Data Compression: The Complete Reference

5.18 WSQ, Fingerprint Compression 619012351113353743454612143638444679151739414749810161840421921272920222830232531332426323452 534850 51 54 5556 57 60 6158 59 62 63Figure 5.68: Symmetric Image Wavelet Decomposition.is how WSQ loses image information. The set of â values is a discrete set of floatingpointnumbers called the quantized wavelet coefficients. The quantization depends onparameters that may vary from subband to subband, since different subbands havedifferent quantization requirements.Figure 5.69 shows the setup of quantization bins for subband k. Parameter Z k isthe width of the zero bin, and parameter Q k is the width of the other bins. ParameterC is in the range [0, 1]. It determines the reconstructed value â. For C =0.5, forexample, the reconstructed value for each quantization bin is the center of the bin.Equation (5.29) shows how parameters Z k and Q k are used by the WSQ encoder toquantize a transform coefficient a k (m, n) (i.e., a coefficient in position (m, n) in subbandk) toanindexp k (m, n) (an integer), and how the WSQ decoder computes a quantizedcoefficient â k (m, n) from that index:⎧ ⌊ ⌋ak (m,n)−Z k /2⎪⎨ Q k+1, a k (m, n) >Z k /2,p k (m, n) = 0, −Z k /2 ≤ a k (m, n) ≤ Z k /2,⌈ ⌉ ⎪⎩ ak (m,n)+Z k /2Q k+1, a k (m, n) < −Z k /2,⎧ (⎪⎨ pk (m, n) − C ) Q k + Z k /2, p k (m, n) > 0,â k (m, n) = 0, p k (m, n) =0,⎪⎩ (pk (m, n)+C ) Q k − Z k /2, p k (m, n) < 0.(5.29)