{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-9632156","patent":{"patent_number":"US-9632156","title":"Efficient redundant haar minimization for parallel MRI reconstruction","assignee":null,"inventors":[],"filing_date":"2012-12-18T00:00:00.000Z","publication_date":"2017-04-25T00:00:00.000Z","cpc_codes":["G06T","G06T"],"num_claims":16,"abstract":"A method for parallel magnetic resonance imaging (MRI) reconstruction of digital images includes providing a set of acquired k-space MR image data v, a redundant Haar wavelet matrix W satisfying WTW=I, wherein I is an identity matrix, a regularization parameter λ≧0, and a counter limit k, initializing a variable z0=Wv, and intermediate quantities p0=q0=0, calculating yi=arg minz½∥z−(pi+zi)∥22+λ∥z∥1 for 0≦i≦k, wherein z denotes values of an MR image sought to be reconstructed, updating pi+1=(pi+zi)−yi, updating zi+1=arg minz½∥z−(qi+zi)∥22+g(z), whereinand updating qi+1=(qi+yi)−zi−l, wherein x=WTz is a solution ofthat specifies a reconstruction of the MR image."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Efficient redundant haar minimization for parallel MRI reconstruction","description":"A method for parallel magnetic resonance imaging (MRI) reconstruction of digital images includes providing a set of acquired k-space MR image data v, a redundant Haar wavelet matrix W satisfying WTW=I","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-9632156","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-9632156","citation_suggestion":"Patentable. \"Efficient redundant haar minimization for parallel MRI reconstruction\" (US-9632156). https://patentable.app/patents/US-9632156","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-9632156","json":"https://patentable.app/api/llm-context/US-9632156","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-06-06T05:36:53.631Z"}