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.

Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a multitude of compression standards due to its remarkable energy compaction properties. Multiplier-free approximate DCT transforms have been proposed that offer superior compression performance at very low circuit complexity. Such approximations can be realized in digital VLSI hardware using additions and subtractions only, leading to significant reductions in chip area and power consumption compared to conventional DCTs and integer transforms. In this paper, we introduce a novel 8-point DCT approximation that requires only 14 addition operations and no multiplications. The proposed transform possesses low computational complexity and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio. The proposed DCT approximation is a candidate for reconfigurable video standards such as HEVC. The proposed transform and several other DCT approximations are mapped to systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45 nm CMOS technology.

A low-complexity 8-point orthogonal approximate discrete cosine transform (DCT) is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation. Moreover, in several image compression scenarios, the proposed transform could outperform the well-known signed DCT, as well as state-of-the-art algorithms.

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric synthetic aperture radar data whose adequacy is attested in this paper. Classification, segmentation, and image analysis techniques that depend on this model are devised, and many of them employ some type of dissimilarity measure. In this paper, we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained that lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such a remote sensing tool, the speckle interference pattern appears in the form of a positive-definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such a distribution is defined by two parameters: the number of looks and the complex covariance matrix. The last parameter contains all the necessary information to characterize the backscattered data, and thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler (KL) distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the KL distance and likelihood ratio statistics.