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The non-sinusoidal transforms with orthogonal functions consists of Hadamard, Walsh, and Haar function. These nonsinusoidal orthogonal functions consists of either square or rectangular waves. The basis function of this transforms are not sinusoidal. A next level of advancement to the theory of transforms is given by the triangular basis function. The triangular basis function and its use in image transform is discussed in the paper and also the orthogonal matrix for the basis function is discussed for transform. General TermsAlgorithm for Image transform based on triangular wave, data compression. Data sharing and watermarking.

Purpose Ultrasonography is currently used for both diagnostic and therapeutic purposes in de Quervain’s tenosynovitis. There is a dearth of information on how effective an ultrasound-guided (USG) steroid injection is when compared to surgical release of the first extensor compartment. Hence, we performed a non-randomized two-armed comparison study to test our hypothesis that USG guided steroid injection is equally effective as surgery. Method 62 consecutive patients participated in the study with 32 of them selecting the option of USG guided injection (Set A), and the rest undergoing surgical release (Set B). We reviewed them after 3 and 6 weeks and 6 months for functional outcome using DASH, PRWE and VAS scores, recurrence, or any complications. They were further followed if they were symptomatic. Results The DASH/PRWE/VAS scores improved at the end of 6 months from 81.7/79.3/6.8 to 1.0/1.7/1.0, respectively for patients undergoing USG guided steroid injection. Similarly, for the patient undergoing surgery, the scores improved from 82.2/81.5/6.7 to 1.7/3.4/1.0, respectively. This was statistically significant in both the groups (p < 0.05) and was comparable to each other. Two patients in Set A came back with recurrence at eight and 10 months and two reported occasional pain on heavy work. Three patients had tenderness and two had numbness in Set B at the scar site. Conclusion We observed that USG guided steroid injections are comparable to surgical release in terms of pain relief, functional outcome, complications.