This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trad...

—To improve the coding performance in JPEG image compression and reduce the computational complexity, this paper proposes a new transform called All Phase Inverse Discrete Sine Biorthogonal Transform (APIDSBT) based on the All Phase Biorthogonal Transform (APBT) and Inverse Discrete Sine Transform (IDST). Similar to Discrete Sine Transform (DST) matrix and Discrete Cosine Transform (DCT) matri...

Image compression is a technique to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form. This paper presents a peculiar Hybrid Transform genesis technique for image compression using two orthogonal transforms. The concept of hybrid transform is to combine the attributes of two different orthogonal transform wavelet to attain the...

Discrete Cosine transform (DCT) is an important tool in digital signal processing. In this paper, a novel algorithm to perform DCT multiplierlessly is proposed. First, by modular mapping and truncating Taylor series expansion, the DCT is expressed in the form of the product of the constants and discrete moments. Second, by performing appropriate bit operations and shift operations in binary sys...

In this paper, we focus on the restoration of images that have incomplete data in either the image domain or the transformed domain or in both. The transform used can be any orthonormal or tight frame transforms such as orthonormal wavelets, tight framelets, the discrete Fourier transform, the Gabor transform, the discrete cosine transform, and the discrete local cosine transform. We propose an...

In this work, we propose an image inpainting optimization model whose objective functional is a smoothed l norm of the weighted non-decimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a non-differentiable term, we give a basic algorithm inspired by Beck and Teboulle’s re...

This paper presents some new results on numerical stability for various fast trigonometric transforms. In a worst case study, we consider the numerical stability of the classical fast Fourier transform (FFT) with respect to different precomputation methods for the involved twiddle factors and show the strong influence of precomputation errors on the numerical stability of the FFT. The examinati...