuracies in the results. In this paper, we present a transform scaling method variant of the Cooley-Tukey algorithm to obtain DFT approximations of large blocksize. The proposed method scales up a givenN-point transformation to anN2-point transformation. Such scaling can be successively applied leading to$\mathop {{N}^2}\nolimits^n $-point transformations. We have fully presented the 324-point DFT approximation which stems from a multiplierless 32-point DFT approximation. The proposed approximation is equipped with a fast algorithm; we also supply the arithmetic complexity assessment and an error analysis.

The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards—such as JPEG and HEVC—adopt the DCT as a fundamental building block for compression. Recent works have introduced low-complexity approximations for the DCT, which become paramount in applications demanding real-time computation and low-power consumption. The design of DCT approximations involves a trade-off between computational complexity and performance. This paper introduces a new multiparametric transform class encompassing the round-off DCT (RDCT) and the modified RDCT (MRDCT), two relevant multiplierless 8-point approximate DCTs. The associated fast algorithm is provided. Four novel orthogonal low-complexity 8-point DCT approximations are obtained by solving a multicriteria optimization problem. The optimal 8-point transforms are scaled to lengths 16 and 32 while keeping the arithmetic complexity low. The proposed methods are assessed by proximity and coding measures with respect to the exact DCT. Image and video coding experiments and hardware realization are performed. The novel transforms perform close to or outperform the current state-of-the-art DCT approximations.

The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a robust estimation process is proposed as a more realistic approach to model this type of data. This article aims at obtaining Rayleigh regression model parameter estimators robust to the presence of outliers. The proposed approach considered the weighted maximum likelihood method and was submitted to numerical experiments using simulated and measured SAR images. Monte Carlo simulations were employed for the numerical assessment of the proposed robust estimator performance in finite signal lengths, their sensitivity to outliers, and the breakdown point. For instance, the nonrobust estimators show a relative bias value 65-fold larger than the results provided by the robust approach in corrupted signals. In terms of sensitivity analysis and break down point, the robust scheme resulted in a reduction of about 96% and 10%, respectively, in the mean absolute value of both measures, in compassion to the nonrobust estimators. Moreover, two SAR datasets were used to compare the ground type and anomaly detection results of the proposed robust scheme with competing methods in the literature.

Satellite images from the same scene observed over time can be composed in an image stack, which could be modeled as a 3-D cube. To handle this type of remote sensing data, on the one side, unidimensional dynamical models have been considered, modeling each pixel separately along the time (pixel-based approach), and exploring the temporal correlation. On the other side, 2-D approaches have been considered to process each image at one date, exploring the spatial correlation. In this article, we propose a new 3-D autoregressive (AR) (3-D-AR) model useful for multitemporal image interpretation exploring the correlation in three dimensions altogether. The 3-D-AR model is statistically defined, and a robust parameter estimation method is discussed. The tools for filtering, forecasting, and detecting anomalies are also introduced. A Monte Carlo simulation study is performed to evaluate the finite signal length performance of the robust estimation and its sensitivity to outliers. The proposed model is applied to a multitemporal normalized difference vegetation index (NDVI) image stack for filtering, prediction, and anomaly detection purposes. The numerical results show the importance of the proposed 3-D-AR model for spatiotemporal remote sensing data interpretation.

This article introduces the Rayleigh autoregressive moving average (RARMA) model, which is useful to interpret multiple different sets of remotely sensed data, from wind measurements to multitemporal synthetic aperture radar (SAR) sequences. The RARMA model is indeed suitable for continuous, asymmetric, and nonnegative signals observed over time. It describes the mean of Rayleigh-distributed discrete-time signals by a dynamic structure including autoregressive (AR) and moving average (MA) terms, a set of regressors, and a link function. After presenting the conditional likelihood inference for the model parameters and the detection theory, in this article, a Monte Carlo simulation is performed to evaluate the finite signal length performance of the conditional likelihood inferences. Finally, the new model is applied first to sequences of wind speed measurements, and then to a multitemporal SAR image stack for land-use classification purposes. The results in these two test cases illustrate the usefulness of this novel dynamic model for remote sensing data interpretation.

