In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. $$(i-j-k)/\sqrt{3}$$ ( i - j - k ) / 3 appears to be an optimal choice.

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Color Image Analysis by Quaternion-Type Moments

Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms

In this paper, we propose a generalized co-prime multiple-input multiple-output (MIMO) configuration for direction of arrival estimation. Compared with the conventional co-prime MIMO radar that requires prototype co-prime arrays for transmitter and receiver, the proposed configuration enlarges the inter-element spacing of transmitter with an integer expansion factor. By vectorizing the sample covariance matrix, the generalized sum and difference coarray (GSDC) concept is defined for exploiting the advantages of proposed configuration. The analytical expressions for the expansion factor, the maximum consecutive lags, and the number of unique lags are derived carefully. It is verified that GSDC can obtain more degrees of freedom (DOFs) with the increase of expansion factor. Specifically, with $\mathcal {O}(M+N)$ sensors, GSDC can provide $\mathcal {O}(M^{2}N^{2})$ DOFs, whereas the conventional one only has $\mathcal {O}(MN)$ DOFs. Simulation results demonstrate the usefulness of proposed configuration utilizing both spatial smoothing and sparse representation algorithms.

Generalized Co-Prime MIMO Radar for DOA Estimation With Enhanced Degrees of Freedom

This paper considers the direction of arrival (DOA) estimation of coherent and uncorrelated targets by exploiting a flexible multiple input multiple output radar. First, the proposed radar is generalized with two coprime expansion factors for enlarging the inter-element spacing of transmit and receive arrays, referred to as sparse arrays with flexible inter-element spacing (SA-FIS), which shows that the conventional nested or coprime ones are the special cases. The range of consecutive lags and the number of unique lags in the sum-difference coarray are derived in closed form. It is verified that SA-FIS can obtain the maximum unique lags and also suppress the mutual coupling effects. We then extend the FIS viewpoint to sparse nonuniform linear arrays, where the two-level nested and coprime arrays are employed to achieve a significant increase in degrees of freedom (DOFs). Furthermore, to fully utilize these unique lags, we propose a reduced-complexity two-step sparse representation algorithm. By modifying and removing the off-diagonal elements of the estimated target covariance matrix, the proposed method can just identify the diagonal ones, thereby leading to further improved performance with much lower computational complexity. Finally, the Cramer-Rao bound on DOAs and correlated coefficients for SA-FIS is derived. Numerical simulations demonstrate the superiority of the proposed method with SA-FIS in terms of DOFs, computations, estimation accuracy, and resolution capability compared with previous ones.

Sparsity-Based DOA Estimation of Coherent and Uncorrelated Targets With Flexible MIMO Radar

Background and objective: Capsule endoscopy investigations currently capture a large number of images that must be processed and transferred inside the capsule. This demands a compression system that is capable of reducing the amount of data processed, encoded and transmitted. In comparison to a lossless system, a near-lossless image compression approach would have lower complexity and reduce the amount of data processed inside the capsule. However, the visual quality of the images compressed using a near-lossless approach must be deemed suitable for diagnostic use by clinicians. Methods: This paper outlines the development and clinical validation of a near-lossless image compression approach based on a Simplified Structure Conversion method, an Optimized Difference Approach, and a Golomb–Rice encoder. Eighteen clinicians participated to assess the suitability of processed videos and images for diagnostic purposes. Results: Our near-lossless approach returned a Peak Signal to Noise Ratio (PSNR) of 43.89182 dB and Structural Similarity measure of 0.996746 and an overall compression ratio (CR) of 5:1. Clinicians assessed the videos compressed by the developed system and rated 82% of the videos as acceptable for diagnostic purposes. Clinicians also compared the images before and after processing with the developed system and rated 86% of the images as “no difference”. Conclusion: The high values of the MSSIM, PSNR, CR and the high acceptance of clinicians provided a reliable indication of the high performance of the developed compression system. This matches the image quality requirements of capsule endoscopy for real-world medical diagnosis.

The development of a clinically tested visually lossless Image compression system for capsule endoscopy

A Remainder Set Near-Lossless Compression Method for Bayer Color Filter Array Images

Generalized design method for the difference co-array of the sum co-array

A BP neural network based algorithm for payload calculation was proposed.A high dimensional input-output system was formed to describe the non-linear relation between electrical parameters and payload.By the use of negative gradient of the network error feedback,network parameters were automatically adjusted,therefore the mapping connection between electrical parameters and payload can be solved.Experimental results and simulations show that the algorithm can solve the problem of the non-linear approximation,and achieve an error probability of e-3with correlation coefficient up to 0.95.

Algorithm for Electrical Parameters and Payload Based on Neural Network

A new color watermarking algorithm of colored images based on modified quaternion fast Fourier transform (QFFT) and discrete cosine transform (DCT) is presented By modifying the image vector, the real part and imaginary part of the carrier image after QFFT are symmetrical Then, the DCT is applied to the colored watermark, and after multiplying a factor, the RGB components of the watermark are embedded into the corresponding part of the carrier image lossless and spread into the whole image, hence enhancing the intangibility The experimental result shows that the presented algorithm improves peak signal-to-noise ratio (PSNR) by 10 dB compared with color watermarking algorithm based on traditional QFFT

Color Watermarking Algorithm Based on Modified QFFT and DCT

When the image is compressed adaptively with compressed sensing theory, the determination of sampling rate and sparsity threshold are highly subjective. In order to solve the problem, an accurately adaptive sampling algorithm with sparsity fitting is proposed in this paper. This algorithm determines the minimum sampling rate under certain sparsity to meet the PSNR requirements by iteration, and an optimal objective function of sampling rate choices is obtained by fitting sparsity and sampling rate data with the method of least squares. The adaptive sampling algorithm is simulated based on TVAL3. Experimental results show that the PSNR values of reconstructed images are higher than that with the same fixed sampling rate algorithm, and the PSNR increment of clear texture distinction images can reach at least 3.5dB. Compared to the roughly adaptive compression method, when the average sampling rate is lower, the reconstructed image obtains a higher PSNR value.

Wang Weijiang

Papers

A Remainder Set Near-Lossless Compression Method for Bayer Color Filter Array Images

Generalized design method for the difference co-array of the sum co-array

Algorithm for Electrical Parameters and Payload Based on Neural Network

Color Watermarking Algorithm Based on Modified QFFT and DCT

A novel algorithm on adaptive image compressed sensing with sparsity fitting