Meaning of Base in Walsh Hadamard Tranform in Image Processing?

1. What is the Hadamard basis?
2. Which values are generated by Walsh Hadamard transform?
3. What is Hadamard transform in image processing?
4. What is the sequence of Hadamard transform?

What is the Hadamard basis?

Definition. The Hadamard transform H_m is a 2^m × 2^m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2^m real numbers x_n into 2^m real numbers X_k. The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.

Which values are generated by Walsh Hadamard transform?

The Walsh-Hadamard transform returns sequency values. Sequency is a more generalized notion of frequency and is defined as one half of the average number of zero-crossings per unit time interval.

What is Hadamard transform in image processing?

The Walsh-Hadamard transform is a non-sinusoidal, orthogonal transform widely used in signal and image processing. In this transform, the signal is decomposed into a set of basis functions (similar to harmonics in Fourier). These basis functions are the Walsh functions, rectangular or square waves with +1 or -1.

What is the sequence of Hadamard transform?

The Hadamard transform can be defined by(22)y=HLx,where x is an N-dimensional data vector and y is an N-dimensional transform vector.