Mario Mastriani

Mario Mastriani

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it is based on Schrodinger equation, which is a partial differential equation that describes how the quantum state of a non-relativistic physical system changes with time. In classic world is named frequency in time (FIT), which is presented here in opposition and as a complement of traditional spectral analysis frequency-dependent based on Fourier theory. Besides, FIT is a metric, which assesses the impact of the flanks of a signal on its frequency spectrum, which is not taken into account by Fourier theory and even less in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N2) for images, c) it does not have phase uncertainties (indeterminate phase for magnitude = 0) as Discrete and Fast Fourier Transform (DFT, FFT, respectively), d) among others. In fact, FIT constitutes one side of a triangle (which from now on is closed) and it consists of the original signal in time, spectral analysis based on Fourier Theory and FIT. Thus a toolbox is completed, which it is essential for all applications of Digital Signal Processing (DSP) and Digital Image Processing (DIP); and, even, in the latter, FIT allows edge detection (which is called flank detection in case of signals), denoising, despeckling, compression, and superresolution of still images. Such applications include signals intelligence and imagery intelligence. On the other hand, we will present other DIP tools, which are also derived from the Schrodinger equation.

Mario Mastriani, Alberto E. Giraldez

Synthetic aperture radar (SAR) images are subject to prominent speckle noise, which is generally considered a purely multiplicative noise process. In theory, this multiplicative noise is that the ratio of the standard deviation to the signal value, the "coefficient of variation," is theoretically constant at every point in a SAR image. Most of the filters for speckle reduction are based on this property. Such property is irrelevant for the new filter structure, which is based on directional smoothing (DS) theory, the enhanced directional smoothing (EDS) that removes speckle noise from SAR images without blurring edges. We demonstrate the effectiveness of this new filtering method by comparing it to established speckle noise removal techniques on SAR images.

Mario Mastriani, Alberto E. Giraldez

The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale variation. In this paper, a new type of Neural Shrinkage (NS) is presented with a new class of shrinkage architecture for speckle reduction in Synthetic Aperture Radar (SAR) images. The numerical results indicate that the new method outperforms the standard filters, the standard wavelet shrinkage despeckling method, and previous NS.

Mario Mastriani

The application of wavelet transforms to Synthetic Aperture Radar (SAR) imagery has improved despeckling performance. To deduce the problem of filtering the multiplicative noise to the case of an additive noise, the wavelet decomposition is performed on the logarithm of the image gray levels. The detail coefficients produced by the bidimensional discrete wavelet transform (DWT-2D) needs to be thresholded to extract out the speckle in highest subbands. An initial threshold value is estimated according to the noise variance. In this paper, an additional fuzzy thresholding approach for automatic determination of the rate threshold level around the traditional wavelet noise thresholding (initial threshold) is applied, and used for the soft or hard-threshold performed on all the high frequency subimages. The filtered logarithmic image is then obtained by reconstruction from the thresholded coefficients. This process is applied a single time, and exclusively to the first level of decomposition. The exponential function of this reconstructed image gives the final filtered image. Experimental results on test images have demonstrated the effectiveness of this method compared to the most of methods in use at the moment.

Mario Mastriani

This work deals with unsupervised image deblurring. We present a new deblurring procedure on images provided by low-resolution synthetic aperture radar (SAR) or simply by multimedia in presence of multiplicative (speckle) or additive noise, respectively. The method we propose is defined as a two-step process. First, we use an original technique for noise reduction in wavelet domain. Then, the learning of a Kohonen self-organizing map (SOM) is performed directly on the denoised image to take out it the blur. This technique has been successfully applied to real SAR images, and the simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Mario Mastriani, Alberto E. Giraldez

In this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman's filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the speckled image into wavelet subbands, we apply the Kalman's filter to the high subbands, and reconstruct a despeckled image from the modified detail coefficients. Experimental results demonstrate that our method compares favorably to several other despeckling methods on test synthetic aperture radar (SAR) images.

Mario Mastriani

This paper describes a novel projection algorithm, the Projection Onto Span Algorithm (POSA) for wavelet-based superresolution and removing speckle (in wavelet domain) of unknown variance from Synthetic Aperture Radar (SAR) images. Although the POSA is good as a new superresolution algorithm for image enhancement, image metrology and biometric identification, here one will use it like a tool of despeckling, being the first time that an algorithm of super-resolution is used for despeckling of SAR images. Specifically, the speckled SAR image is decomposed into wavelet subbands, POSA is applied to the high subbands, and reconstruct a SAR image from the modified detail coefficients. Experimental results demonstrate that the new method compares favorably to several other despeckling methods on test SAR images.

