Discrete Transform Techniques in Image and Video Compression

Discrete transform techniques form the mathematical foundation of modern image and video compression by converting spatial or temporal pixel data into spectral coefficients that reveal salient information patterns and permit efficient quantization. The discrete cosine transform (DCT) and its variants, such as the discrete sine transform (DST) and integer or multiplier-free approximations, achieve strong energy compaction in fixed-size blocks, minimising perceptually irrelevant redundancy. Wavelet transforms offer multiresolution analysis by decomposing signals into subbands with adaptive time–frequency localisation. Advanced methods, including block-wise Karhunen–Loève transforms and adaptive transform selection, aim for optimal decorrelation but often incur greater computational cost. Industry standards from JPEG through HEVC to VVC have extended transform units up to 64×64 pixels and introduced multiple-transform selection to balance compression ratio against complexity. Algorithmic innovations—fast factorised implementations, sliding-window hops and quantization-aware designs—improve throughput and accuracy for edge and real-time systems. Hardware-oriented architectures employing CORDIC algorithms and field-programmable gate arrays now integrate transform, quantization and inverse stages into unified pipelines. These advances address the demands of high-resolution streaming, low-bandwidth networks and power-constrained devices, supporting applications in immersive media, remote sensing and mobile communication.

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Discrete Transform Techniques in Image and Video Compression publication trend

The graph below shows the total number of articles in discrete transform techniques in image and video compression across all publications each year (not limited to Nature Index journals).

Technical terms

Discrete Cosine Transform (DCT): A linear transform that expresses image data as a sum of cosine basis functions, optimising energy compaction for block-based compression.

Discrete Sine Transform (DST): A transform similar to the DCT but based on sine basis functions, used for signal decorrelation in certain compression schemes and spectral analysis.

Quantization: The process of mapping a continuous range of transform coefficients to a finite set of values, enabling lossy compression by discarding less significant information.

Coordinate Rotation Digital Computer (CORDIC): An iterative algorithm that computes trigonometric transforms using only shifts and additions, facilitating hardware-efficient DCT and DST implementations.

Field-Programmable Gate Array (FPGA): A reconfigurable semiconductor device that hosts custom hardware logic, allowing high-throughput, low-latency acceleration of compression transforms.

References

1. An FPGA-Based Architecture for the Versatile Video Coding Multiple Transform Selection Core. IEEE Access (2020).
2. The Development of Fast DST-II Algorithms for Short-Length Input Sequences. Electronics (2024).
3. VLSI Implementation of a Cost-Efficient Loeffler DCT Algorithm with Recursive CORDIC for DCT-Based Encoder. Electronics (2021).
4. Unified FPGA Design for the HEVC Dequantization and Inverse Transform Modules. Computers Materials & Continua (2022).