This paper presents an incoherent change detection algorithm (CDA) for synthetic aperture radar (SAR) images based on logistic regression. The input data consists of a set of 24 SAR images acquired in a test site in northern Sweden [1]. Subsets of these images are trained based on pixel amplitude, flight heading and neighboring features such as local mean, standard deviation and skewness. The proposed method intends to explore the advantadges from both pixel- and object-based approaches, while evaluating multiple features in amplitude-only SAR images. Preliminary results based on K-fold cross-validation have shown that the proposed CDA achieves good performance when compared to the results presented in [1].

This letter proposes a regression model for nonnegative signals. The proposed regression estimates the mean of Rayleigh distributed signals by a structure which includes a set of regressors and a link function. For the proposed model, we present: 1) parameter estimation; 2) large data record results; and 3) a detection technique. In this letter, we present closed-form expressions for the score vector and Fisher information matrix. The proposed model is submitted to extensive Monte Carlo simulations and to the measured data. The Monte Carlo simulations are used to evaluate the performance of maximum likelihood estimators. Also, an application is performed comparing the detection results of the proposed model with Gaussian-, Gamma-, and Weibull-based regression models in synthetic aperture radar (SAR) images.

This paper presents a study on the constant false alarm rate (CFAR) filter design for change detection algorithms (CDA). More specifically, we are interested in CFAR filters used in CDA for low frequency ultra-wideband (UWB) synthetic aperture radar (SAR) systems. The filter design performance was evaluated in terms of false alarm rate (FAR) and probability of detection (PD). For evaluation purposes, we considered a set of SAR images obtained with the CARABAS-II system. The results are compared with the ones presented in [1], where the same CDA was considered, except for the CFAR filter. The results show that relevant FAR performance improvements can be obtained by just modifying the CFAR filter parameters taking into account the image resolution and target characteristics.

The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The DTT transform kernel does not depend on the input data and fast algorithms can be developed to real-time applications. However, the DTT fast algorithm presented in literature possess high computational complexity. In this paper, we introduce a new low-complexity approximation for the DTT. The fast algorithm of the proposed transform is multiplication free and requires a reduced number of additions and bit-shifting operations. Image and video compression simulations in popular standards show good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows a 43.1% reduction in configurable logic blocks and ASIC place and route realization shows a 57.7% reduction in the area-time figure compared with the 2D version of the exact DTT.

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. 3D DCT approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8×8 ×8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.

The authors apply two approaches to reduce the computation time of the residual complexity similarity metric employed in image registration applications aimed at hardware‐based implementations with low‐complexity transforms. First, the similarity metric is computed in image sub‐blocks, which are subsequently combined into a global metric value. Second, the discrete cosine transform (DCT) needed in the computation of the similarity measure is replaced with multiplier‐free low‐complexity approximate transforms. The authors propose a new low‐complexity transform requiring only 18 additions in an 8 × 8 block and compare it to: the round DCT, the signed DCT, the Hadamard transform and the Walsh‐Hadamard transform. Detailed computational complexity analysis reveals that block‐wise processing alone reduces computational cost by a factor of 8‐9 for original DCT composed of multiplications and additions, and up to ≃4.90 when the proposed DCT is utilised; being the computation performed with additions only. Results obtained from computer simulated and realistic X‐ray images demonstrate block‐wise processing and approximate transforms result in successful image registration, making residual complexity similarity measure available to hardware‐accelerated fast image registration applications.

In this letter, we introduce a low-complexity approximation for the discrete Tchebichef transform (DTT). The proposed forward and inverse transforms are multiplication-free and require a reduced number of additions and bit-shifting operations. Numerical compression simulations demonstrate the efficiency of the proposed transform for image and video coding. Furthermore, Xilinx Virtex-6 FPGA based hardware realization shows 44.9% reduction in dynamic power consumption and 64.7% lower area when compared to the literature.

An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also outperform state-of-the-art algorithms in low and high image compression scenarios, exhibiting at the same time a comparable computational complexity.