Mario Mastriani

In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), Karhunen-Loeve Transform, etc. Simulations show that the combined versions are the best, with minor Mean Squared Error (MSE), and higher Peak Signal to Noise Ratio (PSNR) and better image quality, even in the presence of noise.

Mario Mastriani

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

Mario Mastriani

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The process consists of taking each array and then subtracting the projections in common with the previous arrays. This paper introduces an enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for Digital Signal and Image Processing, among others applications.

Mario Mastriani, Juliana Gambini

In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loeve transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version is the best, with minor Mean Absolute Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to Noise Ratio (PSNR) and better image quality. Finally, new technique was far superior to JPEG and JPEG2000.

Mario Mastriani

This paper introduces an Enhanced Boolean version of the Correlation Matrix Memory (CMM), which is useful to work with binary memories. A novel Boolean Orthonormalization Process (BOP) is presented to convert a non-orthonormal Boolean basis, i.e., a set of non-orthonormal binary vectors (in a Boolean sense) to an orthonormal Boolean basis, i.e., a set of orthonormal binary vectors (in a Boolean sense). This work shows that it is possible to improve the performance of Boolean CMM thanks BOP algorithm. Besides, the BOP algorithm has a lot of additional fields of applications, e.g.: Steganography, Hopfield Networks, Bi-level image processing, etc. Finally, it is important to mention that the BOP is an extremely stable and fast algorithm.

Mario Mastriani

We describe a novel method for removing speckle (in wavelet domain) of unknown variance from SAR images. The me-thod is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT-2D) to the speckled image, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bit-slicing to the new highest subbands (to obtain bit-planes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bit-plane set and we obtain two orthonormal output bit-plane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply re-assembling, and, 6) re-sca-ling. Finally, 7) we apply Inverse DWT-2D and reconstruct a SAR image from the modified wavelet coefficients. Despeckling results compare favorably to the most of methods in use at the moment.

Mario Mastriani

We present a 3D zigzag rafter (first in literature) which allows us to obtain the exact sequence of spectral components after application of Discrete Cosine Transform 3D (DCT-2D) over a cube. Such cube represents part of a video or eventually a group of images such as multislicing (e.g., Magnetic Resonance or Computed Tomography imaging) and multi or hyperspectral imagery (optical satellites). Besides, we present a new version of the traditional 2D zigzag, including the case of rectangular blocks. Finally, all the attached code is done in MATLAB, and that code serves both blocks of pixels or blocks of blocks.

Mario Mastriani

A quantum edge detector for image segmentation in optical environments is presented in this work. A Boolean version of the same detector is presented too. The quantum version of the new edge detector works with computational basis states, exclusively. This way, we can easily avoid the problem of quantum measurement retrieving the result of applying the new detector on the image. Besides, a new criterion and logic based on projections onto vertical axis of Bloch's Sphere exclusively are presented too. This approach will allow us: 1) a simpler development of logic quantum operations, where they will closer to those used in the classical logic operations, 2) building simple and robust classical-to-quantum and quantum-to-classical interfaces. Said so far is extended to quantum algorithms outside image processing too. In a special section on metric and simulations, a new metric based on the comparison between the classical and quantum versions algorithms for edge detection of images is presented. Notable differences between the results of classical and quantum versions of such algorithms (outside and inside of quantum computer, respectively) show the existence of implementation problems involved in the experiment, and that they have not been properly modeled for optical environments. However, although they are different, the quantum results are equally valid. The latter is clearly seen in the computer simulations

Mario Mastriani

We describe a new method for superresolution of still images (in the wavelet domain) based on the reconstruction of missing details subbands pixels at a given ith level via Rule of Three (Ro3) between pixels of approximation subband of such level, and pixels of approximation and detail subbands of (i+1)th level. The histogramic profiles demonstrate that Ro3 is the appropriate mechanism to recover missing detail subband pixels in these cases. Besides, with the elimination of the details subbands pixels (in an eventual compression scheme), we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain. Our method does not compress, but facilitates the action of the real compressor, in our case, Joint Photographic Experts Group (JPEG) and JPEg2000, that is, Ro3 acts as a catalyst compression