Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional systems. Due to the extra free parameter order, fractional-order based methods provide additional degree of freedom in optimization performance. Not surprisingly, many fractional-order based methods have been used in image processing field. Herein recent studies are reviewed in ten sub-fields, which include image enhancement, image denoising, image edge detection, image segmentation, image registration, image recognition, image fusion, image encryption, image compression and image restoration. In sum, it is well proved that as a fundamental mathematic tool, fractional-order derivative shows great success in image processing.

Fractional calculus in image processing: a review

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.

A DCT Approximation for Image Compression

Fractional Calculus In Image Processing: A Review

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

Improved 8-Point Approximate DCT for Image and Video Compression Requiring Only 14 Additions

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.

Improved 8-point Approximate DCT for Image and Video Compression Requiring Only 14 Additions

An efficient 8 times 8 sparse orthogonal transform matrix is proposed for image compression by appropriately introducing some zeros in the 8 times 8 signed discrete cosine transform (SDCT) matrix. An algorithm for its fast computation is also developed. It is shown that the proposed transform provides a 25% reduction in the number of arithmetic operations with a performance in image compression that is much superior to that of the SDCT and comparable to that of the approximated discrete cosine transform.

Low-complexity 8×8 transform for image compression

In this paper, a systematic method for developing a binary version of a given transform by using the Walsh-Hadamard transform (WHT) is proposed. The resulting transform approximates the underlying transform very well, while maintaining all the advantages and properties of WHT. The method is successfully applied for developing a binary discrete cosine transform (BDCT) and a binary discrete Hartley transform (BDHT). It is shown that the resulting BDCT corresponds to the well-known sequency-ordered WHT, whereas the BDHT can be considered as a new Hartley-ordered WHT. Specifically, the properties of the proposed Hartley-ordering are discussed and a shift-copy scheme is proposed for a simple and direct generation of the Hartley-ordering functions. For software and hardware implementation purposes, a unified structure for the computation of the WHT, BDCT, and BDHT is proposed by establishing an elegant relationship between the three transform matrices. In addition, a spiral-ordering is proposed to graphically obtain the BDHT from the BDCT and vice versa. The application of these binary transforms in image compression, encryption and spectral analysis clearly shows the ability of the BDCT (BDHT) in approximating the DCT (DHT) very well.

Binary Discrete Cosine and Hartley Transforms

In this paper, a one-parameter eight-point orthogonal transform suitable for image compression is proposed. An algorithm for its fast computation is developed and an efficient structure for a simple implementation valid for all possible values of its independent parameter is proposed. It is shown that an appropriate selection of the values of the parameter results in a number of new multiplication-free transforms having a good compromise between the computational complexity and performance. Applying the proposed transform to image compression, we show that it outperforms the existing transforms having complexities similar to that of the proposed one.

A low-complexity parametric transform for image compression

In this paper, we propose an efficient 8×8 transform matrix for image compression by appropriately introducing some zeros in the 8×8 signed DCT matrix. We show that the proposed transform is orthogonal, which is a highly desirable property. In order to make this novel transform more attractive for recent real-time applications, we develop an efficient algorithm for its fast computation. By using this algorithm, the proposed transform requires only 18 additions to transform an 8-point sequence. Compared to the existing 8×8 approximated DCT matrices, it is shown that savings of 25% in the number of arithmetic operations can easily be achieved using the proposed transform operator without noticeable degradations in the reconstructed images. We also present simulation results using some standard test images to show the efficiency of the proposed transform in image compression.

A fast 8×8 transform for image compression

In this paper, we propose an orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform. Moreover, we develop an efficient algorithm for its fast computation. It is shown that the computational and structural complexities of the algorithm are similar to that of the Hadamard transform. By applying the proposed transform to image compression, we show that it outperforms the existing transforms having complexities similar to that of the proposed one.

Saad Bouguezel

Papers

Low-complexity 8×8 transform for image compression

Binary Discrete Cosine and Hartley Transforms

A low-complexity parametric transform for image compression

A fast 8×8 transform for image compression

A novel transform for image compression